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Atoms and Elements

Atoms, on a simple level, can be thought of as consisting of negatively charged electrons moving around a nucleus which contains positively charged protons and neutral neutrons (collectively known as nuclides).  Since, in an atom, the electrical charges must balance, the atom must have the same number of protons and electrons.  How many protons the atom has (its atomic number) defines what element it is (the number of neutrons is irrelevant).  An atom with one proton (and one electron to balance the charge) would be an atom of the element hydrogen.  Six protons would make it a carbon atom; 92 protons would make it uranium.  But there could be two atoms with the same number of protons (they would be the same element) but with different numbers of neutrons.  

If you wanted to write the chemical symbol for uranium, you would use the accepted abbreviation, U, which makes sense in English.  However, there are some surprises.  K stands for potassium which doesn’t seem to make any sense; you have to know that the ‘K’ is from the Latin for potassium which is kalium (besides, P already stands for phosphorus), ‘Na’ for sodium, Latin natrium (S already stands for sulfur), and ‘Fe’ for iron, Latin ferrum.  W stands for tungsten; the W comes from the German word for tungsten, wolfram. 

The atomic number in the lower left of the symbol for the element is the number of protons the element has (the atomic number) which defines the element as in 6C, 8O, and 26Fe. It is often not written because, especially for the more common elements, it is assumed that you already know from the letter symbol not only what the element is but what the atomic number is; hydrogen is obviously 1, helium 2, carbon 6, and so on. For more obscure elements, the atomic number may be included to remind you what its atomic number is as in 92U (uranium) and 90Th (thorium). Some elements are designated with two letters, such as Ca (calcium) since a lone C already stands for carbon. The first letter is always capitalized but the second letter is always lower case; there are no three-letter symbols for elements.

The atomic mass (sometimes incorrectly called the atomic weight) of an atom is the sum of the masses of the protons and neutrons it has (the neutron is ever so slightly more massive than the proton). The mass of the electrons is usually ignored because their mass is much, much less than that of protons or neutrons. The simplest possible atom is one with one proton, no neutrons, and one electron which is a ‘kind’ of hydrogen. I say ‘kind of’ because there are other possible ‘kinds’ of hydrogen. You could have an atom with one proton (by definition it would be hydrogen) but it could also have one neutron. That ‘kind’ of hydrogen would have double the atomic mass of the hydrogen without a neutron. A third possibility is a hydrogen with two neutrons or how about one with three neutrons? They would all be hydrogen but hydrogen with different atomic masses.

The atomic mass is usually written to the upper left of the symbol for the element as in 2H, 3H, 12C, 14C, 235U, and 238U. Since the atomic mass is the sum of the number of protons plus neutrons and the atomic number is the number of protons, you can figure out how many neutrons there are by subtracting the atomic number from the atomic mass. For example, 12C has 12 – 6 = 6 neutrons and 14C has 14 – 6 = 8 neutrons. The elements are most usefully arranged into what is known as the Periodic Table in which elements in the same column share similar properties:

Periodic Table of the Elements
Periodic table of elements


A better, technical word for different ‘kinds’ of an element (different atomic masses, same element), is ‘isotope.’  ‘Isotope’ would apply, not only to different ‘kinds’ of hydrogen but to different ‘kinds’ of an atom of any element.  For example, there are two important isotopes of uranium; one uranium isotope has 146 neutrons and the other, 143 neutrons.  Since, by definition, uranium has 92 protons, the atomic mass of the first isotope would be 92 + 146 = 238 amu (atomic mass units) and that of the second isotope, 92 + 143 = 235 amu.  

Writing the symbol for an isotope can be done several different ways (aside from using the name of the isotope if there is one). That first isotope of uranium could be written: uranium-238, or U-238, or 92U238. In that last version, the 92 (atomic number or number of protons) is written as a subscript on the lower left of the symbol for the element. The atomic mass (protons + neutrons) is (should be) a superscript to the upper left of the element symbol. Unfortunately, the word processing program used to write this section does not allow for the use of both a subscript and a superscript on the same side so I have to put the superscript to the right of the element symbol; the upper right of the elemental letter symbol is usually reserved for an electric charge symbol.

You might note that not all single letters of the alphabet stand for an element. D is not an element but it is sometimes used to stand for deuterium (hydrogen-2). The molecular formula for water is the familiar H2O in which it is assumed that the two hydrogens are H-1 and the oxygen is O-16. But what if one or both of the hydrogens happen to be deuterium? You could write it as DHO or D2O, respectively (aka deuterated water). There is no letter symbol for O18, in which case you would have to write water as H2O18. In any of those cases, the substituted isotopes are heavier than the normal isotopes so you would have a version of heavy water. Biologists sometimes use deuterated water as a tracer in living organisms. Deuterated water is also used as a moderator (to slow down neutrons) in some nuclear reactors.

You could play the same trick with T for tritium.  Note that the T doesn’t stand for any element; it’s not Tin (Sn because the Latin for tin is stannum).  Nor is it element #22 Titanium (Ti), #43 Technetium (Tc), #65 Terbium (Tb), #69 Thulium (Tm), #73 Tantalum (Ta), #81 Thallium (Tl), #90 Thorium (Th), or #117 Tennessine (Ts).  Who knew there were so many elements starting with T and every one of them a double letter?  Tritiated water (water with at least one tritium substituted for hydrogen) is used in tracing the slow movement of water through aquifers.  You spike the groundwater with some tritiated water and later take samples down-gradient, checking for radioactivity from the tritium, the presence of which would indicate that the groundwater had reached that down-gradient location.  

Electromagnetic Radiation

The electrons of an atom occupy what a physicist would call energy levels and a chemist would describe as electron shells around the nucleus of the atom.  These energy levels/electron shells are only found at certain very definite distances from the nucleus, distances which are unique to a particular element.  The electrons cannot be at any other distances which is because the electrons have both particle and wave-like properties (all matter does but it is only at the very small scale of an electron that the wave-like properties of matter normally become important – quantum physics).  

The particular energy level/electron shell that an electron occupies corresponds to a certain amount of energy; the farther away from the nucleus that the energy level is, the greater the amount of energy that the electron in that level has.  The lowest energy level (closest to the nucleus) can hold two electrons; the next energy level can hold eight, and so on.  An atom is at rest when all of its electrons are in the lowest possible energy levels.  Depending on how many electrons an atom has, there may be an energy level that is not completely filled with electrons.  

The Electromagnetic Spectrum

An atom is said to be at rest if all of its electrons are at the lowest possible energy levels/electron shells.  For example, if a particular atom (of oxygen) has eight electrons, two of them would be at the lowest level and six of them would be in the second level.  Since the second level can hold eight electrons, that level would be two electrons short of being fully occupied.  

An atom is excited when one or more of its electrons are at a higher energy level.  This is not a stable state and the electron will drop down to a lower energy level, emitting electromagnetic radiation in the process: the greater the drop, the shorter the wavelength (which corresponds to more energy) of the emitted electromagnetic radiation.  Electromagnetic radiation, then, has a spectrum or range of wavelengths (energies) which runs from very long wavelength (low energy) radio waves at one end of the spectrum to very short wavelength (very high energy) gamma radiation.  

Visible light is part of the spectrum but is restricted to a very narrow range of it.  That narrow visible light part of the spectrum can be subdivided into the familiar colors of the rainbow where red light has the longest wavelength of visible light and purple/indigo the shortest.  

An important constant is the speed of light, around 186,000 miles/sec or 300,000 km/sec (in a vacuum; it slows down slightly in air, more in water, and even more in glass).  More accurately, that is the speed of the entire electromagnetic spectrum; radio waves and gamma rays move at the speed of light.  An index of refraction is actually a ratio of the speed of light in a vacuum divided by the speed of light in a transparent medium.  

