(C) The decay constant $\lambda$ is given by the formula: $\lambda = \frac{2.303}{t} \log \left( \frac{N_0}{N} \right)$.Given $t = 2.303 \ s$ and $\fr

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(C) The decay constant $\lambda$ is given by the formula: $\lambda = \frac{2.303}{t} \log \left( \frac{N_0}{N} \right)$.Given $t = 2.303 \ s$ and $\frac{N}{N_0} = \frac{1}{10}$,so $\frac{N_0}{N} = 10$.Substituting the values: $\lambda = \frac{2.303}{2.303} \log(10) = 1 \times 1 = 1 \ s^{-1}$.The half-life period $t_{1/2}$ is given by: $t_{1/2} = \frac{0.693}{\lambda}$.Therefore,$t_{1/2} = \frac{0.693}{1} = 0.693 \ s$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

Medium

The radioactivity of a radioactive element becomes $\frac{1}{10}$ of the original radioactivity after $2.303 \ s$. The half-life period is: (in $s$)

A
$2.303$
B
$0.2303$
C
$0.693$
D
$0.0693$

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Rate of decay and Half-life

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The radioactivity of a radioactive element becomes $\frac{1}{10}$ of the original radioactivity after $2.303 \ s$. The half-life period is: (in $s$)

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$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

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