Chapter 24, Problem 43A

Interpretation Introduction

Interpretation:

The difference between positron emission and electron capture needs to be explained.

Concept introduction:

Positron emission and electron capture are two common radioactive decays that occur in nuclei with low neutron-to-proton ratios. These two processes lead to an increase in the neutron-to-proton ratio of the neutron deficient atom, taking the atom closer to, if not within, the band of stability.

Answer to Problem 43A

Difference between positron emission and electron capture is as follows:

Positron emission	Electron capture
1. In positron emission a proton is transferred into a neutron within a nucleus.	1. In electron capture an atom consumes an electron from the inner shell and converts a proton into a neutron.
2. Emits a positron along with an electron neutrino.	2. Emits an electron neutrino and gamma radiation.

Explanation of Solution

Positron emission is a method of radioactive decay, including the emission of a positron from a nucleus. A positron is a particle having same mass with an electron but charge is opposite; it is denoted by symbol $\text{β}$ or ${\text{e}}^{+}$. A proton in the nucleus is transferred to a neutron and a positron during positron emission and the positron is then released.

$\text{p}\to \text{n}+{\text{e}}^{+}$

Electron capture is the other common radioactive-decay process that reduces the number of protons in unstable nuclei extending below the band of stability. Electron capture happens when the nucleus of an atom moves in an encompassing electron, usually one from the lowest energy level. This gained electron combines with a proton to produce a neutron.

$\text{p}\text{+}{\text{e}}^{-}\to \text{n}$

Conclusion

In positron emission, a proton decay to produce a neutron and a positron, while in an electron capture process, an electron is absorbed by a proton rich nucleus atom and proton changes to neutron.