a
એક મહિના પછી અવિભજીત   \({\text{N}} = {{\text{N}}_{\text{0}}}{e^{ - \lambda (1)}}\,\, \Rightarrow \,\,\frac{N}{{{N_0}}} = {e^{ - \lambda }}\,\,\,\,\,\,\,\,......(i)\)

ક્ષય  \({\text{ }} = {\text{1 - }}\frac{{\text{N}}}{{{{\text{N}}_{\text{0}}}}} = \,10\% \,\)

\( \Rightarrow 1 - \frac{N}{{{N_0}}} = \frac{{{\text{10}}}}{{{\text{100}}}}{\text{ }} \Rightarrow \,\frac{{\text{N}}}{{{{\text{N}}_{\text{0}}}}} = \frac{{{\text{90}}}}{{{\text{100}}}}\,\,\,\,.....(ii)\)

ચાર મહિના પછી, અવિભંજીત   \( N' = N_0e-\lambda(4) \)

સમીકરણ  \({\text{(i)}}\)અને\({\text{(ii)}}\) પરથી \({e^{ - \lambda }} = \frac{{90}}{{100}}\,\,\,\,\,\,\,.....(iii)\)

\(\therefore\) વિભજીત અંશ \( = {\text{1 - }}\frac{{{\text{N'}}}}{{{{\text{N}}_{\text{0}}}}} = 1 - {e^{ - 4\lambda }} = 1 - {\left( {\frac{{90}}{{100}}} \right)^4} = 0.3439\)

પ્રતિશતમાં \(= 34.39\%\)