Physics Problems & Solutions: Nuclear & Particle Physics

A sample of radioactive nuclei of a certain element can decay only by $\gamma$ -emission and $\beta$ -emission. If the half-life for $\gamma$ -emission is 24 minutes and that for $\beta$ -emission is 36 minutes, the half-life for sample is

A. 30 minutes
B. 24 minutes
C. 20.8 minutes
D. 14.4 minutes
E. 6 minutes

(GR0177 #66)

Solution:

Total half-time for 2 or more processes:

$\frac{1}{T}=\frac{1}{t_1} +\frac{1}{t_2} +...$

For the sample with $\gamma$ and $\beta$ emissions:

$\\\frac{1}{T}=\frac{1}{24}+\frac{1}{36}=\frac{36+24}{24\times 36}=\frac{60}{864}\rightarrow T=14.4$

Answer: D

Physics Problems & Solutions

Nuclear & Particle Physics - Radioactive

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