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  • A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is __________.(Nearest integer) (Given : antilog 0.125=1.333,antilog 0.693=4.9

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is __________.(Nearest integer)

(Given : antilog 0.125=1.333,antilog 0.693=4.93)

Option: 1

75


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\text { Half life }=200 \text { days }\\

\mathrm{{t_{1/2}}=\frac{\ln 2}{k}}

\mathrm{k=\frac{\ln 2}{{t_{1/2}}}=\frac{ln2}{200}}\quad-(1)

Now, integrated rate equation for a first order reaction is given as 

\mathrm{A=A_{0} e^{-k t} }

\mathrm{kt=ln\frac{A_0}{A_t}}\quad -(2)

Using equations (1) and (2), we have 

\mathrm{\frac{ln2}{200}(83)=ln\left (\frac{A_0}{A_{83}} \right )}

\mathrm{log\left (\frac{A_0}{A_{83}} \right )=\frac{log2}{200}(83)=\frac{0.3 \times 83}{200}\simeq0.125}

\mathrm{\left (\frac{A_0}{A_{83}} \right )=antilog(0.125)=1.333=\frac{4}{3}}

In percentage -

\mathrm{\frac{A_{83}}{A_{0}}=\frac{3}{4} \times 100%=75 \%}

Hence, (75) is answer

Posted by

Gaurav

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