Question

${}_{87}^{221}\text{Ra}$ undergoes radioactive decay with $t_{1/2}$ = $4$ $days$. What is the probability that a nucleus undergoes a decay in two half lives(8 days)?

• A. $1$
• B. $1/2$
• C. $3/4$
• D. $1/4$

Answer 1

The correct option is C $3/4$

Consider $N_0$ nuclei of the substance. After two half lives, the number of nuclei left are:
$N=\frac{N_0}{2^2}=\frac{N_0}{4}$
This implies that $N_0-\frac{N_0}{4}=\frac{3}{4}{N}_0$ nuclei underwent disintegration.
Hence probability that a random nuclei chosen would have disintegrated is $\frac{\frac{3}{4}{N}_0}{N_0}=\frac{3}{4}$