18.4.2 Beta Decay

A beta particle is basically a very energetic electron. A beta decay is represented by the equation

$\displaystyle {}_{Z}^{A}X\to {}_{{Z+1}}^{A}Y+{}_{{-1}}^{0}e$

If you compare the A and the Z numbers of the parent and daughter nuclei carefully, you will realize that the nucleus has lost one neutron, gained one proton and thrown out one electron. What the heck happened? Well, a neutron has decided to split itself into a proton and an electron. The electron is ejected at high speed (as the beta particle), while the proton stays behind in the nucleus.

Why Beta-Decay has an Energy Spectrum

Let’s use the beta-decay of bismuth-210 as an example. After one of its neutrons has changed into a proton, bismuth transmuted into polonium.

$\displaystyle {}_{{83}}^{{210}}Bi\to {}_{{84}}^{{210}}Po+{}_{{-1}}^{0}e$

The total mass of a polonium-210 and an electron is smaller than the mass of a bismuth-210. From the mass difference, the total energy released can be calculated to be a 1.16 MeV.

If Po-210 and the beta particle are the only two product nuclei, then they must have equal but opposite momentum (as dictated by PCOM). This translates to a fixed KE ratio between them which is equal to the inverse of their mass-ratio. Since Po-210 is almost 400,000 times as massive as the electron, we would expect the daughter nucleus to show negligible recoil and carry negligible KE. This means that all the beta particles should have KE of 1.16 MeV.

However, it was observed that the beta particles produced by bismuth-210 have a continuous energy spectrum (unlike alpha radiation, which are mono-energetic). Furthermore, the recoil of the polonium-210 nucleus is not always in opposite direction to the beta particle.

OMG, what happened to the principles of conservation of energy and momentum? Physicists were so stumped that Niels Bohr actually believed that the time had come for us to dump these most fundamental conservation laws.

In 1931, Wolfgang Pauli suggested humorously that there was probably an as yet unobserved particle emitted during a beta decay. He gave this particle a very cute sounding name, neutrino, which means the little neutral one. Having no charge and almost negligible mass, the neutrino is practically undetectable. However, having this “imagined” particle to carry some of the “missing” energy and momentum does provide an answer to the beta decay conundrum and a lifeline for PCOM and PCOE.

So the beta process was updated to include the emission of a neutrino.

Beta-minus decay: $\displaystyle {}_{Z}^{A}X\to {}_{{Z+1}}^{A}Y+{}_{{-1}}^{0}e+\bar{\upsilon }$

The symbol $\displaystyle \bar{\upsilon }$ denotes an anti-neutrino. They had to do this because they have given the neutrino to the positive beta decay.

Beta-positive decay: $\displaystyle {}_{Z}^{A}X\to {}_{{Z-1}}^{A}Y+{}_{1}^{0}e+\upsilon$

The symbol $\displaystyle \upsilon$ denotes a neutrino, and $\displaystyle {}_{1}^{0}e$ is a positron.

The beta-decay in the H2 syllabus refers to the negative beta decay only. You are also not required to know anything about the neutrino, other than the context in which its existence was predicted. By the way, the elusive neutrino evaded experimental detection until 1956, a remarkable 26 years after its “discovery”.

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Concept Test

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Beta Boy