Electromagnetic Spectrum

Atoms can become excited by heat.  Temperature is a measure of how fast atoms are moving, or vibrating in place if they happen to be part of a solid.  That movement is heat which excites the atom.  Electrons are continuously being bounced up to higher energy levels as they absorb the heat energy and then the energy is released again as the electrons drop back down to lower energy levels.  Your body is warm enough to generate infrared radiation.  If something like iron is heated enough to raise electrons to even higher energy levels, the electrons, when they make bigger drops down to lower energy levels, may emit visible light.  The iron first becomes red hot, then glows orange, yellow, and finally becomes white hot.  The tungsten filament of an incandescent light bulb becomes so hot it glows white hot which is hotter than the surface of the sun which is only yellow hot.  Tungsten is used because it has such a high melting point that it can get white hot without melting.  

Although electrons only move between specific energy levels, heating something produces a continuous spectrum (all the colors of the rainbow if it is hot enough, which combine to look white).  This happens because, although temperature is a measure of how fast everything is moving/vibrating, there is a range of speeds/vibrations; some particles are moving a little slower or faster than others.  Movement is kinetic energy which means there is a range of kinetic energies that atoms can have at a given temperature.  It is the collision of atoms with other atoms, with a range of kinetic energies, that produces a continuous (thermal) spectrum.  

An emission spectrum is produced when the dropping of electrons from higher to lower energy levels produces a very specific set of discrete wavelengths characteristic of a particular element.  An emission spectrum can be produced by exciting atoms with high voltage electricity.  If the voltage is high enough, you can even produce x rays.  Such a spectral ‘fingerprint’ is very useful in identifying elements in stars, and in water.  The emission spectrum of hydrogen is relatively simple, consisting of a bright red line, a bright blue line, and two fainter purple lines. 

Hydrogen Emission Spectrum
Hydrogen Emission Spectrum

The Atomic Absorption Spectrophotometer (AAS)

The AAS is a very important instrument in a water lab.  If you want to know how much calcium, iron, arsenic, or other elements are dissolved in your drinking water, it is an AAS that will determine that.  How it works begins with a tube/lamp with a filament which, when excited with the right voltage of electricity, will produce the emission spectrum of a particular element.  

Suppose, for example, you are interested in how much dissolved copper is in your water.  The lab would have a ‘copper’ tube which would produce the emission spectrum of copper which would consist of specific wavelengths of visible light characteristic of that element.  Unfortunately, if you want to analyze a water sample for another element, you would need to swap out the copper tube for another tube for that other element.  There are a few tubes which can simultaneously produce the emission spectra for two or three elements but it still involves the swapping out of a lot of tubes when analyzing for different elements.  For this reason, the lab usually analyzes many water samples for one thing, swaps tubes, and then analyzes all of them for something else.  

Great.  We now have a source of the emission spectrum of copper.  At the other end of the machine is a photometer which is a fancy name for a device that measures the intensity of light at a very specific wavelength.  If it is copper you are interested in, then you dial the photometer to measure one of the emission wavelengths coming from the copper tube.  But it is what is in between the copper lamp and the photometer that is important.  

There is a tank of oxygen and a tank of acetylene that feed a combined gas to a burner in between the ‘copper’ lamp and the photometer.  The burner ignites the gas and produces a flame through which the copper ‘light’ must pass to get to the photometer.  below the burner is a beaker of water from which water is fed into an atomizer whose purpose is to turn the water into a mist (just like the head of a perfume bottle) which is sprayed into the flame which turns the water mist into a water vapor cloud.  Of course, this is a flame so if you want to maintain that water vapor cloud, you have to continuously feed water into it.  

 The copper light must now pass through the water vapor cloud on its way to the photometer.  If there happens to be some copper in the water, then some of the copper light will be absorbed by the copper in the water which means that the photometer will see less light.  The more copper in the water cloud, the less copper light will get through to the photometer.  What the photometer sees is the opposite of an emission spectrum; it is a spectrum (actually the photometer only looks at one wavelength) in which the intensity of specific wavelengths are reduced, in this case, those of copper.  What it is is an absorption spectrum from which you get part of the name of the AAS, atomic absorption spectro- (spectrum) plus the name of the device that sees it, the photometer. 

Schematic of Atomic Absorption Spectrophotometer
Schematic of Atomic Absorption Spectrophotometer

This procedure is exactly how an astronomer can tell what is in a cold cloud of gas/dust in distant space.  Stars produce a spectrum in which it is relatively easy to see the unique emission lines of a particular element and the more intense those lines are, the more of that element is in the star.  Cold clouds, however, don’t produce emission spectra but if some starlight behind the cold cloud passes through the cloud, the cloud will absorb the starlight at the specific wavelengths characteristic of particular elements.  See the similarity?  Other lab instruments look at the entire absorption spectrum, not just a single wavelength, and may include part of the near infrared and/or ultraviolet part of the electromagnetic spectrum.  Such instruments can be used to identify compounds, including complex organics.  Is that white powder sugar or is it cocaine?  Each compound has a unique absorption spectrum which can serve as a kind of fingerprint for that compound.  

If you want to quantify exactly how much copper is in the water, you must calibrate the AAS for copper.  You start out with a sample of pure water; it doesn’t have any copper in it.  You feed it into the flame and then tell the AAS computer that whatever the intensity of the copper wavelength that it is looking at, that intensity represents zero copper in the water.  Next you successively feed at least two standard water samples into the flame.  These are standards because you know how much copper is in the water because you put it in.  Each time, you tell the AAS computer that whatever intensity of light the photometer sees, this represents whatever the copper concentration in the standard is.  The machine is now calibrated and ready to analyze unknown water samples for copper.  

You should also now recognize why such an analysis takes so long. You have to swap out lamps for each different element and recalibrate the AAS. There are cheaper and quicker methods of measuring specific elements dissolved in water but they are not very accurate; they can be screening tests. If accuracy is important, such as at level three or four testing, you really do need the AAS.

Isotope Stability/Instability and Nomenclature

There is an important difference in isotopes.  Hydrogen isotopes with one neutron or none at all are quite stable but the hydrogen isotope with two neutrons is not fully stable.  Over time, it will literally fall apart, in the process, emitting radiation and turning into something else (we will discuss the details of this later).  The hydrogen isotope with three neutrons is completely unstable; if you could somehow make it, it would immediately fall apart and, so, it doesn’t really exist.  A particular element, then, may have stable isotopes and some radioactive unstable isotopes.  There are even some elements which do not have any stable isotopes at all; uranium is one example of that although it takes a very long time for U-238 to decay (fall apart), emitting radiation in the process.  

Sometimes individual isotopes are given their own name.  H-1 (hydrogen with no neutrons) is known as protium.  H-2 is deuterium and H-3 is tritium.  There are no other isotopes of hydrogen; any others are completely unstable.  Carbon has several isotopes, the most important being C–12 (98.9% of all carbon), C–13 (1.1%), and C–14 (<< 1%); the other isotopes fall apart very quickly.  C–13, like C–12, is completely stable and C–14 is unstable but doesn’t fall apart very quickly.  None of the carbon isotopes have their own names and are simply referred to as C–14, etc.  

There are three isotopes of radon, none of them stable, including thoron (Rn–220) and actinon (Rn–219).  As it turns out, if you have radon gas, it will be almost entirely the Rn–222 isotope which does not have an isotopic name.  It is usually the case that if you do not specify a particular isotope of an element, it is assumed that you mean the most abundant isotope of that element which would mean H–1 (protium), C–12, and Rn–222, respectively, for the examples above.  Do be careful not to confuse the name of an isotope with the name of an element.  

