CBSE Class 12 Physics 2019 Delhi Set 2 Paper

Question : 6 of 6

Marks: +1, -0

(a) Write the relation between half life and average life of a radioactive nucleus.
(b) In a given sample two isotopes,

{A}

and B are initially present in the ratio of

1: 2

. Their half lives are 60 years and 30 years respectively. How long will it take so that the sample has these isotopes in the ratio of

2: 1

Solution:

(a) Relation between average life and half life
(b) Finding the required time
(a)

T=\;{1}/{λ}

Alternatively

(\;{T_{1 \/ 2}}/{\ln 2}) \/ (\;{T_{1 \/ 2}}/{0.6931}) \/ 1.44 T_{1 \/ 2}

(b) We have

N=N_0 e^{-λ . t}

\;\;{N_{0_1}}/{N_{0_2}}=\;{1}/{2}, \;{N_1}/{N_2}=\;{2}/{1}

\; ∴ \;{N_1}/{N_2}=\;{N_{0_1}}/{N_{0_2}} \exp (- (λ_1-λ_2) t)

\; ∴ \;\; 2=\;{1}/{2} \exp (- (λ_1-λ_2) t)

\;⇒ \;\; \exp (- (λ_1-λ_2) t) =4

\;⇒ \;\; - (λ_1-λ_2) t=2 \ln 2

\;⇒-\ln 2 (\;{1}/{60}-\;{1}/{30}) t=2

\;⇒ \;\; \;{t}/{60}=2

\;⇒ \;\; t=120 \;\text " years "\;

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