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  • Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If <img alt="\mathrm{\lambda _{A}}" src="https://entrancecorner.onc

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average
life of B. If \mathrm{\lambda _{A}} and \mathrm{\lambda _{B}} are decay constants of A and B respectively, then choose the correct relation from the
given options.
 

Option: 1

\mathrm{\lambda _{A}=2\lambda _{B}}


Option: 2

\mathrm{\lambda _{A}=\lambda _{B}}


Option: 3

\mathrm{\lambda _{A} \ln2=\lambda _{B}}


Option: 4

\mathrm{\lambda _{A}=\lambda _{B}\ln2}


Answers (1)

best_answer

                    \mathrm{A} \: \: \: \: \: \mathrm{B} \: \: \: \: \: \mathrm{T} \rightarrow \text { half life }
\mathrm{t}=0 \quad \mathrm{~N}_0 \: \: \: \: \mathrm{~N}_0 \quad \tau \rightarrow \text { average life }
\mathrm{T}_{\mathrm{A}}=\tau_{\mathrm{B}} \rightarrow \text { given in question }
\text { Now } \frac{\ln (2)}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \Rightarrow \quad \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \cdot \ln (2) \\
 

Posted by

Ritika Kankaria

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