Half-Life and Decay Constant

There is a very wide range of instability; some isotopes fall apart very quickly, within fractions of a second, others much more slowly. One useful way of describing how fast a specific isotope falls apart (decays) is half-life (t1/2) which is the length of time it would take for half of a given amount of an unstable isotope to decay and disappear. For example, tritium (H3 or H–3) has a half–life of 12.3 years. This means that you would only have half of the tritium you started out with after 12.3 years. After another 12.3 years, you would have half of half of the original amount or only one quarter of the original amount and so on. You might notice that the tritium would never completely disappear; you would have half of half of half of … forever. Practically speaking, unless you start out with huge amounts of some radioactive isotope, after about ten half–lives it is essentially gone. The most abundant isotope of uranium, U–238, has a half–life of about 4.5 billion years which, you might note, is about the age of the Earth. This means that the Earth has lost about half of the U-238 it had when it first formed.

Coming back to tritium, you can see it would be easy to figure out how much tritium was left after one half-life or some multiple of the half-life but how much tritium would be left after ten years or a hundred years? To calculate how much of an isotope is left for any length of time (N), you need this equation:

N = N0 e–λt

where N0 is the amount of the isotope you started out with (at t = 0) and t is the time that has passed.  The ‘e’ (~ 2.71828) is the base of what are known as natural logarithms and it is raised to the –λt power in this equation.  This would be an example of exponential increase but because there is a negative sign in front of it, it becomes exponential decrease.  In other words, the isotope is decaying exponentially.  That leaves the Greek letter, λ which is known as the decay constant.  The decay constant is a probability, how likely it is that a given atom of an unstable isotope will decay in a specified time period.  The larger the decay constant is, the more unstable the isotope is. 


The decay constant is related to the half–life by: 

t1/2 = (ln 2) / λ = 0.693 / λ

or, turning it around,

λ = 0.693 / t1/2

Since we know that the half–life of tritium is 12.3 years, we can now calculate the decay constant for tritium. Note, however, the units for the decay constant, per time. The units in –λt must cancel out if the first equation is to work. The t for tritium is in years so in order for the units in –λt to cancel out, the unit for the decay constant, per time, must be per year. Using the second equation to calculate m for tritium yields a dimensionless result of about 0.0563 which is a probability. It might be easier to understand if that decimal is turned into a percentage which would be 5.63%. This means that, for tritium, there is a 5.63% chance every year that any given atom of tritium will decay. It should be easy to see now that the larger the decay constant, the faster the unstable isotope will disappear.

Some Radioactive Nuclides (Isotopes)
Parent Daughter(s) t1/2 in yrs most stable isotope of parent  
H3 He3 12.3 H1
6C14 7N14 5730 C12
13Al26 14Si26 740,000 Al27
92U235 Pb207 713 million U238
19K40 8A40 + 20Ca40 1.3 billion K39
19K40 Pb206 4.51 billion U238
90Th232 82Pb208 14.1 billion Th232
37Rb87 38Sr87 47 billion Rb85 + Rb86
82Pb204 80Hg200 140 quadrillion Pb207
> 9000 atoms of K40 decay every second in the human body

Sources of Radiation from Unstable Isotopes

When an unstable isotope decays, it spits out radiation; unstable isotopes are radioactive.  There are three main types of radiation produced: alpha (α), beta (β–), and gamma (γ) radiation whose names come from the first three letters of the Greek alphabet; it is equivalent to our A, B, and C.  There are other possible radiation types; an unstable nucleus could, for example, spit out a neutron, proton, or positron, and there are other modes of decay such as β+ decay, electron capture, and fission, but α, β–, and γ are the most common forms of radiation produced in the decay of an unstable nucleus.  Gamma radiation is exactly that, radiation; it is from the extreme end (very high energy, very short wavelength) of the electromagnetic spectrum.  The other two, however, are actually particles with a lot of kinetic energy (energy of motion).  

Physicists recognize four forces today (is there a fifth force? time will tell): gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force.  Although very important at a human scale and larger, gravity, at the scale of an atomic nucleus, is so weak compared to the other three forces that it can be completely ignored at that scale.  

The electromagnetic force which, among many other things, dictates that like charges repel also mandates that the positively charged protons in an atomic nucleus repel one another, introducing an instability in an atomic nucleus with more than one proton.  Opposing this electromagnetic repulsion is the strong nuclear force whose attraction between nucleons (protons and neutrons in the nucleus of an atom) overwhelms the repulsion of the electromagnetic force. 

The problem is that the strong nuclear force is a very short-range force; its strength drops drastically over short distances, becoming less and less effective as an atomic nucleus becomes larger.  The consequence is that there is a limit to how big an atomic nucleus can get and still hold itself together.  Another factor is the number of protons and neutrons in a nucleus.  For lighter, smaller, nuclei, a stable ratio of protons to neutrons is 1:1 but as nuclei become bigger and heavier, more neutrons, compared to the number of protons, become necessary to form a reasonably stable isotope.  

Elements beyond hydrogen and helium (and a trace of lithium) are mostly created by fusion reactions in stars (nucleosynthesis), supernovas, and merging neutron stars. These processes can create short-lived isotopes of elements beyond uranium such as Aluminum-26 (t1/2 ≈ 740,000 yrs) and Plutonium-239 (t1/2 ≈ 24,400 yrs) which, although important in the early Solar System, are now long gone. Any of those isotopes on Earth today exist because humans made them. Natural radioactive (unstable) isotopes that remain important today include: Potassium-40 (t1/2 = 1.27 billion yrs), Thorium-232 (t1/2 = 13.9 billion yrs), Uranium-235 (t1/2 = 713 million yrs), and Uranium-238 (t1/2 = 4.51 billion yrs).

About 89% of the time Potassium-40 undergoes beta decay and becomes stable Calcium-40. 11% of the time it becomes stable Argon-40 gas through electron capture. Although 19K40 is only about 0.012% of all potassium (most K is potassium-39), it has a very long half-life, and only some 11% ends up as argon gas, its importance can be seen in that it normally is the most abundant radioactive isotope normally present in the human body (C-14 is a close second) and the argon gas it has produced over the eons makes up just under 1% of the Earth’s entire atmosphere.

Unlike K-40, Thorium and the two Uranium isotopes do not decay into stable isotopes but create a chain of radioactive daughter isotopes which eventually end up as different stable isotopes of lead. Each intermediate radioactive daughter in the three chains of decay has a different half-life (none of them nearly as long as the original thorium or uranium isotope) and the daughters produce radiation through a series of alpha and beta decays. These three important decay chains include isotopes of radium and radon and will be discussed later – first, what are alpha and beta decay?

Alpha Decay

Alpha decay is common in large, unstable atomic nuclei (the plural of nucleus) such as the nucleus of a uranium atom.  In effect, it is as if a nucleus undergoing alpha decay puts together a bundle of two protons and two neutrons and throws that bundle out of the nucleus with great speed (lots of kinetic energy).  You might notice that an alpha particle looks a lot like the nucleus of a helium–4 atom but there are two important differences.  The alpha particle is not associated with any electrons (it’s not an atom; it’s a He-4 nucleus) and it has a huge amount of (kinetic) energy.  

An isotope that throws out an alpha particle drops its atomic number by two and its atomic mass by four.  Both alpha decay and beta decay are examples of the transmutation of elements (one element changes into another element).  Unfortunately, there is no natural decay chain that will transmute a lead isotope (element #82) into gold (element # 79).  It actually has been done by colliding other elements together but it cost more to do it than the gold was worth.  

