Modern Physics



1fm = 1 femtometer = 1 x 10-15 meters



Although the strong nuclear force binds nucleons together at distances of about 1fm, it becomes a powerful repulsive force at distances of around 0.7fm. This strange repulsive property is responsible for the physical size of the nucleus!

Radioactive Decay

Whether you know it or not, you benefit from the effects and uses of radioactivity. Radioactivity or “radioactive decay” powers NASA’s deep space probes that venture far away from the sun; heats the core of the Earth powers volcanoes and plate tectonics, and allows for our protective magnetosphere; provides energy for our houses through nuclear power plants; and provides treatments for cancer. While dangerous in some applications (like nuclear weapons), radioactive decay plays a very important role in our daily lives. So what is it?


Radioactive decay is the spontaneous emission of an ionizing particle from an unstable atomic nucleus. There are three types of radioactive decay because three different types of emissions occur:


• Alpha particles

• Beta particles

• Gamma rays


Radioactivity is “stochastic,” meaning random and unpredictable. It can’t be predicted which atom will release a particle, but because there are billions of atoms in any hunk of material the statistical odds of decay are constant with time.


You will recall that an atom is made up of a nucleus and orbiting electrons. This is one of the foundations of quantum physics. The nucleus of the atom is made up of nucleons, a word we haven’t used so far that simply means positively charged protons and neutrally charged neutrons. The nucleus is much smaller than the atom so the atom is mostly empty space like a mini-solar system. The mass number (A) of a nucleus is then the sum of the number of protons (Z) and the number of neutrons (N) so:


A = Z + N


Elements are often written specifying their mass number and proton number (from which the number of neutrons can be easily calculated). As an example, helium can be written thus:




indicating it has a total mass of 4 (2 protons and 2 neutrons) and a total number of protons of 2.


You might wonder what holds the nucleons (neutrons and protons) in the nucleus together. In classical physics, two protons repel each other because they each have a positive charge. This is analogous to trying to push the north poles of two magnets together. This is true in quantum physics as well, but at very tiny distances, around 1 femtometer (1 fm), the attractive nuclear strong force is stronger than the repulsive electrostatic force, and binds the nucleus together. In the case of beta decay, the weak nuclear force is also involved. This tug of war between the very weak attractive force of gravity (essentially irrelevant for our purposes here), the electrostatic repulsive force, and the nuclear strong force holds the nucleus of protons and neutrons together as a stable nucleus for all elements with atomic numbers less than or equal to 82 (lead).


Radioactive decay occurs at some level for all elements with atomic number 83 (Bismuth) or greater. For these elements, radioactive decay is influenced heavily by the ratio of protons to neutrons in the nucleus. The greater the deviation of this ratio from a value of 1, the greater the element’s chances of releasing energy from its nucleus by emitting particle (alpha or beta decay) or electromagnetic (gamma decay) energy through radioactive decay.


In addition, the strong nuclear force diminishes rapidly with distance between nucleons, much more rapidly than does the repulsive electrostatic force between protons. It is this fact that causes instability in larger atomic nuclei (e.g. with atomic number greater than 82).


A neutron has a slightly greater mass than a proton. Both are far more massive than electrons. The masses of each particle, in kg and atomic mass units are:


                                Mass in kg               Mass in AMU

Neutron                1.675 x 10-27            1.0087

Proton                   1.673 x 10-27            1.0073

Electron                 9.109 x 10-31            5.4858 x 10-4


Note: Because kg are unfathomly bigger than the particles involved in the nucleus, a more appropriate unit of measurement is used: An atomic mass unit (AMU) is officially the mass of one-twelfth of the mass of an atom of carbon-12, and has a value of 1.660538921(73)×10−27 kg. Don’t memorize that!


