A radioactive sample decays <math><mrow><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mrow></math> times its original quantity in 15 minutes. The half-life of the sample is

N0→t=15min (N0−78N0)=N08So, N=N02t/t1/2⇒N08=N02t/t1/2⇒23=2 (15minT)⇒T=15min3=5min

A radioactive sample decays&nbsp;<math><mrow><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mrow></math>&nbsp;times its original quantity in 15 minutes. The half-life of the sample is

7.5 min

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Physics Class 12th Nuclei Physics NCERT Exemplar Solutions Class 12th Chapter Thirteen

A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is

Option 1 -

5 min

Option 2 -

7.5 min

Option 3 -

15 min

Option 4 -

30 min

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 months ago

Correct Option - 1

Detailed Solution:

$N_{0} \to_{}^{t = 15 m i n} (N_{0} - \frac{7}{8} N_{0}) = \frac{N_{0}}{8}$

So, $N = \frac{N_{0}}{2^{t / t_{1 / 2}}} \Rightarrow \frac{N_{0}}{8} = \frac{N_{0}}{2^{t / t_{1 / 2}}}$

$\Rightarrow 2^{3} = 2^{(\frac{15 m i n}{T})}$

$\Rightarrow T = \frac{15 m i n}{3} = 5 m i n$

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A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is