Lecture 13

$\alpha, \beta$ and $\gamma$ Radioactivity

$\alpha$ Decay.

$\alpha$ radiation occurs when an unstable, heavy nucleus emits a Helium nucleus, i.e. a cluster of two protons and two neutrons bound together. Due to the original historical denomination, Helium nuclei are still referred to as $\alpha$ particles; these were the ones used by Rutherford in his famous experiment. When emitting an $\alpha$ particle, that is when undergoing $\alpha$ decay, the original nucleus will find itself with two less neutrons and, more importantly, two less protons: it will therefore transform itself into the nucleus of a different element. Example :

$^{210}_{84}Po \longrightarrow ^{206}_{82}Pb + \alpha$ ( = ⁴₂He)

We then see how radioactive decay achieves the old Alchemist's dream of transmuting one substance into another : but, to do so, one needs to operate at the nuclear level, something that was beyond the possibility of the Alchemists, or of Chemistry in general, since Chemistry only deals with the atomic electrons.

If we were to measure the masses of the final Lead and Helium nuclei we would see that they weigh less than the original Polonium nucleus. An additional measurement of the velocity of the decay products would show that the "missing energy" is accounted for by the kinetic energy of the Pb and He nuclei produced in the decay. A radioactive decay is an example of transformation of mass into (kinetic) energy.

Because of their "bulkiness", $\alpha$ particles are not very penetrating and can in priciple be shielded even by a very thin absorber. On the other side, they can be very harmul if an $\alpha$ emitter penetrates the body (e.g. by breathing Radon gas).

$\beta$ Decay.

It might be of a surprise to you, but neutrons, copiously present as ordinary ingredients of all matter, are not stable particles. In a matter of minutes, a free neutron will spontaneously decay into a proton, an electron and another particle, the neutrino, that we will for now ignore. This decay does not violate the rules of energy/mass conservation, since the mass of the neutron is larger than the combined masses of proton+electron (the neutrino has negligible, maybe 0, mass).

Why then do we not observe continuous neutron decays within all ordinary matter? Somewhat loosely speaking, this is because neutrons, when bound within the nucleus, have a mass smaller than free neutrons, i.e. smaller than the proton+electron mass. This mass defect was given away as energy when the nucleus formed. But there are exceptions: in some particular case, i.e. for some unstable isotopes, a neutron can find itself in the position to decay into a proton and an electron. The electron comes out of the nucleus with considerable energy : this is what was originally called $\beta$ radiation. Note that this electron is neither one of the orbital electrons nor it was originally present in the nucleus. It is just born as the product of neutron $\beta$ decay.

$\beta$ decay electrons have energies of the order of MeV's, they are so energetic that they escape their own atom without being affected by the orbital electrons.

As in $\alpha$ decay, $\beta$ decay has the effect of transmuting an element into another. Examples :

$^{14}_{6}C \longrightarrow ^{14}_{7}N + e^-$

$^{60}_{27}Co \longrightarrow ^{60}_{28}Ni + e^-$

etc.

$\gamma$ Decay.

When capable of doing so, a nucleus will always move from less stable configuration to a more stable one. As we have seen, this can result in either $\alpha$ or $\beta$ radiation, but sometimes it can be achieved just by rearranging the protons and neutrons within the nucleus, to move from a higher to a lower energy state. In doing so, the nucleus will shake off the excess energy in the form of a gamma ray. i.e. a very high energy photon. In this context, $\gamma$ emission can be interpreted in a way similar to the spectral emissions from the atomic electrons: the same way that an atomic electron jumps from an outer to an inner shell, by emitting a photon to account for the energy balance, so we can think of the neutrons and protons within the nucleus to belong to "nuclear shells", and to perform quantum jumps from one shell to another. The main difference is that the energy differences among nuclear shells are of the order of hundreds of thousands or even millions of electron-Volts, rather than a few or a few tens.

$\gamma$ decay is often the aftermath of a previously occurred $\alpha$ or $\beta$ decay : the decay might leave the nucleus in an excited state (in terms of the allowed nuclear shells) and $\gamma$ decay intervenes to fall back into the lowest energy configuration.

In summary :

• $\alpha$ radioactivity = emission of a Helium nucleus
• $\beta$ radioactivity = emission of an electron
• $\gamma$ radioactivity = emission of electromagnetic radiation of very high energy (=very high frequency)
  
  

Radioactivity is not a new "invention". Radioactive substances do exist in nature, in fact most elements present in nature contain a small fraction of some unstable isotope, and any living organism is subjected to a certain amount of irradiation from these sources. In addition, another source of radiation is represented by cosmic rays, high energy particles, mostly protons, that can then generate other particles when they undergo hard collisions with the atmospheric molecules. The average flux due to cosmic rays at sea level is about 1 particle/minute/cm², and this flux increases with altitude (the atmosphere is a good protective shield against cosmic rays): airline crews receive larger than average dosages of radiation, and astronauts can receive a rather hefty amount during any space mission.

Radiation doses absorbed by the human body are measured in sieverts, Sv (not "seiverts"). Average annual doses for the US population are:

Source dose in mSv

Cosmic rays 0.3

Natural radioactivity 0.3

Own body radioactivity 0.4

Inhaled Radon ? 2.0 ?

Nuclear Power stations 0.0005

Consumer Products 0.1

Diagnostic x-rays 0.4

Nuclear medicine 0.1

Total 3.6 Maximum permissible

for radiation workers 50

What is a safe level of radiation ? It is hard to say, since it is a statistical process. We know for sure what are dangerous levels of radiation, but we can never be sure that a small amount has no effect whatsoever. But we can talk in terms of probabilities and state, for instance, that the probability of being severely affected by some low amount of radiation is less than that of being involved in a fatal accident while driving to work....

QUESTION : in which of the following fields some aspect of radioactivity has not been employed ?

A Weapons Production

B Energy Generation

C Medical Field

D Food Industry

E Archeology

F Applications exist in all the above fields

Lifes and Families

We have seen how the nucleus of an unstable isotope will eventually undergo some sort of decay. The question is : how long will it take for it to decay ? We cannot answer for sure, we can only say that a given nucleus has a certain probability of decaying in a given time interval, and this probability is the same for all the nuclei with the same combinations of protons and neutrons. Different isotopes will have different decay probabilities : an isotope corresponding to a very unstable configuration will have a high decay probability, while a more stable one will have a lower probability. If we monitor two identical samples of the two isotopes over a given time interval, we will observe many more decays of the former than the latter.

The standard way to quantify the decay probability of a given isotope is the half-life, defined as the time after which, in the average, one half of the nuclei contained in an initial sample have decayed. Note that, as it should be for it to be meaningful, the half-life does not depend on how much material is in the original sample : if I start with 10¹⁰ nuclei, after one half-life approximately 0.5 x 10¹⁰ will have decayed, if I start with 100 nuclei, after one half-life approximately 50 will have decayed.

Of all the radioactive isotopes found in nature, the longest lived is probably Uranium-238, with a half-life of 4.5 x 10⁹ years !!! This figure also corresponds to the estimated age of the Earth, so we can assume that the Earth still contains roughly half of its original supply of Uranium.

When decaying, U-238 starts a long sequential chain of decays, giving birth to the various generation forming the Uranium family. Such decay chains explain why we can find in nature relatively short lived isotopes, since they are continuously created as Uranium goes through its slow decay process.

Apart from the natural decay chains, nowadays unstable isotopes can also be produced by artificial nuclear bombardment in the laboratory. Nuclear Physicists have acquired a large wealth of know-how on how to produce given isotopes of the appropriate half-life for most elements, to be utilized in medicine, material science, etc.