Activity of a radioactive sample falls from 700 mathrm{s}^{-1} to 500 mathrm{s}^{-1} in 30min . Its

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13.Nuclei

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The activity of a radioactive sample falls from $700 \;\mathrm{s}^{-1}$ to $500\; \mathrm{s}^{-1}$ in $30\;min$. Its half life is close to.........$min$

A

$66$

B

$52$

C

$72$

D

$62$

(JEE MAIN-2020)

Solution

$A=A_{0}\left(\frac{1}{2}\right) \frac{t}{T_{1 / 2}}$

$500=700\left(\frac{1}{2}\right) \frac{t}{T_{1 / 2}}$

$0.7 \approx\left(\frac{1}{2}\right) \frac{t}{T_{1 / 2}}$

$\left(\frac{1}{2}\right)^{1 / 2} \approx \frac{t}{T_{1 / 2}}$

$\frac{30}{\mathrm{T}_{1 / 2}} \approx \frac{1}{2} \Rightarrow \mathrm{T}_{1 / 2}=60$

Standard 12

Physics

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