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JEE Main 202125 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Evening Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2021 · 25 July · Evening Shift · Physics · Nuclear Physics

The nuclear activity of a radioactive element becomes ((1)/(8)) ^...

The nuclear activity of a radioactive element becomes (18)th{\left(\dfrac{1}{8}\right)}^{\text{th}} of its initial value in 3030 years. The half-life of radioactive element is ________ years.

Correct answer

0

Step-by-step solution

A=A0e−\lambdatA = {A}_{0}{e}^{- \lambdat}

A08=A0e−\lambdat⇒\lambdat=ln⁡8\dfrac{{A}_{0}}{8} = {A}_{0}{e}^{- \lambdat} ⇒ \lambdat = \ln 8

\lambdat=3ln⁡2\lambdat = 3\ln 2

ln⁡2λ=t3=303=10years\dfrac{\ln 2}{\lambda} = \dfrac{t}{3} = \dfrac{30}{3} = 10years

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