(B) The law of radioactive decay is given by $N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$.Given:Initial number of nuclei,$N_0 = 10^{10}$.Hal

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(B) The law of radioactive decay is given by $N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$.Given:Initial number of nuclei,$N_0 = 10^{10}$.Half-life,$T_{1/2} = 1 \text{ minute} = 60 \text{ seconds}$.Time elapsed,$t = 30 \text{ seconds}$.Substituting the values:$N = 10^{10} \times \left(\frac{1}{2}\right)^{\frac{30}{60}}$$N = 10^{10} \times \left(\frac{1}{2}\right)^{1/2}$$N = \frac{10^{10}}{\sqrt{2}}$Using $\sqrt{2} \approx 1.414$:$N = \frac{10^{10}}{1.414} \approx 7.07 \times 10^9 \approx 7 \times 10^9$.

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

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There are $10^{10}$ radioactive nuclei in a given radioactive element. Its half-life time is $1 \text{ minute}$. How many nuclei will remain after $30 \text{ seconds}$? $(\sqrt{2} = 1.414)$

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A
$2 \times 10^{10}$
B
$7 \times 10^{9}$
C
$10^{5}$
D
$4 \times 10^{10}$

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

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There are $10^{10}$ radioactive nuclei in a given radioactive element. Its half-life time is $1 \text{ minute}$. How many nuclei will remain after $30 \text{ seconds}$? $(\sqrt{2} = 1.414)$

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