Half lives for α and β emission of a radioactive material are 16 years and 48 years respectively.

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13.Nuclei

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Half lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When material decays giving $\alpha$ and $\beta$ emission simultaneously then time in which $\frac{3}{4}$ th of the material decays is ....... years

A

$29$

B

$24$

C

$64$

D

$12$

(AIIMS-2017)

Solution

(b)

$1$ material is giving two products

Let initial number be $=N_0$

Let time when $\frac{3}{4} N_0$ decay be $t$

Effective half life $=\frac{T_1 T_2}{T_1+T_2}=12$ years

$\frac{N}{N_0}=\left(\frac{1}{2}\right)^n$

$\frac{1}{4}=\left(\frac{1}{2}\right)^n \quad n=2$

Hence, time will be $24$ years

Standard 12

Physics

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