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JEE Main202118 Mar 2021Morning ShiftPhysicsNuclear PhysicsActual

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

Options

  1. AT 1 / 2 = T 1 / 2 ( 1 ) + T 1 / 2 ( 2 ) T 1 / 2 ( 1 ) - T 1 / 2 ( 2 )
  2. BT 1 / 2 = T 1 / 2 ( 1 ) + T 1 / 2 ( 2 )
  3. CT 1 / 2 = T 1 / 2 ( 1 ) T 1 / 2 ( 2 ) T 1 / 2 ( 1 ) + T 1 / 2 ( 2 )
  4. DNone of the above

Correct answer

C. T 1 / 2 = T 1 / 2 ( 1 ) T 1 / 2 ( 2 ) T 1 / 2 ( 1 ) + T 1 / 2 ( 2 )

Step-by-step solution

λ e q = λ 1 + λ 2 1   T 1 / 2 = 1   T 1 / 2 ( 1 ) + 1   T 1 / 2 ( 2 ) T 1 / 2 = T 1 / 2 ( 1 ) T 1 / 2 ( 2 ) T 1 / 2 ( 1 ) + T 1 / 2 ( 2 )

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