M: Alright, we now have all the tools to understand the first two basic types of nuclear radiation. Alpha decay and gamma decay. Let's start with alpha.

Let us summarize:

1. The nucleus is an energy well. The source of this energy is the nuclear force which is stronger than the electric repulsion between the protons, but it is very short range.
2. Each nucleus has some average binding energy. Helium is unusually stable and so protons and neutrons like to group themselves in bunches of four (alpha particles or helium nuclei) inside the nucleus.
3. The most stable atom is iron. Atoms below iron would like to grab some alpha particles, but this is very rare. Atoms bigger than iron can eject an alpha particle to become more stable.
4. Alpha particles are stuck inside the potential well (see Fig. "Alpha Radiation") but sometimes they can randomly get out of the nucleus - lets see how that happens.

The ultimate mechanism for alpha radiation relies on quantum tunneling which we will not cover in this class— <a href="https://www.youtube.com/watch?v=cTodS8hkSDg" target="_blank">look here</a> if you want to learn more about it.

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Polonium PO 84

Let us look at an example. Polonium is a highly radioactive element discovered by Marie and Pierre Curie. Its atomic number is 84 (this means it has 84 protons). There are no stable isotopes of Polonium. For every number of neutrons, polonium is highly radioactive and will mostly want to undergo alpha decay.

A reminder. The number of protons inside the nucleus differentiates different elements. 8 protons is oxygen while 7 protons is nitrogen, etc. For any given number of protons, we can have different number of neutrons (different _isotopes_). Oxygen 16 is oxygen with 8 neutrons (for a total of 16), the most common version of oxygen. Oxygen 17 is an isotope of oxygen with 8 protons and 9 neutrons, it is stable. Wikipedia always gives the list of all stable isotope for each elements, just look up oxygen and see the properties on the right.

For example, polonium 208 (84 protons and 124 neutrons) is unstable, it is radioactive. It will after some time emits an alpha particle and becomes lead Pb 204 which is very stable. Note that the total number of nuclei dropped by four (208 -> 204) and that polonium (element 84) became lead (element 82) (so two less protons). See the <a href="http://www.webelements.com" target="_blank">table of elements</a> to check for yourself.

Marie Curie spend her life studying radioactive materials and she won a Nobel prize in physics _and_ chemistry in recognition of her work. (Very, very few people have ever done that.) Unfortunately, she died of cancer. Her lab notebook and other furniture from her lab, are being kept in Paris but they cannot be seen by the public because they are too radioactive and unsafe still to this day!

• S: Why would the notebook be radioactive, it is not made of Polonium?
• M: No, but it contains traces of polonium dust(or other radioactive materials that Curie discovered) which emit alpha particles.
• S: It is sad that she died because of her research.
• M: Well you can die of cancer for other causes, but, yes, she was in contact with many dangerous materials. Now we do nuclear research much more safely and Marie lives on thru the many discoveries she made!

Radioactive vs Radiation: This is an important distinction. Radioactive material emits radiation. The emitted radiation is what is dangerous, and this is because alpha particles and gamma radiation are particularly hazardous to humans.

Gamma Radiation

The other type of nuclear radiation is a photon. To understand why, we need to go back to the "electron in a box from previous weeks). You will remember that when you put a particle in a box, its energy is quantized (see Fig. "Energy Levels H").

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The energy in the square box goes like <lrn-math> E_n = n^2 E_1</lrn-math>, where <lrn-math>E_1</lrn-math> is the ground state energy which depends on the size of the box. The ground state energy goes like <lrn-math>E_1 \propto 1/L^2</lrn-math>, the smaller the nucleus (L) the bigger the energy. Because the nucleus is so much smaller than the atom, the ground state energy is bigger and the energy of the photon emitted is bigger as well.

A typical electron transition in an atom creates photons with energy of about 1 eV. Via <lrn-math>E=hf</lrn-math>, this amount of energy corresponds to frequencies of about <lrn-math>10^{14}</lrn-math> Hz, or visible light.

A typical nuclei transition inside the atom create photons with energy of about <lrn-math>10^6</lrn-math> eV which are gamma rays!

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Mass Defect

Let us say that an atom's nucleus decays from an excited state and emits a 1 MeV gamma ray. The atom is at rest at the beginning and so shooting out a photon will make it recoil a bit, but not very much (remember conservation of momentum?). But where does that gamma ray's energy come from?

It came from the mass of the nucleus. An excited atom that emits a 1 MeV gamma ray weighs more before than after. The atom loses mass. Exactly as predicted by <lrn-math>E=mc^2</lrn-math>.

Same thing happens when polonium emits an alpha particle. The mass of the alpha particle plus the final lead atom is actually less than the original mass of the polonium. The mass difference between the end products and the beginning products all goes into kinetic energy of the alpha particle and the lead atom!