The alpha particle inevitably collides with something else, transfers some of its momentum to whatever it hit, and slows down a bit.  If whatever it hit is a compound, the transferred energy may break bonds which, in a living cell, could promote cancer.  The alpha particle continues to collide with other atoms/molecules, transferring some of its momentum to whatever it hits and slowing down (it loses kinetic energy).  Eventually, the alpha particle slows down enough (loses enough kinetic energy) that it can acquire two electrons at which point it becomes an ordinary helium atom.   

There are two interesting results from all of this (aside from any bond-breaking).  You might wonder where the helium comes from that fills balloons and dirigibles.  Let helium gas loose in the atmosphere and it will escape into space.  The alpha decay of elements like uranium and thorium deep within the earth produces helium gas which will attempt to rise up to the surface of the Earth where it can escape.  Sometimes, however, the rock through which the gas is trying to rise is impermeable enough that the rock traps the helium underground.  Such rock might also trap natural gas (methane) underground.  If there is enough trapped natural gas, someone may drill a well into the rock to extract it.  Along with the natural gas comes a small amount of helium which can be separated from the methane by cooling and compressing the methane until it liquifies, leaving the helium as a gas which can now be easily separated from the liquified methane.  

Another interesting consequence of alpha decay is that it produces heat.  Temperature can be thought of as a measure of how fast atoms, ions, or molecules are moving or vibrating in place; the higher the temperature, the faster everything is moving/vibrating.  As the alpha particle transfers momentum to whatever it hits and slows down, whatever it hits speeds up a little and passes on a little of its momentum to whatever it hits.  Everybody now moves a little faster (has a little bit more kinetic energy).  The temperature goes up a tiny fraction of a degree.  This is how radioactive decay can heat the Earth.  Without it, the Earth would be a very different place, probably no plate tectonics or volcanism which, by the way, would not be a good thing.  

Beta Decay

Unlike protons, free neutrons (unassociated with protons) have a short half–life of about 10.5 minutes.  It is only within the nucleus of an atom that a neutron is ~ stable.  In a large nucleus with an excess of neutrons, however, the excess neutrons tend to form a skin around the outer surface of the nucleus.  These excess neutrons are farther from the stabilizing influence of the protons.  It may happen that the weak nuclear force, which holds a particular neutron in the outer skin together, weakens enough to allow the neutron to decay.  

Beta decay is the decay of a neutron.  What happens is that the neutron splits into what looks a lot like an electron (with one important difference), a proton, and an anti-neutrino.  The ‘electron’ and the anti-neutrino are thrown out of the nucleus at great speed, in the process releasing a lot of energy in the form of kinetic energy (the great speed) and gamma radiation (beta radiation is associated with gamma radiation). It is that huge kinetic energy that distinguishes a beta particle from an ordinary electron.  The proton left behind increases the atomic number of the daughter isotope by one (transmutation of an element).  

That the daughter isotope has one more proton than the parent isotope means that the newly-formed daughter isotope is short one electron.  When another electron is acquired, it must drop down many energy levels to get as close as possible to the nucleus of the isotope.  In doing so, there is a release of electromagnetic energy and since the drop of the electron is quite large, the emitted electromagnetic energy is gamma radiation which is why beta decay is associated with the emission of gamma radiation.  

The story of the beta particle is similar to that of an alpha particle.  It hits other particles (atoms, ions molecules), transfers some of its momentum to whatever it hits, possibly breaks bonds (ionizing radiation), creates heat, and eventually loses enough kinetic energy to become an ordinary electron.  


Some very large unstable isotopes, such as U–235 and Pu–239, instead of spitting out alpha or beta particles, may simply split (fission) into several larger radioactive chunks along with a shower of smaller particles and a lot of energy.  Unaided (spontaneous) fission is usually quite rare, for example, in U–238 there is only one spontaneous fission for every 2,230,000 α decays.  Another way of looking at it is that the half–life of U–238 due to spontaneous fission is a whopping 350 quadrillion years as compared with 4.5 billion years for alpha decay.  

But fission can be induced in some isotopes by hitting their nuclei with neutrons of the right speed (kinetic energy).  It wouldn’t work for U–238 which would just absorb the neutron and turn into U-239 which would quickly (half–life 23.5 minutes) spit out a beta particle and turn into Np-239 which would quickly (half-life 02.35 days) spit out another beta particle and turn into Pu-239 (half-life 24,400 yrs) which is fissionable.  Normal nuclear reactors are not optimized to produce fissionable plutonium; some do accumulate in used fuel rods.  Breeder reactors are designed to much more efficiently convert the much more abundant but non-fissionable U-238 into fissionable Pu-239.  The two most important fissionable (you can induce it to fission) isotopes are U-235 and Pu-239.  The fissionable U-235 is much less common than U-238, making up only 0.3% of uranium.  U-238 makes up 99.7% of uranium and separating the two isotopes is very very difficult and expensive which is maybe not such a bad thing.  

The larger radioactive ‘chunks’ produced in fission include some important radioactive isotopes found in the environment as a result of atomic bomb testing or nuclear reactor failures:  tritium, cobalt-60, strontium-90, iodine-131, cesium-137, and americium-241.  Plutonium-239 from plutonium processing and storage facilities can also escape confinement and end up in groundwater as is known to have happened near Hanford, Washington, the site of a breeder reactor and the source of the plutonium in the atomic bomb dropped on Nagasaki, Japan.  Incidentally, plutonium is not only dangerously radioactive (alpha radiation) but is very chemically toxic too. 

Natural Sources

Granite is the common rock with the greatest concentration of trace uranium, typically on the order of several ppm which is not normally enough to pose any significant health threat.  However, through weathering and erosion, granite can become a source of uranium which can be naturally concentrated in deposits in other areas.  Mining of that uranium can produce tailings with elevated levels of uranium which can enter the aquatic ecosystem; some 21 states have or have had uranium mines.  Uranium has an affinity for phosphate and can be found associated with phosphate deposits such as in central Florida.  The uranium concentrations are not high enough to be economic but uranium daughters such as radium and radon can be a problem in that area.  

Uranium is also associated with black shales (reducing environments) and can sometimes be present in high enough trace concentrations to pose a radon risk to structures built on that kind of rock.  Granite, or rather the radon from the uranium in it, can be a significant problem as is the case in the granite state (New Hampshire), Galway, Ireland, and many more areas of granite.  Radon is usually considered to be an air problem but there are towns in New England that are supplied with well water from wells drilled into granite whose water needs to be treated for radon.  The immediate parent of radon is radium and radium is present in significant concentrations in the artesian springs of Saratoga Springs, New York.  

There is no natural source of plutonium; every bit of plutonium on the Earth today was made by humans and, except a small amount of tritium produced by the interaction of cosmic radiation with air molecules, the same can be said of the fission isotopes described above.  The Earth may have had some of these radioactive isotopes when it first formed but with such relatively short half-lives, they all disappeared shortly thereafter and there are no natural processes to generate more of them.  

