b
\({\text{I}} = {{\text{I}}_{\text{0}}}{e^{ - kx}} \Rightarrow \,\,\frac{I}{{{I_0}}} = {e^{ - kx}}\,\,\,\,\,\)   \(In\left( {\frac{I}{{{I_0}}}} \right) =  - kx\)

\( \to \,\ln \,\left( {\frac{1}{8}} \right) =  - k\, \times 36\,\,\,\)

\(\therefore \,\,\,\ln \,({2^{ - 3}}) =  - k \times 36\,\)  અથવા 

\({\text{3ln}}\,{\text{2}} = {\text{k}}\, \times {\text{36}}\,\,\,\,\,\,\,.....{\text{(1)}}\)

\( \to \,\,{\text{ln}}\,\,\left( {\frac{{\text{1}}}{{\text{2}}}} \right)\, =  - k \times x\,\,\)

\(\,\ln ({2^{ - 1}}) =  - kx\,\,\)  

\(\therefore\)\(\,\,\ln \,2 = kx\,\,.....(2)\)

સમીકરણ \((1)\) અને \((2)\) પરથી ,

\(3 ×(kx) = k × 36\)   

\(\therefore\) \(x = 12 \,mm\)