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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2016 · 3 April · Physics · Nuclear Physics

Half-lives of two radioactive elements A and B are 20minutes and...

Half-lives of two radioactive elements AA and BB are 20minutes20minutes and 40minutes40minutes, respectively. Initially, the samples have an equal number of nuclei. After 80minutes80minutes, the ratio of decayed numbers of AA and BB nuclei will be:

Options

  1. A1:41: 4
  2. B5:45: 4
  3. C1:161: 16
  4. D4:14: 1

Correct answer

B. 5:45: 4

Step-by-step solution

t=80min=4TA=2TBt = 80min = 4{T}_{A} = 2{T}_{B}

no. of nuclei of A decayed =N0−N024=15N016= {N}_{0} - \dfrac{{N}_{0}}{{2}^{4}} = \dfrac{15{N}_{0}}{16}

no. of nuclei of B decayed =N0−N022=3N04= {N}_{0} - \dfrac{{N}_{0}}{{2}^{2}} = \dfrac{3{N}_{0}}{4}

required ratio =54= \dfrac{5}{4}
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