Question

${}_{87}{Ra}^{221}$ is a radioactive substance having half life of 4 days. Find the probability that a nucleus undergoes decay after two half lives
[IIT-JEE-2006]

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

Answer 1

The correct option is D $\frac{1}{4}$

Ok, the probability that a nucleus undergoes decay after two half lives = $\frac{No.ofnucleiremaining.}{totalnumberofnuclei}$

Now, after one half life, half the nuclei are remaining, after another one half life only half of that is remaining.

That is, $\frac{1}{4}th$ Nuclei, are remaining.
$\therefore Probability=\frac{\frac{1}{4}{N}_0}{N_0}=\frac{1}{4}.$