A radioactive nucleus can decay by two differ | vedclass

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Question

$\lambda_{	ext {eq }}=\lambda_{1}+\lambda_{2}$

$\frac{\ln 2}{\left( t _{1 / 2}ight)_{ eq }}=\frac{\ln 2}{\left( t _{1 / 2}ight)_{1}}+\frac{\ln

Vedclass · Accepted Answer

$1.80$

Vedclass · Answer

$\lambda_{	ext {eq }}=\lambda_{1}+\lambda_{2}$

$\frac{\ln 2}{\left( t _{1 / 2}ight)_{ eq }}=\frac{\ln 2}{\left( t _{1 / 2}ight)_{1}}+\frac{\ln 2}{\left( t _{1 / 2}ight)_{2}}$

$\left( t _{1 / 2}ight)_{ eq }=\frac{\left( t _{1 / 2}ight)_{1} 	imes\left( t _{1 / 2}ight)_{2}}{\left( t _{1 / 2}ight)_{1}+\left( t _{1 / 2}ight)_{2}}$

$=\frac{3 	imes 4.5}{3+4.5}=\frac{3 	imes 4.5}{7.5}=\frac{3 	imes 3}{5}=1.8 \; hr$

A radioactive nucleus can decay by two different processes. Half-life for the first process is $3.0\, hours$ while it is $4.5\, hours$ for the second process. The effective half- life of the nucleus will be $.........\,hours.$

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