You will note that the mass of an individual proton and neutron are each slightly greater than 1 AMU. Yet something does not quite add up for the total mass of an atom. Let’s take carbon-12 for example. Carbon-12 (12C) has 6 neutrons and 6 protons in the nucleus. Its atomic mass is 12.011 AMU. Adding up the masses of its individual particles we get:


6(1.0087) + 6(1.0073) + 6(5.4858 x 10-4) = 12.0993. This is 0.883 AMU greater than the quoted mass of the carbon atom. What’s wrong? The excess mass of the individual particles goes into creating the binding energy of the nuclear strong force via Einstein’s E = mc2. This “missing” mass is called the “mass deficit”.



Alpha Decay


Alpha particles are nuclei of the element helium, with two protons and two neutrons. Because they have the highest bonding energies and so are most difficult to split apart, alpha particles are a commonly emitted particle in radioactive decay processes for relatively massive nuclei (generally heavier than nickel). Because they are relatively large, they do not penetrate very far into other materials. They travel only a few inches and a piece of paper, for example, will stop most alpha particles. Nuclei with an excess of protons (high proton/neutron ratios) are good candidates for alpha particle decay since the release of this energy helps to rebalance the nucleus. In alpha particle decay as in other decay mechanisms both mass and energy are conserved. As an example, uranium 238 (238U) decays into thorium 234 (234Th) plus an alpha (α) particle. This can be written as:

          238U ➙ 234Th + α     -or-

238U ➙ 234Th + 4He


Beta Decay


Beta particles are electrons or, in some cases, positrons (electrons with a positive charge). Basically, in attempting to create a more balanced or stable ratio of protons to neutrons, an atomic nucleus may eject an electron (OK and an antineutrino) from its nucleus. This process, known as Beta-Minus Decay, changes a neutron into a proton thus increasing the element’s atomic number, changing it to a different element entirely. This process of changing an element from one thing to another is called nuclear transmutation. (Illustrations from Jefferson Lab, US Dept. of Energy)


In Beta-Plus Decay, a nucleus ejects a positron and a neutrino, changing a proton in the nucleus into a neutron. Since, in this case, the atom loses a proton, transmutation occurs. Notice that although the numbers of protons and neutrons increase or decrease, the total number of nucleons in the nucleus remains constant.




Gamma Decay


Gamma Decay is the spontaneous emission of a high energy gamma ray photon (γ) in order to lower the energy state of an unstable nucleus. Gamma rays are most damaging to living things as they penetrate much further than alpha particles or beta particles and have extremely high energies. In gamma decay, the number of protons and the number of neutrons in the nucleus remain the same so transmutation does not occur. Gamma decay occurs in nuclear explosions, releasing high energy gamma rays. (US Govt image)



Half Life


Although you cannot predict when any particular atom will undergo a decay event (emit a particle or high energy ray), you can say with very high certainty how a large group of such atoms will decay. The decay rate of a group of atoms is often referred to as the substance’s half life. The half life of a substance is the time it would take for half of a given amount or mass of that substance to decay into something else. This “something else” can be either a different isotope (if the daughter atom has a different number of neutrons than the parent) or another atom entirely (if the daughter atom has a different number of protons). Let’s look at an example.


Plutonium-238 is the radioactive substance that powers spacecraft venturing far from the sun into the deep reaches of the outer solar system. Out there, the sun’s rays are too weak to rely on solar cells for power, so Radioisotope Thermoelectric Generators or RTGs are used. Pu238 is a powerful alpha particle emitter and does not emit significant amounts of other, more penetrating particles or high energy radiation. This makes it a perfect source for spacecraft power systems. So, the power from Pu238 comes from alpha decay. By ejecting alpha particles (remember helium nuclei), Pu238 decays to uranium-234 and eventually to lead-206. It’s half life is 87.7 years. One gram of plutonium-238 generates approximately 0.5 watts of power.

If I start with one gram of 238Pu, in 87.7 years I will have only ½ gram. In another 87.7 years, I am left with ¼ gram, and so on. So the radioactive decay power curve is exponential. For practical purposes, after 10 half lives, we can consider a substance entirely decayed.


Left: Spacecraft powered by RTGs





Radioactive decay & Supernovae


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