is a radioactive substance having a half-life of 4 days. Find the probability that a nucleus undergoes decay after two half-lives. [2006]

Question

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

Smart Achievers · Accepted Answer

(3)

For a nucleus to disintegrate in two half lives, $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$ i.e., The probability is $\frac{3}{4}$ as 75% of the nuclei will disintegrate in this time.

Solution

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

1 $1$

2 $\frac{1}{2}$

3 $\frac{3}{4}$

4 $\frac{1}{4}$

Ans.
(3)

For a nucleus to disintegrate in two half lives, $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$ i.e., The probability is $\frac{3}{4}$ as 75% of the nuclei will disintegrate in this time.

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Solution

Q. Ra87221 is a radioactive substance having a half-life of 4 days. Find the probability that a nucleus undergoes decay after two half-lives. [2006]

1 1

2 12

3 34

4 14

Ans. (3) For a nucleus to disintegrate in two half lives, 12+14=34 i.e., The probability is 34 as 75% of the nuclei will disintegrate in this time.