Tag Archive: Nuclear Physics

In addition to his usual amazingly funny physics-related humor, xkcd has published a very handy comparison chart that helps to visualize the relative doses for a variety of different types of radiation exposer. Click on the image to be brought to the full-size chart on xkcd’s site.

Radiation dose comparison sheet (xkcd)

Radiation symbol (Cary Bass, via Wikipedia)

Why this Article?

The terrible tragedy in Japan has sparked a huge discussion about nuclear power, radioactivity and nuclear meltdown. Unfortunately, major media in the United States continually report about “high doses” and “low doses” without quoting any actual measurements of radiation radiation levels. This is probably due to the fact that most reporters do not understand nuclear power and radiation themselves. It is a huge problem because it does not provide the public with the detailed information that it would need in order to fully understand the measurements and how it would affect their own health and livelihood.

One unfortunate result of this nebulous reporting, whether it is intentional or not, is that it is rather easy to scare people with the mere mention of the word “radiation” simply because it is very easy to scare people with things that they do not understand. On the other hand, people with a better understanding of radiation will recognize that the level of risk arising from radiation is dependent on the type, the length and the amount of exposure to it. They will be able to compare the measurements of reported radiation doses with background levels. Except in certain tragic circumstances, this generally means that people can be less fearful and more conscientious about their radiation risk.

In this article, I will describe where radiation comes from, a number of ways in which it is measured and what the likely risks are for various levels of exposure. This piece is not really a news article in and of itself, but it is intended to be a guide to help interpret news in those rare cases where the press actually reports the numbers that you need to know.

First, let’s look at the different types of particles that make up the atom and the forces that make them stick together. The complicated part of quantum physics is in making calculations and in deriving physical laws to explain them. Understanding how they work is not so bad, give it a try. : )

Subatomic Particles

One aim of physics is to try to understand the Universe by looking at how its constituents interact. By the 1970s, physicists had put together a detailed model, called the Standard Model, (we physicists sometimes have problems with creativity when it comes to naming things) that describes all of the known fundamental particles and their interactions.

Fundamental particles are simply particles that we believe can not be divided into smaller parts. They are broken down into two major categories, depending on a property called spin: Fermions and Bosons. Spin is a measure of the intrinsic angular momentum of a particle. According quantum mechanics, subatomic particles can only have certain values of spin. Fermions are particles with spins of 1/2, 3/2, 5/2 and so on, while Bosons are particles with spins of 0, 1, 2, and so on, and particles from either of these two families have very different properties.

Fermions can broken into a couple of subgroups, called Leptons and Quarks. These groups are determined by the amount of electric charge that they carry. The Leptons include the electron and its cousins, the muon and the tauon (usually the tau). Each lepton is associated with another particle called a neutrino. Neutrinos are particles that rarely interact with matter. In fact to be sure that you would capture a neutrino about 60% of the time, you would need a lead wall roughly 8 light-years thick! That is 47 trillion miles.

The other subgroup, the Quarks, are a group of particles with electrical charges of either +2/3 or -1/3. They make up subatomic particles like protons and neutrons.

Fermions (Spin = 1/2, 3/2, 5/2, etc.)

Leptons (Spin = 1/2)
Flavor Symbol Mass (GeV/c2) Electric Charge
Electron e 0.000511 -1
Electron Neutrino νe <1×10-8 0
Muon μ 0.106 -1
Muon Neutrino νμ <0.0002 0
Tau τ 1.7771 -1
Tau Neutrino ντ <0.02 0
Quarks (Spin = 1/2)
Flavor Symbol Mass (GeV/c2) Electric Charge
Up u 0.003 +2/3
Down d 0.006 -1/3
Charm c 1.3 +2/3
Strange s 0.1 -1/3
Top t 175 +2/3
Bottom b 4.3 -1/3

All of the matter that you deal with every day, whether it is atoms inside you, the air you breathe, or even those in the Earth itself, are all made of Fermions. How all of those particles interact is determined by force-carrying particles, the Bosons. There are four fundamental forces that we know of right now. Two are likely fairly familiar from everyday experience and two are not so familiar: Gravity, Electromagnetism, the Weak Nuclear Force and the Strong Nuclear Force. Most people deal with gravity and electromagnetism every day, but few people worry about the weak and strong forces, but the weak and strong forces govern radioactive decay.

