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  • A radioactive nucleus can decay by two different processes. Half-life for the first process is ho

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

Option: 1

\mathrm{3.75\: hours}


Option: 2

\mathrm{0.56\: hours}


Option: 3

\mathrm{0.26\: hours}


Option: 4

\mathrm{1.80\: hours}


Answers (1)

best_answer

Let the half life for 1st, 2nd and effective be \mathrm{T_{1},T_{2}\, and\: T} respectively

\mathrm{\because \: \lambda_{\text {eff }}=\lambda_{1}+\lambda_{2}}
\mathrm{\therefore \: \frac{1}{T_{\text {eff }}}=\frac{1}{T_{1}}+\frac{1}{T_{2}}}
                  \mathrm{=\frac{1}{3}+\frac{1}{4.5}}

\mathrm{\frac{1}{T_{\text {eff }}}=\frac{3+2}{9}}

\mathrm{T_{\text {eff }}=1.8\, \mathrm{hrs}}

The correct option is (4)
 

Posted by

Rishi

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