(A) The radioactive decay law is given by $N(t) = N_0(1/2)^n$, where $n = t/T_{1/2}$ is the number of half-lives.Given that $(7/8)$ of the sample deca

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(A) The radioactive decay law is given by $N(t) = N_0(1/2)^n$, where $n = t/T_{1/2}$ is the number of half-lives.Given that $(7/8)$ of the sample decays, the remaining amount $N(t)$ is $N_0 - (7/8)N_0 = (1/8)N_0$.Substituting this into the decay formula: $(1/8)N_0 = N_0(1/2)^n$.$(1/2)^3 = (1/2)^n$, which implies $n = 3$.Since $n = t/T_{1/2}$, we have $3 = t / 15 \text{ hr}$.Therefore, $t = 3 \times 15 \text{ hr} = 45 \text{ hr}$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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The half-life of the isotope $^{11}Na^{24}$ is $15 \text{ hr}$. How much time does it take for $(7/8)$ of a sample of this isotope to decay (in $\text{ hour}$)?

MHT CET 2026 All MHT CET

A
$45$
B
$60$
C
$75$
D
$90$

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Nuclei

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Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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The half-life of the isotope $^{11}Na^{24}$ is $15 \text{ hr}$. How much time does it take for $(7/8)$ of a sample of this isotope to decay (in $\text{ hour}$)?

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