Question

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

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

Answer 1

The correct option is C $\frac{3}{4}$

Given, $t=8\text{days}$; $T_{1/2}=4\text{days}$

Number of half-days life,

$n=\frac{t}{T_{1/2}}=\frac{8}{4}=2$

Remaining atom :

$N=\frac{N_0}{2^n}=\frac{N_0}{2^2}=\frac{N_0}{4}$

Number of decayed atoms $=N_0-N$
$=N_0-\frac{N_0}{4}=\frac{3N_0}{4}$

Probability of decay,

$\frac{N_0-N}{N_0}=\frac{\left(\frac{3N_0}{4}\right)}{N_0}=\frac{3}{4}$

Hence, $\left(C\right)$ is the correct answer.