Question

A certain radioactive substance has a half life of $5$ years. For a nucleus in a sample of the element, the probability of decay in ten years is

• A. $50\%$
• B. $75\%$
• C. $100\%$
• D. $60\%$

Answer 1

Answer: (B)

Number of half lives, $n=\frac{10}{5}=2$
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$
$\Rightarrow N=\frac{1}{4}{N}_0$
Amount decayed $=N_0-N$
$=N_0-\frac{1}{4}{N}_0=\frac{3}{4}{N}_0$
Hence, the probability of decay in ten years is $75\%$.