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JEE Main 202118 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Morning Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2021 · 18 March · Morning Shift · Physics · Nuclear Physics

A radioactive sample disintegrates via two independent decay...

A radioactive sample disintegrates via two independent decay processes having half lives T1/2(1){T}_{1/2}^{( 1 )} and T1/2(2){T}_{1/2}^{( 2 )} respectively. The effective half- life T1/2{T}_{1/2} of the nuclei is :

Options

  1. AT1/2=T1/2(1)+T1/2(2)T1/2(1)−T1/2(2){T}_{1/2} = \dfrac{{T}_{1/2}^{( 1 )} + {T}_{1/2}^{( 2 )}}{{T}_{1/2}^{( 1 )} - {T}_{1/2}^{( 2 )}}
  2. BT1/2=T1/2(1)+T1/2(2){T}_{1/2} = {T}_{1/2}^{( 1 )} + {T}_{1/2}^{( 2 )}
  3. CT1/2=T1/2(1)T1/2(2)T1/2(1)+T1/2(2){T}_{1/2} = \dfrac{{T}_{1/2}^{( 1 )}{T}_{1/2}^{( 2 )}}{{T}_{1/2}^{( 1 )} + {T}_{1/2}^{( 2 )}}
  4. DNone of the above

Correct answer

C. T1/2=T1/2(1)T1/2(2)T1/2(1)+T1/2(2){T}_{1/2} = \dfrac{{T}_{1/2}^{( 1 )}{T}_{1/2}^{( 2 )}}{{T}_{1/2}^{( 1 )} + {T}_{1/2}^{( 2 )}}

Step-by-step solution

λeq=λ1+λ2{\lambda}_{eq} = {\lambda}_{1} + {\lambda}_{2}
1T1/2=1T1/2(1)+1T1/2(2)\dfrac{1}{{T}_{1/2}} = 1{T}_{1/2}^{( 1 )} + 1{T}_{1/2}^{( 2 )}
T1/2=T1/2(1)T1/2(2)T1/2(1)+T1/2(2){T}_{1/2} = \dfrac{{T}_{1/2}^{( 1 )}{T}_{1/2}^{( 2 )}}{{T}_{1/2}^{( 1 )} + {T}_{1/2}^{( 2 )}}
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