JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Modern Physics

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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 and B are decay constants of A and B respectively, then choose the correct relation from the given options.

(A) $λ_{A} = λ_{B}$
(B) $λ_{A} = 2 λ_{B}$
(C) $λ_{A} = λ_{B} ln 2$ ✓ Correct
(D) $λ_{A} ln 2 = λ_{B}$

Answer: (C)

Solution

The half-life is

T_{1/2} = \frac{ln 2}{λ}

and the average life is

τ = \frac{1}{λ}

. Setting the half-life of A equal to the average life of B gives

\frac{ln 2}{λ _{A}} = \frac{1}{λ _{B}}

. Rearranging,

λ_{A} = λ_{B} ln 2

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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