The Uranium and Thorium Decay Chains

Decay Chain of Uranium and Thorium
Decay of  235U Decay of  238U Decay of  232Th
Isotope Half-Life Isotope Half-Life Isotope Half-Life
92U235 713 million yrs 92U238 4.51 billion yrs 90Th232 14.1 billion yrs
90Th231 25.6 hrs 90Th234 24.1 days 88Ra228 6.7 yrs
91Pa231 34,300 yrs 91Pa234 6.7 hrs 89Ac228 6.13 hrs
89Ac227 * 21.2 yrs 92U234 248,000 yrs 90Th228 1.91 yrs
90Th227 18.2 days 90Th230 76,000 yrs 88Ra224 3.64 days
88Ra223 11.7 days 88Ra226 1620 yrs 86Rn220 56 sec
86Rn219 4.0 days 86Rn222 3.82 days 84Po216 0.15 sec
84Po215 0.0018 sec 84Po218 3.05 months 82Pb212 10.6 hrs
82Pb211 36.1 months 82Pb214 26.8 months 83Bi212 60.5 min
83Bi211 **  2.15 months 83Bi214 19.7 months 84Po212 0.0000003 sec
81Tl207 4.78 months 84Po214 0.000164 sec 82Pb208 stable
82Pb207 stable 82Pb210 22 yrs * 33.7% of  83Bi212 decays to:
* 1.2% of 89Ac227 decays to: 83Bi210 5.0 days  81Tl208 3.1 min
87Fr223 21 min 84Po210 138 days 82Pb208 stable
88Ra223 etc. 82Pb206 stable
** 0.30% of  83Bi211 decays to:  * 0.04% of  83Bi214 decays to: Present-day Ratios
84Po211 0.52 sec 81Tl210 1.3 min Th / U  =  3.9
82Pb207 stable 82Pb210 etc. 92U235 / 92U238  =  0.7257%

Although the table above doesn’t specify how a particular isotope decays or what kind of radiation it emits, this can easily be figured out by comparing the parent isotope with its daughter isotope.  If it is an alpha decay, the atomic number (lower left) will be two less in the daughter and the atomic mass (upper right) will be four less.  If it is a beta decay, the atomic number will be one more in the daughter but the atomic mass will remain the same.  Beta decay is associated with gamma radiation and the wavelengths of the emitted gamma radiation is characteristic of the decay of a specific isotope.  By measuring the energy/wavelengths of the gamma radiation, you can identify what isotope is emitting it.  

You should also note that there is considerable variation in the half-lives and that, although there is not a strict alternation between alpha and beta decay, there are plenty of both in the decay chains to a stable isotope of lead.  Some configurations of protons and neutrons within the nucleus are more stable than other configurations which is why there is a variation in the half-lives.  As to whether a given isotope emits an alpha or a beta particle depends on the stability of the neutrons near the surface of the atomic nucleus.  

A free neutron (one not in an atomic nucleus) is not stable; it has a half-life of about 10.3 minutes.  It is, however, stable in an atomic nucleus – well, sort of.  It is the weak nuclear force that holds a neutron together but it is not strong enough (after all, it is the weak nuclear force) unless it is associated with protons; this is probably an interaction between the three quarks that make up protons and neutrons.  The strong nuclear force is 100xs the strength of the electromagnetic force near the nucleus and 1 million times the weak nuclear force.  Within a nucleus, then, the weak nuclear force holds the individual neutrons together and the strong nuclear force (probably another interaction between quarks) binds the protons together against the repulsion of the electromagnetic force. 

In a large, heavy nucleus, extra neutrons are required to spread out the strong nuclear force to hold a larger nucleus together.  The protons and neutrons form shells or layers sort of analogous to the energy or shell layers of electrons outside of the nucleus.  Excess neutrons tend to form a ‘neutron skin’ around the rest of the nucleus.  

If there aren’t too many excess neutrons in a given nucleus, the ‘neutron skin’ will be thin and clusters of alpha particles may be found in it.  These surface alpha clusters are not as tightly bound to the nucleus because they are at the nuclear surface, farther from the stabilizing influence of the other nucleons, a stabilizing influence which is not equal in all directions.  It may also happen that the nucleus is not spherical; some nuclei can be ellipsoidal which would make alpha clusters at an end of the ellipsoid even less stable, more weakly bound to the nucleus.  Such conditions would promote alpha decay.  

Should there be more excess neutrons, the neutron ‘skin’ would be thicker and surface alpha clusters would tend not to form.  The stabilizing influence of the protons would be spread over more surface neutrons, lessening the effect for each neutron, which would make the neutrons less stable.  Result, beta decay.  

Measuring Radiation

There are a wide variety of methods for measuring radiation and, depending on the instrumentation, important differences in what is actually measured.  Some instruments measure Activity (from which, radioactivity) which is how many disintegrations per second (dps) or minute (dpm) occur in a given quantity of a radioactive isotope.  Other instruments measure the energy of the emitted energy.  But how much energy is emitted is not the same as the amount of energy absorbed by something such as a particular material or a human being; how much energy is absorbed requires yet another set of units.  How much damage occurs as a result of the absorption of a given amount of energy depends on the type of energy, whether it is alpha, beta, or gamma radiation, yielding even more units.  Finally, there are units which are used to describe the effect of the radiation on an entire population.  

Measurement Systems

Further complicating the many different units of radiation are three different sets of units from: the English system, the standard (mks) metric system, and the non-standard (cgs) system. The differences in these three measurement systems can be demonstrated in describing the density of water which would be in units of mass per volume.

In the English system you might think that density would be lbs/ft3 or lbs/in 3 but pounds is not a unit of mass but a unit of weight. You can appreciate the difference between mass and weight by considering the weight of a gallon of water; note that we have another problem with many different ways of describing volume in the English system; we have already mentioned cubic feet, cubic inches, and now, gallons. On the surface of the Earth, that gallon of water would weigh about 8.33 lbs but in space it would weigh nothing. On the surface of the Earth, that gallon would have a mass of about 0.259 slugs. Slugs?! In the English system, the unit of mass is slugs (1 slug ≈ 14.6 kg). A pound is a unit of weight which is a force. A slug is a unit of mass. The point is that the gallon of water would have the same mass whether on the surface of the Earth or in space; it would not have the same weight.

You might think that there is only one metric system but there are two versions of the metric system that are still in use although there are efforts to try to get everyone to use the “standard’’ metric system. The cgs version of the metric system is most convenient when dealing with smaller quantities of things. The cgs stands for the basic units used: centimeter, gram, and second. Thus, the density of water could be described as about 1 g/cm3, a unit which is still very commonly used in describing density. Incidentally, a cubic centimeter is sometimes abbreviated as cc which means that you might see the density described as 1 g/cc. Another interesting note is that a cc is the same as a ml (milliliter) so that you could even describe the density of water as about 1 g/ml.

The standard metric system is based on mks which stands for meter, kilogram, and second. In the mks version, the unit of density is kg/m3. The metric system is very conveniently based on multiples of tens so it is easy to scale up that 1 g/ml. Multiplying top and bottom by 1000 results in 1000 g / 1000 ml but 1000 g is a kg and 1000 ml is a liter so the density becomes 1 kg/L. Multiplying top and bottom by 1000 again results in 1000 kg / 1000 L but 1000 L is the same as a cubic meter, resulting in an mks density of 1000 kg / m3. So, if you have the density of something in g/cm3 and want the density in kg/m3, simply multiply by 1000. Summing all this up, the density of water is about 1 g/cm3 = 1 g/cc = 1 g/ml = 1 kg/L = 1000 kg/m3.

We could have converted the 1000 kg to 1 metric (long) tonne, resulting in a water density of 1 tonne/m3 but that would result in yet another non-standard version of the metric system. Incidentally, since 1 kg = 2.2 lbs (at least on the surface of the Earth), and the English ton = 2000 lbs, the metric long tonne would equal 2200 lbs which is why it is sometime called the ‘long’ ton; it is 200 lbs “longer” than the English ‘short’ ton. Note also that the metric tonne is spelled differently than the English ton even though the pronunciation is the same.

