Question

Tritium has a half life of 12.5 years undergoing beta decay. What fraction of sample of pure tritium will decay in 50 years?

• A. $\frac{3}{4}$
• B. $\frac{15}{16}$
• C. $\frac{63}{64}$
• D. $\frac{7}{8}$

Answer 1

The correct option is B $\frac{15}{16}$

$t_{\frac{1}{2}}=12.5yearst=4t_{\frac{1}{2}}=4\times 12.5=50years$
let initial nucleus be $N_o$ $\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{2}\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{4}\stackrel{t_{\frac{1}{2}}}{\to }\frac{N_0}{8}$
$\downarrow t_{\frac{1}{2}}$
$\frac{N_0}{16}$
$\Rightarrow$ remaining $\frac{N_0}{16}$
decayed $\frac{15N_0}{16}$