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Law of Radioactivity

A radioactive...

Question

A radioactive sample decays by two different processes. Half-life of first process is $t_{1}$ , and for second process is $t_{2}$ . Then, the effective half-life is

t_{1} - t_{2}

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t_{1} + t_{2}

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\frac{t_{1} t_{2}}{t_{1} + t_{2}}

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\frac{t_{1}^{2} t_{2}^{2}}{t_{1} - t_{2}}

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Solution

The correct option is B $\frac{t_{1} t_{2}}{t_{1} + t_{2}}$
Given, $λ = λ_{1} + λ_{2}$
$\frac{1}{t} = \frac{1}{t_{1}} + \frac{1}{t_{2}} = \frac{t_{2} + t_{1}}{t_{1} t_{2}}$
$\Rightarrow t = \frac{t_{1} t_{2}}{t_{1} + t_{2}}$

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