Each Boson carries a separate force. Here is a summary:

Bosons (Spin = 0, 1, 2, etc.)

Name Symbol Mass (GeV/c2) Electric Charge Spin Forces carried
Photon γ 0 0 1 Electromagnetic Force
W-minus W 80.4 -1 1 Weak Nuclear
W-plus W+ 80.4 +1 1 Weak Nuclear
Z-nought Z0 91.187 0 1 Weak Nuclear
Gluon g 0 0 1 Strong Nuclear
Graviton G 0 0 2 Gravity (not yet detected)

A particle such as an electron would not experience the electromagnetic force, for example, if it did not interact with photons. A person feels the pull of gravity from the Earth because we think that Earth is continuously emitting a very large number of gravitons that interact with the particles that make up a person. Without those graviton interactions, there would be no gravity. Physicists believe that the particles in the two tables above can fully explain all of the interactions between all of the objects in the Universe (possibly excluding Dark Energy and Dark Matter, but that is another story). It is only a matter of working out the details to try to understand how the Universe works, though there are complications because – well – it turns out that the interactions can be complicated. It is still good to have goals!

E = mc2

Einstein proposed his most famous equation during his annus mirabilis (miracle year) when he wrote four papers that set the groundwork for 20th century physics. Inertia is the resistance of an object to changes in motion. We measure this resistance with the quantity mass. E = mc2 says that any object with a mass, m, has a certain amount of energy, E, locked up in that mass. It is a lot of energy per unit mass, because c is the speed of light and light happens to be quite fast: c = 3.0×108 m/s = 186,000 mile/sec!

It happens one gram of sugar has 2.4 Calories (kcal) of chemical energy in it and when we eat sugar, that is roughly how much energy we gain from it. If we measure that in Joules (J, the SI unit for energy), we have 10,000 J of chemical energy in a gram of sugar. But one gram of any substance has (0.001kg)*(3.0×108 m/s)2 = 9×1013 J of energy locked up in its mass! That is roughly enough energy to supply the United States with power for three days!

The tables above give the masses of each particle in units of GeV/c2 (giga-electron volts). The prefix giga- means billion, so 1 GeV = 109eV. And one electron volt is defined as the amount of kinetic energy that a single electron gains from a voltage drop of 1 Volt. So you can see that this definition of mass came after E=mc2. It is possible to use these conversions:

1 eV = 1.6×10-19 J – a really small unit!
1 GeV/c2 = 1.783×10-27 kg – roughly the mass of a proton

These are reallly small units, but remember that a cubic centimeter has something like 1023 = 100,000,000,000,000,000,000,000 atoms!

All of the above particles have an anti-matter equivalent that has the same mass but opposite electric charge. When a particle collides with an anti-particle, both particles annihilate, giving off photons with total energy E=mc2. Photons are their own anti-particles, too.

Nuclear power allows us to tap a little bit of that energy that is stored in mass, but first let us take a look at atoms to see how.


Now that we have covered the subatomic particles, let’s make atoms. Most people learn in middle school that atoms are composed of protons, neutrons and electrons. The Protons and neutrons reside in the nucleus at the center of the atom and the electrons move around in the electron cloud that surrounds it. Protons and neutrons are (very) roughly 2000 times heavier than an electron so they carry most of the mass of of the atom, considering that an electrically neutral atom has the same number of protons and electrons.

When we talk about nuclear power, we are primarily concerned about the nucleus of the atom. So we are going to ignore the electrons in the electron clouds for now, however we will occasionally encounter electrons that are created by nuclear reactions.

Protons and Neutrons are particles called Baryons. Baryons are composed of three quarks (Mesons are particles made with two quarks). Here is how it works: A proton is made from two up quarks and one down quark. Up quarks have charges of +2/3 and a down quark has a charge of -1/3, so if you add up the charges, you get: 2/3 + 2/3 – 1/3 = +1. Neutrons are made of two downs and one up, so they are electrically neutral.

