JEE Main 2023PhysicsNuclear PhysicsMediumNumerical

JEE Main 2023 — Nuclear Physics Question with Solution

JEE Main 2023 (30 Jan Shift 2)

Question

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be α11 s. The value of α is ______.

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Show full solutionCorrect answer: 300
Correct answer
300

Step-by-step explanation

Decay law for both process can be written as,

dN1dt=-λ1N   ...Eq(1) and

dN2dt=-λ2N   ...Eq(2)

Hence, net decay will become

dNdt=dN1dt+dN2dt=-(λ1+λ2)N

⇒λeq=λ1+λ2

⇒ln2t12=ln2300+ln230

⇒t12=30011

Hence, required value of α=300.

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About this question

This is a previous-year question from JEE Main 2023, covering the Nuclear Physics chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.