This was quite a tangent but the point is that you can expect as many as three different measurement systems in measuring radiation, with different variations within a given system. Energy, for example, in the English system can be described as foot-pounds, BTUs (British Thermal Units), and horsepower-hours. In the metric system, you will encounter ergs (cgs version – g•cm2/s2) and joules (mks version – kg•m2⋅s−2). Older units are often in cgs units; the preferred standard metric units, mks units, are underlined.

Activity – Curies (Ci) and Becquerels (Bq)

Activity was originally described in units of Curies (Ci – named, of course, after Madame Marie Curie, discoverer of radium, and is defined as the activity of one gram of radium (Ra226) which turns out to be 1 Ci = 3.7 x1010 dps. The number of disintegrations that occur in one second depends upon two factors: the number of radioactive atoms present, and the decay constant (λ) which predicts the probability that a given atom will decay in that second.

1 Ci is a huge amount of activity. If you are anywhere near a source of activity that high, you might have enough time to write out a will if you hurry. One Ci = 1000 mCi; one mCi = 1000 µCi; one µCi = 1 1000 nCi; 1 nCi = 1000 pCi; 1 Ci = 1012 pCi. As an indication of just how much activity a Ci is, consider that the standard for indoor radon exposure is 4 pCi/L.

Since radon is a gas, the activity of radon is measured as the activity of radon in a liter of air. A picoCurie (pCi) is one millionth of one million of a Curie and yet, at a concentration of only 4 pCi/L, radon is considered a significant health hazard (lung cancer). Both radium and its daughter isotope, radon, happen to be alpha emitters.

You might think that activity is simply disintegrations per second or per minute but it is more complicated than that. One complication is that a geiger counter or a scintillator measures counts per second (cps) or counts per minute (cpm) and not dps or dpm. The difference is because these instruments, as good as they may be, will miss some disintegrations; they have an efficiency factor. If you know the efficiency of the measuring instrument, you can convert cps to dps. For example, if you get a reading of 12 cps and you know that the efficiency of the counter is 90%, then (12 cps)/(0.9) = 13.3 dps.

Curies and fractions of Curies are still used in the U.S. but there is a movement to try to convert activity to Becquerels (Bq), named after Henri Becquerel, the discoverer of spontaneous radiation or radiation from the fission of uranium. Since a Bq is one disintegration per second, 1 Ci = 3.7 x1010 Bq or 1 Bq = 27 pCi. Note that these units say nothing about the type or energy of the ionizing radiation. Your body typically has an activity of several thousand Bq due mostly to K40 and C14.

Energy of the Emitted Ionizing Radiation – ElectronVolts (eV) and Joules (J)

The (kinetic) energy of a typical alpha or beta particle is on the order of a million electron volts (MeV). A joule is defined as the energy required to lift 100 grams a vertical distance of one meter and is equal to 6 x 1012 MeV.

Ionizing Radiation Exposure – Roentgens (R) and Coulombs/kilogram (C/kg)

As ionizing radiation travels through air, it will ionize (knock electrons off of) air molecules. A Roentgen (named after Roentgen, discoverer of x rays) is a measure of that ionization in terms of the electrostatic charge of a cm3 of air (cgs units); it is equivalent to about 88 ergs or 2.58 x 10–4 C/kg in the mks system. Since different atoms will decay in different ways, that is, release radiation of different types and energies, the relation of Curies to Roentgens depends on what type of atom is decaying. Background radiation is sometimes described in terms of microRoentgens/hr (µR/h) which in northeastern Pennsylvania is usually on the order of 10 µR/h.

Granite is the common rock which has the most amount of trace uranium in it, usually several ppm.  Buildings, such as Grand Central Station in NYC and some buildings in Washington, D.C. which are constructed of granite, can have several times higher background radiation levels because of gamma radiation coming from the granite which might merit some mild concern after many years of exposure.  Radiation from a kitchen granite countertop is probably insignificant.  

Groundwater from granite bedrock, such as is found in the New England states, is not rendered radioactive because of exposure to the granite.  The water, however, may pick up significant amounts of radon gas from the granite which can be released into the air in a home (see the section on radon gas).  

Radiation Absorbed Dose – RADs and Grays (Gy)

Not all of the radiation to which you might be exposed will be absorbed by your body; just like light, some will be reflected. How much radiation is absorbed depends on what the material is. The rad (you should recognize that it is an acronym) is an older cgs unit (100 erg/gram) most often applied to how much radiation is absorbed by human tissue. Since soft body tissue will absorb 97 ergs per gram, the rad, for body tissue, is roughly equivalent to the roentgen. Its mks equivalent is the Gray (J/kg). 1 Gy = 100 rads. A typical hospital CT scan results in about 7 mGy.

Relative Biological Effectiveness (RBE), aka Quality Factor

Rads and Grays still say nothing about the type of radiation which is important in how much damage the radiation can do to human tissue. As it happens, alpha particles will do twenty times the damage to tissue than beta or gamma radiation will do, even when the amount of radiation absorbed is the same. The RBE is a factor which allows comparison of the relative effectiveness of different types of radiation to damage tissue.

Radiation Equivalent Dose – REMs and Sieverts (Sv)

Rem is another acronym, Roentgen Equivalent Man, and is Rads x RBE. Since the Rad is a cgs unit, so too is the Rem. Note that for beta and gamma radiation, 1 Rad = 1 Rem but for alpha radiation, 1 Rad = 20 Rem. The mks equivalent of the Rem is the Sievert which is Grays x RBE. 1 Sv = 100 Rems. A typical background radiation exposure results in a few mSv. A CT scan can add up to another 10 mSv. Nuclear employees in the U.S. are limited to 20 mSv/yr.

Radiation RBE Factor
alpha 20
fast neutron 10
slow neutron 5
beta 1
gamma 1

Radiation Effective Dose – REMS and Sieverts (Sv)

The effective dose links the equivalent dose with the risk of developing long-term health effects, some type of cancer. A dose of 1 Sv corresponds to a 5.5% chance of developing a cancer.

Population Effective Dose – Man-rems and Person-Sieverts (pSv)

The amount of radiation exposure of a population from a radiation source is expressed in man-rems or, simply, the exposure in rems x population. 1000 people exposed to 1 mrem or 100 people exposed to 10 mrem, etc., would be equivalent to one man-rem. It has been estimated that for every ten thousand man-rems, one latent cancer will appear in the next 30 years and there will be one genetic defect in later generations in the population. 100 man-rems = 1 person-sievert.

Sources of Radiation

Some Radioactive Nuclides
Parent Daughter t1/2 in yrs Most Stable Isotope    
19K40 18Ar40 + 20Ca40 1.3 x109 K39
37Rb87 38Sr87 4.7 x 1010 Rb85 + Rb86
82Pb204 80Hg200 1.4 x 1017 Pb207
90Th232 82Pb208 1.41 x 1010 Th232
92U235 Pb207 7.13 x 108 U238
92U238 Pb206 4.51 x 109 U238
13Al26 14Si26 740,000 Al27
H3 He3 12.3 H1
6C14 7N14 5730 C12

Some Naturally-Occurring Radionuclides in the Crust
Isotope End Product Concentration Half-life (yrs) Radiation
Uranium-238 92U238 82Pb206 4 ppm 4.5 billion alpha
Radium-226 88Ra226 82Pb206 2 ppb 1,620 alpha
Uranium-235 92U235 82Pb207 28 ppb 713 million alpha, gamma
Thorium-232 90Th232 82Pb208 12 ppm 14 billion alpha, gamma
Potassium-40 19K40 89% 20Ca40 + 11% 18Ar40 3 ppm 1.3 billion beta, gamma
Rubidium-87 37Rb87 38Sr87 75 ppm 47 billion beta, gamma

