JEE Advanced 2021 Paper 1 Q04 Physics Modern Physics Radioactivity Medium

JEE Advanced 2021 Paper 1 · Q04 · Radioactivity

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

  1. A. 50
  2. B. 75
  3. C. 350
  4. D. 525
Reveal answer + step-by-step solution

Correct answer:D

Solution

In 60 minutes, the nucleus undergoes 60/20 = 3 half-lives. Remaining nuclei = 1000 × (1/2)³ = 125. Total decays in 1 hour = 1000 − 125 = 875. Since alpha-decay branching ratio = 0.60, number of alpha-decays = 875 × 0.6 = 525.

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