JEE Main 2014PhysicsNuclear PhysicsMediumMCQ

JEE Main 2014 — Nuclear Physics Question with Solution

JEE Main 2014 (19 Apr Online)

Question

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If the half-life of C14 is 5730 years, then the age of the wooden piece placed in the museum is approximately
[This question was awarded a bonus and proper correction was made to avoid that]

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Show full solutionCorrect option: C
Correct answer
C19042 years

Step-by-step explanation

We know that,

The rate of decay at the time t is

A=A0e-λt

2=20·e-λt

∴ 110=e-λt

∴ eλt=10

⇒lneλt=ln10

⇒λt=ln10

∵ λ=ln2T1/2

t=ln10ln2T1/2

∵ ln10=2.303 and ln2=0.693

t=2.3030.693×5730

=3.32×5730

≈19042 years

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About this question

This is a previous-year question from JEE Main 2014, 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.