But wait a second! If you have 2 ups and 1 down, that only adds up to (2*(0.003) + 0.006) GeV/c2 = 0.012 GeV/c2 of mass, but a proton has a mass of about 1 GeV/c2! It does not add up, and here is why. Experiments have confirmed that the quarks in a proton and a neutron are held together by the strong nuclear force, carried by gluons. It is a complex set of interactions, but simply put, the interactions keeping the quarks together are very high energy, so high in energy that they account for the rest of the mass!

Atomic Nuclei and Radioactive Decay

β-decay (Wikipedia)

It also happens that a neutron is about 0.14% more massive than a proton. This corresponds to a mass of about 15 MeV/c2 (1000 MeV = 1 GeV), so if we could convert a neutron into a proton, we should get some energy out (1n -> 1p + 1e + 1νe). In fact, this happens with free neutrons because they are unstable because of interactions governed by the weak nuclear force. A free neutron will decay into a proton, an electron, and an anti-electron neutrino with a half-life of around 8 minutes. (The half-life is the time over which half a collection of one type of particles will convert into other types of particles.) This is the iconic reaction in one form of β-decay (beta-decay), known as β-decay. Another form of β-decay is β+-decay: Energy + 1p -> 1n + 1e + νe, where a proton absorbs energy that causes it to break into a neutron, an anti-election (also called a positron) and an electron neutrino. β+-decays can not occur in isolation. You will often see electrons referred to by the term “β-particles”.

The simplest atomic nucleus is that of Hydrogen, just a single proton. We do not usually see single neutrons around unless we are near a radioactive source because neutrons are unstable as we have mentioned. Protons are stable, however, so we do see Hydrogen, the most abundant element in the Universe.

Atomic nuclei are held together by the “residual strong nuclear force”, which is a manifestation of the strong nuclear force itself. Nuclei are held together by virtual mesons that carry gluons between protons and neutrons inside. There is a lot of activity taking place inside a nucleus all of the time!

It is possible to create an atom with the same chemical properties as single-proton Hydrogen if we add neutrons to the nucleus. These are isotopes, nuclei with the same total charge (which governs the chemistry) but differing numbers of neutrons. For example, Deuterium, another isotope of Hydrogen, has one proton and one neutron. It is nearly identical to Hydrogen chemically, but it is much more rare than plain, old Hydrogen because at some point, a free neutron would only have about 8 minutes to latch onto a proton to form it. Another isotope, Tritium, has one proton and two neutrons, and that is even more rare.

α-decay (Wikipedia)

Helium normally has a pair of protons and a pair of neutrons. It has other isotopes, but it happens that the normal Helium nucleus is very stable and when bigger atoms break apart, they often do so by giving off Helium nuclei, or α-particles (alpha-particles). That process is known as α-decay.

Heavy elements such as Uranium (U) have a very large number of protons (92) and often even more neutrons. 235U, for example has 143 neutrons! Nuclei with either too many or too few neutrons relative to the number of protons are unstable. In addition, large nuclei are often unstable simply because the strong nuclear force is a very short range interaction. If a nucleus is too large, the strong force can not hold it together effectively. This means that there is a “Band of Stability” for atomic nuclei, shown here by plotting the number of neutrons against the number of protons in known isotopes. The colors indicate whether each isotope is stable (black squares) or if not, their primary modes of decay.

The Band of Stability of Nuclear Isotopes, showing observed isotopes (Wikipedia)

Other atoms may split into components that are larger than α-particles. For example, 235U can break into a Krypton-92 (92Kr) nucleus, a Barium-141 (141Ba) nucleus. This is known as fission. The inverse process if known as fusion.

During most of these different types of radioactive decays, high-energy photons are released that are known as γ-radiation or γ-rays. Each one of these decay modes results in different energetics, so when we are concerned about how radioactive decay effects the human body, we need to worry about the specific consequences of human exposure to α-, β- and γ-radiation.

