QJEEM24Ch40a5: JEE Main 2024 Chemistry - Class 12 JEEM24Ch40a5 Solution: The half-life of radioisotope bromine - 82 is 36 hours. The…

Half life of bromine $-82=36$ hours

$\begin{aligned}& \mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{~K}} \\& \mathrm{~K}=\frac{0.693}{36}=0.01925 \mathrm{~hr}^{-1} \\& 1^{\text {st }} \text { order rxn kinetic equation } \\& \mathrm{t}=\frac{2.303}{\mathrm{~K}} \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}} \\& \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{\mathrm{t} \times \mathrm{K}}{2.303}(\mathrm{t}=1 \text { day }=24 \mathrm{~hr}) \\& \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{24 \mathrm{hr} \times 0.01925 \mathrm{hr}^{-1}}{2.303} \\& \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=0.2006 \\& \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\mathrm{anti} \log (0.2006) \\& \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=1.587 \\& \text { If }=1 \\& \frac{1}{1-\mathrm{x}}=1.587 \Rightarrow 1-\mathrm{x}=0.6301=\text { Fraction remain } \\& \mathrm{after} \text { one day }\end{aligned}$