Verified Solution • 2025–26 Session moderate

QJEEAdv21Ph36cd: JEE Advanced 2021 Physics - Class 12 JEEAdv21Ph36cd Solution: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay …

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

Multiple Choice Options

  • A 50
  • B 75
  • C 350
  • D 525

Step-by-Step Verified Solution

Out of 1000 nuclei of Q, 60% may go α\alpha -decay

⇒\Rightarrow 600 nuclei may have α\alpha -decay

λ=ln⁡2t1/2=ln⁡220\lambda = {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over {20}}

t = 1 h = 60 min

Using,

N=N0e−λt=600×e−ln⁡220×60N = {N_0}{e^{ - \lambda t}} = 600 \times {e^{ - {{\ln 2} \over {20}} \times 60}}

N = 75

⇒\Rightarrow 75 nuclei are left after one hour

So, number of nuclei decayed = 600 −- 75 = 525

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