Skip to main content
Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

A heavy nucleus Q of half-life 20 minutes ...

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

(A) 50          (B) 75          (C) 350          (D) 525

Solution

If $N_0$ be the initial number of nuclei and N the number after n half-lives, then

$\frac {N}{N_0}=(\frac {1}{2})^n$

Here, $\frac {N}{1000}=(\frac {1}{2})^3$

$\therefore N = 125$

Total number of decays = 1000 - 125 = 875

Total number of alpha-decays = 60% of 875 = 525

Hence, Option (D).