Some Atmospheric Products of Cosmic Radiation
Isotope Concentration (dist/min/m3) Half-life Radiation  
Phosphorus-32 15P32 0.02 14.3 days beta
Phosphorus-33 15P33 0.015 25 days beta
Beryllium-7 4Be7 1 53 days gamma
Sulphur-35 16S35 0.015 87 days beta
Hydrogen-3  (tritium) 1H3 10 12.3 years beta
Carbon-14 6C14 4 5760 years beta

Some Radionuclides Generated in Fallout and Power Generation
Isotope Half-life Radiation
Iodine-131 53I131 8.1 days beta, gamma
Xenon-133 54Xe133 11 days beta, gamma
Strontium-89 38Sr89 51 days beta
Krypton-85 36Kr85 11 days beta
Cobalt-60 27Co60 5.26 years beta, gamma
Tritium 1H3 12.3 years beta
Strontium-90 38Sr90 28.9 years beta
Cesium-137 55Cs137 30.2 years beta
Carbon-14 6C14 5760 years beta
Plutonium-239 94PU239 24,400 years alpha, gamma
15% of the energy of a nuclear bomb is in the radioactive isotopes it produces.
One pound of fissioned U-235 yields 0.999 pounds of radioactive isotopes.
One pound of plutonium dust could lethally contaminate 3 square miles of land for 250,000 years.
Isotopes typically must be stored 10 to 20 times the half-life before they are safe (gone).

Natural Background
~  1/4 from cosmic radiation
~  1/4 from radiation in the body
~  1/2 from soil and rocks (including radon)
110 mrem/yr  (or 0.01 to 0.02 mrem/hr)
medical x-rays 55 mrem/yr
fallout 10 mrem/yr
radiation work 0.56 mrem/yr
air travel (additional cosmic radiation) 0.36 mrem/yr

Radiation and Effect

What tissues are affected by radiation depends on the type of radiation.  While gamma radiation can penetrate the entire body and beta less so, alpha radiation cannot even penetrate the outermost dead skin cells of the body.  Alpha radiation does damage when it is in the body so that the first thing it hits is living cells.  Radon gas, an alpha emitter, does its damage when it is inhaled into the lungs which is why it is associated with lung cancer.  Radon in water, when consumed, does not appear to be associated with things like stomach cancer; it is only associated with lung cancer. 

Other radioactive isotopes may be preferentially concentrated in certain body organs, one of the most specific of which is Iodine-131, a beta and gamma emitter, which is concentrated in the thyroid.  Doctors take advantage of this specificity by treating hyperthyroidism and carcinoma of the thyroid with calibrated doses of I-131 which will will, at a low dose, kill some of the hyperactive thyroid cells, reducing their activity, or, at a higher dose, kill all of the cancerous thyroid cells.  The I-131 which doesn’t decay in the body is naturally excreted from the body which leads to an interesting story.  

A nuclear power plant was under construction in our area and as part of the process, the local area was tested for sources of radioactivity.  Power plants (and not just nuclear power plants) need water for their cooling towers, water which is usually drawn from a river.  Such was the case with this power plant which, when it tested the river water coming into the plant, discovered that there were detectable levels of I-131 in the river water which was strange because, although the fission of uranium does produce I-131, no nuclear fuel had yet entered the plant.  Not wanting to be later accused of being the source of this I-131 when operations did begin, the power plant asked us at Wilkes University to track the source of this radioactive isotope.  

It should be stated that detectable does not necessarily mean dangerous.  The amount detected in the river water was very low and no threat whatsoever but the power plant did not want to be held responsible for even that much.  The level was so low that we found it easier to track the I-131 upriver, not by sampling the water itself, but by taking samples of river diatoms which concentrated iodine in their shells.  We followed the I-131 up to the treated effluent discharge of the local sewage treatment plant; there was no I-131 in the river water upriver of the effluent discharge.  Some of our physics majors had the joy of sampling the sewage as it traveled through the sewage treatment process and we confirmed that it was in the sewage.  

It then occurred to us that the source of the I-131 might be some of the local hospitals.  We asked the hospitals to tell us when they used I-131 for treatment of hyperthyroidism or carcinoma of the thyroid.  Sure enough, every time there was a treatment, we would see I-131 within a day or two in the sewage.  

Nuclear power plants often have large supplies of non-radioactive iodine pills.  Should there be a release of fission products from the nuclear plant, which could include I-131, the iodine pills would be distributed to the local population, the purpose of which would be to saturate the thyroid with non-radioactive iodine so that it would not concentrate any I-131 that might get into the body.  

Major nuclear plant accidents (Chernobyl, Fukushima Daiichi) and nuclear bombs can release enough radiation to generate acute radiation effects, including death.  The likelihood of death as a result of exposure to toxic chemicals as well as radiation can be described in an LD50 which is the exposure at which half of a population can be expected to die within a short time.  For radiation exposure, the LD50 (lethal dose-50% of population) is about 500 rems.  But effects can be long-term too.  The classic long-term effect for radiation exposure is some form of cancer which might not develop for decades.  Madame Marie Curie died of aplastic anemia (too few bone marrow cells meaning too few red blood cells produced) induced by exposure to radiation.

Dose and Effect
Dose in rems Effect on Humans
100,000 death in minutes
10,000 death in hours, destruction of central nervous system
1000 death in days, irreversible intestinal damage
700 death for 90% within months
500 death for 50% within months, irreversible destruction of bone marrow
200 death for 10% within many months, some permanent hair loss, cataracts, low fertility, tendency to develop leukemia
100 no immediate deaths but chances of cancer and other forms of reduced life expectancy greatly increased; nausea, fatigue, vomiting, etc.
25-100 decrease in number of white blood cells, susceptibility to infection
<  25 no observable short-term effects

Acute Radiation Symptoms (100 rems)
Primary (within a few hours to several days) nausea, fatigue, vomiting, diarrhea, nervous disorders
Secondary (after a week or more) anemia, susceptibility to infection, loss of hair, hemorrhages below skin, ulceration of mouth and gut.

Organs Affected by Various Isotopes
Radioisotope Affected area Principal Radiation Type
Sr90, Sr89 bones beta
Cs137 soft tissue, gonads beta and gamma
C14 whole body beta and gamma
I131, I129 thyroid beta and gamma
H3 whole body beta
Pu239 bones, liver, spleen, skin, lungs alpha
Kr85 lungs, skin beta
Rn222 lungs alpha; beta &  gamma (from daughters)

Relative Risk and Setting Limits

Radiation is a scary word for many people especially since it is linked with another scary word, cancer which often results in an unrealistic perception of the danger of radiation compared to other risks in our lives.  One example of this is the NMR machines found in universities.  NMR stands for nuclear magnetic resonance which is a great way to determine the composition and structure of many materials.  Such a noninvasive instrument is very useful in hospitals too but patients were upset about the use of the word, nuclear.  So, the NMR in the hospital became the MRI or magnetic resonance imaging.  Under either label, the instrument had nothing to do with ionizing radiation but perception dictated a name change.  

Another good example is radon which is not only radioactive and can cause cancer but is an invisible, odorless, tasteless gas; it is a jackpot of scary words.  It was in the early 80s that radon was first recognized as an indoor problem.  Eventually, the EPA decided to set a standard for indoor radon at 4 pCi/L (see the section on radon for more details of this).  We developed a radon testing lab and radon chamber at Wilkes University and began testing much of Pennsylvania for indoor radon levels.  One fellow had a result of 4.1 pCi/L and was quite concerned about it.  We spent almost six hour talking about it and he was chain-smoking the entire time.  Now, both radon and cigarette smoking are linked to lung cancer.  Statistically speaking, radon is responsible for about 15% of lung cancer in the U.S. but cigarette smoking makes up the remaining 85% of the risk of developing lung cancer.  He apparently found radon much scarier than cigarette smoking.  

