Question

Half lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When material decays giving $\alpha$ and $\beta$ emission simultaneously, time in which $3/4^{th}$ material decays is

• A. $29$ years
• B. $24$ years
• C. $64$ years
• D. $12$ years

Answer 1

Answer: (B)

$24$ years

Effective half life is calculated as:
$\frac{1}{T}=\frac{1}{T_1}+\frac{1}{T_2}$
$\frac{1}{T}=\frac{1}{16}+\frac{1}{48}\Rightarrow T=12years$
Time in which $\frac{3}{4}$ will decay is 2 half lives $=24$ years