A radioactive nucleus can decay by two different processes. The half-life for the first process is t1 and that for the second process is t2. The effective half-life of the nucleus is given by

-dN1dt=λ1N ; -dN2dt=λ2N ;-dN1dt+dN2dt=λ1N+λ2N∴λN=λ1+λ2N⇒0.693t=0.693t1+0.693t2⇒1t=1t1+1t2 ⇒t=t1t2t1+t2

A radioactive nucleus can decay by two different processes. The half-life for the first process is t1 and that for the second process is t2. The effective half-life of the nucleus is given by

-dN1dt=λ1N ; -dN2dt=λ2N ;-dN1dt+dN2dt=λ1N+λ2N∴λN=λ1+λ2N⇒0.693t=0.693t1+0.693t2⇒1t=1t1+1t2 ⇒t=t1t2t1+t2

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A radioactive nucleus can decay by two different processes. The half-life for the first process is t₁ and that for the second process is t₂. The effective half-life of the nucleus is given by

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$\frac{1}{t^{2}} = \frac{1}{t_{1}} + \frac{1}{t_{2}}$

$\frac{1}{t} = \frac{1}{t_{1}^{2}} + \frac{1}{t_{2}^{2}}$

$\frac{1}{t} = \frac{1}{t_{1}} + \frac{1}{t_{2}}$

$\frac{1}{t} = \frac{t_{1} t_{2}}{{(t_{1} + t_{2})}^{2}}$

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$- \frac{{dN}_{1}}{dt} = λ_{1} N; - \frac{{dN}_{2}}{dt} = λ_{2} N;$

$- (\frac{{dN}_{1}}{dt} + \frac{{dN}_{2}}{dt}) = (λ_{1} N + λ_{2} N)$

$∴ λN = (λ_{1} + λ_{2}) N$

$\Rightarrow \frac{0 .693}{t} = \frac{0 .693}{t_{1}} + \frac{0 .693}{t_{2}}$

$\Rightarrow \frac{1}{t} = \frac{1}{t_{1}} + \frac{1}{t_{2}} \Rightarrow t = \frac{t_{1} t_{2}}{t_{1} + t_{2}}$

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A radioactive nucleus can decay by two different processes. The half-life for the first process is t1 and that for the second process is t2. The effective half-life of the nucleus is given by

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A radioactive nucleus can decay by two different processes. The half-life for the first process is t₁ and that for the second process is t₂. The effective half-life of the nucleus is given by