Question

${}_{87}^{221}Ra$ undergoes radioactive decay with a half-life of $4$ days. The probability that a $Ra$ nucleus will disintegrate in $8$ days is

• A. $\frac{1}{2}$
• B. $\frac{3}{8}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

Number of half-lives $n=\frac{8}{4}=2$
As, $N=\frac{N_0}{2^n}=\frac{N_0}{2^2}=\frac{N_0}{4}$
Thus, remaining atom $N=\frac{N_0}{4}$
Decayed atoms $=N_0-N=N_0-\frac{N_0}{4}=\frac{3}{4}{N}_0$
$\therefore$ Probability of decay $=\frac{N_0-N}{N_0}=\frac{\frac{3}{4}{N}_0}{N_0}=\frac{3}{4}$.