Question

${}_{87}^{221}Ra$ is a radioactive substance having half-life of $4$ days. Find the probability that a nucleus undergoes decay after two half-lives

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

Answer 1

Answer: (C)

$\frac{3}{4}$

Given: $t_{1/2}=4days,t=2\times 4=8days$

Hence, $\lambda =0.693/t_{1/2}=0.693/4$

The probability that a nucleus undergoes after 2 half lives:

$P=1-e^{-\lambda t}$

$P=1-e^{-0.693\times 8/4}=1-e^{-1.386}$

$P=1-0.25=0.75=3/4$