Physics GRE - #28

lalalala test element $^A_ZX$ decays by natural radioactivity in two stages to $^{A-4}_{Z-1}Y$. The two stages would most likely be which of the following?

	First stage	Second stage
1.	$\beta^-$ emission with an antineutrino	$\alpha$ emission
2.	$\beta^-$ emission	$\alpha$ emission with a neutrino
3.	$\beta^-$ emission	$\gamma$ emission
4.	Emission of a deuteron	Emission of two neutrons
5.	$\alpha$ emission	$\gamma$ emission

Solution :

Choice 1 is the answer.

For choice 1, we have \[^A_ZX\rightarrow ^A_{Z+1}X+e^-+\bar{v}_e\] for the $\beta^-$ emission, and then \[^A_{Z+1}X \rightarrow ^{A-4}_{Z-1}Y+^4_2\text{He}\] for the $\alpha$ emission. Everything works out, charge/lepton/baryon numbers are conserved as they should be.

For choice 2, lepton number is not conserved as the $\beta^-$ emission does not occur with an antineutrino.

For choice 3, the atomic number remains unchanged under both emissions.

For choice 4, the emissions specified are extremely rare. In other words, this type of emission is impossible for the 'natural radioactivity' specified in the question.

For choice 5, the atomic numbers do not match up (there are fewer protons than needed with this decay path).