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13.Nuclei
medium
The mean life of a radioactive material for alpha decay and beta decay are, respectively, $1620$ years and $520$ years. What is the half life of the sample (in years) ?
A
$1483$
B
$394$
C
$273$
D
$1123$
Solution
There exists two channels for the decay. Therefore the mean life is obtained from
$\frac{1}{\tau}=\frac{1}{\tau_{1}}+\frac{1}{\tau_{2}}$
or $\quad \tau=\frac{\tau_{1} \tau_{2}}{\tau_{1}+\tau_{2}}$
$\frac{1620 \times 520}{1620+520}=394 \mathrm{\,y}$
The half life ${\rm{T}} = 0.693\,\tau $
$=0.693 \times 394 $
$=273 $
Standard 12
Physics
