JEE Main 2021PhysicsNuclear PhysicsMediumMCQ

JEE Main 2021 — Nuclear Physics Question with Solution

JEE Main 2021 (20 Jul Shift 1)

Question

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years, respectively. What will be the time after the which one third of the material remains ? (Take ln3=1.1)

Choose an option

Show full solutionCorrect option: D
Correct answer
D740 years

Step-by-step explanation

 

Given λ1=ℓn2700/year λ2=ℓn21400/year
∴λnet =λ1+λ2=ln21700+11400
=3ln21400/year
Now, let initial number of radioactive nuclei be
N0, 
∴N03=N0e-λmatt

⇒ℓn13=-λnett
⇒1.1=3×0.6931400t⇒t≈740 years
Hence, option 4.

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About this question

This is a previous-year question from JEE Main 2021, 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.