Effects of radiation on Humans

So suppose you are walking along a path in a forest far from any radiation source. You just happen to be carrying your trusty Geiger Counter and decide to turn it on just for fun. You will hear the Geiger Counter click sporadically and you may be shocked to find that the clicks increase when you move the Geiger Counter closer to your body. There are radioactive isotopes everywhere! Background levels of radiation are generally due to trace isotopes found in rocks, cosmic rays that reach earth from space, and any life form will have some 13C (Carbon-13). In fact the process of live itself bioaccumulates 13C. Well, a quick check of the Band of Stability graph shows that an isotope of Carbon-13 (with 6 protons and 7 neutrons), will β-decay to form stable 12C. The half-life of Carbon is about 5730 years. About 1.1% of all Carbon on Earth is in the form of Carbon-13 and by comparing the abundance of carbon in biological material with that of the world at large, it is possible to date the material through Carbon Dating. The electrons that are released in the β-decay can be picked up by the Geiger Counter.

The Geiger Counter will essentially count the number of decays it detects per unit time, measured with the SI unit of the Becquerel (Bq). 1 Bq = one decay per second. While this unit gives the number of radioactive decays taking place per unit time, it does not indicate anything about their effect. In order to do that, we need to take into account how much energy the decay products are carrying and how much of that energy is absorbed by the human body.

A typical human body produces about 4,000 Bq of activity, due to 40K (Potassium-40) beta decays alone.

The SI units for the dose of radiation that are absorbed by the human body are Grays (Gy). 1 Gy = 1 J/kg. It is strictly a measure of the total energy deposited in the body and does not quantify the net effect of the radiation. In order to understand the effects, we will need to look at the differences in how each type of radiation interacts with the body.

A high-energy photon (γ-radiation) that is absorbed by body tissues generally breaks apart the molecules it strikes. The radicals (essentially the electrically charged pieces of broken molecules) that are created when this happen can then react chemically with other molecules around them. The overall effect is limited relative to other forms of radiation, however, because a single ion gives rise to a small number of radicals so there is little overall damage from a single γ-ray relative to other forms of radiation. γ-rays can also scatter off molecules through the Compton Scattering, which frees lower energy recoil electrons that can interact with molecules in tissue.

Gamma radiation is usually not completely absorbed by the human body. That is how it is possible for medical X-rays to work, because only a fraction of the X-rays are absorbed by the body while the rest pass through. Some of those that do pass through expose a piece of film or a detector to create an image.

A β-ray (an electron) does similar damage to a photon, but for different reasons. They do not usually penetrate as deeply, though electrons carry some momentum, and they carry electric charge that can ionize some molecules as they pass near them. In other cases, the electron can be absorbed by a molecule or scatter other electrons to create radicals.

A high-energy neutron that is released by radioactive decay has a lot of momentum. When it smashes into tissue, a game of molecular bumper cars ensues. If the neutron has enough energy, then it is possible to break molecular bonds and to release reactive radicals into the body. Given the fact that neutrons can have a good deal of momentum, they generally produce more radicals than a single γ-ray. Neutrons can deposit their energy deep in tissue and are readily absorbed by some isotopes found in the body. This can cause further radioactive decays.

Protons do carry roughly the same momentum as a neutron, they also carry electric charge that results in ionization. They do more damage than electrons but do not penetrate as deeply as neutrons due to their electric charge.

α-particles and heavy nuclei cause the worst damage because they have the most momentum, but they penetrate the least. These particles carry a ton of momentum and they break up molecules and create radicals until they are stopped. They are highly likely to interact with the tissue rather than pass through it.

When determining the net effect on the body, one also has to consider that the different types of tissue in the body each react differently to radiation at different energies. Studies have been done in an attempt to average the effects over the body and these have led to a standards regarding the Relative Biological Effectiveness (RBE) of the various types of radiation. These are used to determine the equivalent absorbed does, given in Sieverts (Sv). 1 Sv = 1 J/kg just like Grays, only now the dose in Grays is multiplied by a weighting factor, WR, to account for the relative impact of various sorts of radiation on the body. (Sieverts can be related to the outdated unit, the rem with 1 mSv = 0.1 rem.) These weights are determined by experimentation under ideal circumstances compared to the relatively complex circumstances found inside a nuclear reactor, but they do offer insight to the impact on people nonetheless.

