c
Half life of bromine \(-82=36\) hours

\( \mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{~K}} \)

\( \mathrm{~K}=\frac{0.693}{36}=0.01925 \mathrm{hr}^{-1} \)

\(1^{\text {st }}\) order rxn kinetic equation

\( t=\frac{2.303}{K} \log \frac{a}{a-x} \)

\( \log \frac{a}{a-x}=\frac{t \times K}{2.303} \quad(t=1 \text { day }=24 \mathrm{hr}) \)

\( \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{24 \mathrm{hr} \times 0.01925 \mathrm{hr}^{-1}}{2.303} \)

\( \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=0.2006 \)

\( \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\operatorname{anti} \log (0.2006) \)

\( \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=1.587 \)

\( \text { If } \mathrm{a}=1 \)

\( \frac{1}{1-\mathrm{x}}=1.587 \Rightarrow 1-\mathrm{x}=0.6301=\text { Fraction remain } \) after one day