Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B . If λ _ A and λ _ B are decay constants of A and B respectively, then choose the correct

Correct answer: C. λ _ A = λ _ B 2 It is given that T(1)/(2) ( A ) = T _ av ( B ) The half life of a substance is given by T(1)/(2) = ( 2)/(λ) So, 2 λ _ A = 1 λ _ B ⇒ λ _ A = λ _ B 2

JEE Main 202311 AprilMorning Shift

Exam: JEE Main
Year: 2023
Date: 11 April
Shift: Morning Shift
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2023 · 11 April · Morning Shift · Physics · Nuclear Physics

Two radioactive elements A and B initially have same number of...

Two radioactive elements

A

and

B

initially have same number of atoms. The half life of

A

is same as the average life of

B

. If

{\lambda}_{A}

and

{\lambda}_{B}

are decay constants of

A

and

B

respectively, then choose the correct relation from the given options.

Options

A ${\lambda}_{A}\ln 2 = {\lambda}_{B}$
B ${\lambda}_{A} = {\lambda}_{B}$
C ${\lambda}_{A} = {\lambda}_{B}\ln 2$
D ${\lambda}_{A} = 2{\lambda}_{B}$

Correct answer

C. ${\lambda}_{A} = {\lambda}_{B}\ln 2$

Step-by-step solution

It is given that

$T\dfrac{1}{2} ( A ) = {T}_{av} ( B )$

The half life of a substance is given by $T\dfrac{1}{2} = \dfrac{\ln 2}{\lambda}$

So,

$\dfrac{\ln 2}{{\lambda}_{A}} = \dfrac{1}{{\lambda}_{B}}$

$⇒ {\lambda}_{A} = {\lambda}_{B}\ln 2$

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