That radon limit of 4 pCi/L illustrates another issue; where did this limit come from?  Many exposures to undesirable things can never be zero and that is certainly true of radiation exposure. In the case of radon, the outdoor level of it is typically about 0.2 pCi/L which is not zero.  Can exposure to 0.2 pCi/L produce lung cancer?  Yes, but the chance of it, while not zero, is very low.  So how do you set a limit on how much radiation exposure, or exposure to other undesirable things like toxic chemicals, should be allowed while recognizing that many risks can never be zero and that reducing risks can become exponentially more expensive?  

One common method, one used in setting that 4 pCi/L limit for radon, is to set the exposure limit at one additional undesirable effect in a population of one million.  The EPA calculated that a long-term exposure to 4 pCi/L of radon would result in one additional case of lung cancer in a population of one million people and based the limit on that.  A similar reasoning can be applied to many of the primary standards in drinking water and other risks we routinely face.  

One of the most difficult problems in relative risk is to place the risks in a comparative context.  That chain-smoker, rather than worrying about a radon level of 4.1 pCi/L, would be better served by quitting smoking, losing weight, taking blood pressure medication, and consistently using a seat belt.  We all have limited resources and we should apply those resources to reducing the greatest risks to our lives and health. 

The Size of Things

Water treatment often involves some sort of filtration such as activated charcoal filters (AC filters) and reverse osmosis (RO membranes). What can pass the filters depends on the size of a substance and the size of the pore spaces in the filter. Activated charcoal has micropores with diameters < 2000 pico-meters (pm; one picometer is 10–12 meters). The semipermeable membrane used in reverse osmosis has pore spaces on the order of 1000 pm. It might seem simple enough, anything smaller than the filter pore space will pass through the filter, but it is considerably more complicated than that.

The first problem is what is meant by size?  The size of something that is approximately spherical can be described in terms of its radius or its diameter.  The sizes of an atom and an ion are usually given in terms of their radii (plural of radius) while the size of molecules is described as a diameter.  Since the pore space of the filters mentioned above is in terms of their diameters, I will convert all radii to diameters for easier comparison.  

But many molecules are anything but spherical and cannot be described in terms of a simple diameter.  Consider the extreme case of a DNA molecule whose width is about 2000 pm but can be meters long.  If the DNA strand were a little thinner or the pore spaces a little larger, you might think that a DNA strand could fit through the filter but it won’t.  You might remember a certain huge cargo ship that became stuck in the Suez Canal and held up canal traffic for almost a week.  As big as it was, it wasn’t nearly as wide as the Suez Canal.  However, it was much longer than it was wide, much longer than the width of the canal.  Even in a straight section of the canal it managed to wedge itself into the sides of the canal and become stuck.  There is a similar situation in the filters and, even worse, the path from pore space to pore space is anything but straight.  Can you imagine something like that cargo ship trying to navigate sharp turns in the canal?  (the canal avoids sharp turns for exactly that reason)

The next problem is which radius/diameter do you use?  If you look up the size of atoms, ions, and molecules on the internet you will encounter a bewildering variety of radii/diameters.  Oxygen has:

Oxygen as a single atom
Atomic radius 60 pm
Bohr radius 48 pm
Covalent radius 73 pm
Ionic radius 140 pm
Van der Waals radius 142 pm
Oxygen as a diatomic molecule (O2)
Molecular diameter 299 pm
Kinetic diameter 346 pm and even more measurements as an ion

You may encounter other variations such as the root mean square charge radius of a proton.  If you are wondering what some of those strange measurements are, you can look them up on the net.  

And then there is the problem of how the size is determined.  For example, the chloride ion (Cl–) has an empirical (measured) ionic radius of 100 pm but a calculated (theoretical) ionic radius of 79 pm.  Depending on the source, you may find (hopefully slightly) different values for a measured or theoretical radius/diameter.  

Having said all that, the following is a table of the sizes of some things, all converted to diameters in pico-meters (pm) for easy comparison.  Some of the original measurements were in nanometers (1 nanometer = 1000 pm) or in Angstroms (Å; 1 Å = 100 pm).  These values are the atomic, ionic, or molecular diameters.  

Substance Diameter Substance Diameter Substance Diameter
proton 0.0008 Ca++ ion 188 ethanol molecule 360
He atom 62 Na+ ion 190 K atom 392
H atom 74 Cl atom 200 PO4-3 ion 476
H2 molecule 106 Mg atom 260 SO4= ion 484
Cl2 molecule 106 K+ ion 266 O2 molecule 598
O atom 120 H2O molecule 270 RO membrane pores 1000
Fe+++ ion 126 Na atom 308 AC filter micropores < 2000
Mg++ ion 132 Fe atom 312 DNA width 2000

A longer, more inclusive table would make some trends more obvious but they include: (1) the higher the atomic number of an element, the bigger it tends to be, (2) the more positively charged an ion is, the smaller it tends to be, and (3) the more negatively charged an ion is, the bigger it tends to be.  

But most importantly, based on the sizes given, the only things in the table that RO and AC filters should stop are stray strands of DNA, the coronavirus, and Giardia cysts, and yet those filters do somehow stop all of the ions.  How?  

First, consider what might reasonably be expected to be in water.  Individual atoms would not be in the water although they could be present as ions; things like calcium and iron in water are present as dissolved ions, not as atoms.  Polar molecules like ethanol can be mixed in the water in any proportions because water itself is polar but non-polar molecules like gasoline would only be present in very small amounts (although some non-polar compounds could still be a problem even in very small amounts) because non-polar compounds have a very low solubility in water.  Activated carbon (AC) filters can remove such organic contaminants although RO filters might not.  

This next part is speculative (we don’t have all of the answers and if you have a better explanation, do let us know).  Gases like helium and radon (maybe methane, VOCs, and other smaller non-polar organics) would probably pass through an RO filter, although they would likely adsorb onto the charged surfaces in an AC filter and be stopped that way, but there may be a another reason why ions much smaller than the pore spaces in both types of filter are prevented from passing through the filters.  

Ions, by definition, have electrical charges which means that they are attracted to the opposite partial charges on a polar water molecule.  Negatively charged ions are attracted to the hydrogen ends of the polar water molecule and positively charged ions to the oxygen end of the water molecule.  If the attractions are strong enough, the ion is said to form complexes with the water molecule.  The ion and the surrounding water molecules start to act as a larger unit.  Let us consider a human analogy.  

Doorways are designed to allow a single person (the ion) to easily pass through the door (the filter pore spaces).  Imagine, however, that there are a number of other people (the surrounding water molecules) who are holding on to you.  The doorway is big enough for you to pass but you can’t get through it as a group; everybody gets in everybody else’s way, blocking the entrance.  This story is unnecessary for the AC filter with its charged surfaces to hold passing ions but it could explain how an uncharged RO membrane can hold back smaller ions.  

Water molecules are also attracted to the opposite polar ends of other water molecules making them cling together enough to make the melting and boiling points surprisingly high for that size of a molecule but such attractions (hydrogen bonds) are weaker than those between an ion and a water molecule because the charges on a polar water molecule are only ‘partial’ charges compared to the full charge of an ion.  Hydrogen bonds are continually forming and breaking and reforming between the water molecules in liquid water making it relatively easy to push individual water molecules through the filter pore spaces while blocking the larger ion complexes. 

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