Typical background doses vary from place to place, depending on which specific isotopes can be found in the local environment, but Wikipedia gives some general levels that can be used as guidelines if you read dosage numbers in the press. These can be found in the table here, where doses are given in mSv/yr unless otherwise noted for one-time total doses.

Wikipedia has an excellent table that describes the types of symptoms, timescales and fatality rates of radiation sickness. Radiation doses above ~1000 mSv can cause radiation sickness. The higher the dose, the worse the symptoms. Doses up to about 2000 mSv can cause nausea, dizziness, fatigue and a reduced white blood cell count. 5% of people die within a month of receiving 2000 mSv of radiation. Doses between 2000 and 6000 mSv can cause cognitive impairment, purpura, hemorrhage and skin loss and above 5000 mSv, fatality becomes nearly certain, though the period of suffering can last up to a month. Higher doses lead to increasingly severe symptoms. Doses above ~30,000 mSv can cause seizures and death within 48 hours.

The geometry of a nuclear power plant such as the Fukushima-I plant can lend to dramatic variations in radiation levels on site. This is due to the fact that concrete, metal and water shield their surroundings from radiation to different degrees. Given the complicated geometry of a nuclear power plant, there could be low-radiation regions very near high-radiation areas. It is very difficult to calculate the dosage that any worker would have received because one would need to know the radiation level at every single point along that worker’s path through the course of the day. Radiation detecting badges are helpful, but the relative dose that an individual receives can vary from one side of his or her body to the other.

The situation in Fukushima-I is especially complicated because there has been a good deal of damage to the plant. Several large Hydrogen gas explosions have spread trace radioactive material far from the plant, but it typically becomes less concentrated if it is spread over a large area – unless an explosion launches a chunk of radioactive material skyward.

The situation further from the plant is generally a bit easier to estimate because the distribution should typically be a bit smoother than the conditions inside the plant. I must include the caveat that I said estimate, not predict. If a measurement is made far away from the plant, material will be dispersed relatively uniformly around a field, for example, so radiation measurements will be more indicative of nearby surrounding areas. There can still be large-scale variations in dispersal patters. Wind currents could blow radioactive material in either one general direction, or it could be widely dispersed, carried aloft at high altitudes as it was in the case of Chernobyl.

Dispersal of Radioactive Material after Chernobyl. The human body has a natural radioactivity of ~4kBq. (UNEP)

The primary variable in long-range dispersal is how high the radioactive material is sent by explosions at the plant. Chernobyl experienced a large explosion that sent radioactive material high aloft, where it could be dispersed over a wide area for a long period of time. The explosions in Japan have not been nearly as large, though some radioactivity has been detected within ~100km or so from the site that has led to some precautionary measures. Clearly, the fewer explosions that take place in the reactors, the better off everyone will be because there will be less dispersal of radioactive material.

Protecting yourself

Unless otherwise necessary, it is generally best to avoid radioactive material and to avoid areas that have high levels of radiation. In an emergency, however, it is generally best to find a way to shield yourself from the radiation and this means placing material in between you and the radiation source. All material absorbs some radiation, but it is best to use dense materials because they tend to be more effective. How much radiation is absorbed by a material is measured by its “Halving Thickness”, or the thickness of that material to reduce gamma radiation by a factor of 2. If a material can stop a gamma ray, it can generally stop everything else. An effective fallout shelter using 1 m of dirt accounts for ten halving thicknesses, decreasing the effective radiation fluence by a factor of ~1000.

I hope that this is useful to people who are interested in learning a bit more about radiation and radioactivity. I believe that if people know its effects and how one can treat it properly and protect one’s self, that it tends to alleviate unnecessary fear. The world will not end if the Japanese plants were to go into meltdown. A meltdown would imply significant environmental impacts, and it may also mean that there would be a portion of Japan that will be unlivable. People living outside of Japan are not likely to be significantly affected, except in the absolute worst case scenario. Good luck to everyone working to prevent a meltdown, and please be safe.