Physics - Modern Physics Question with Solution | TestHub

Given: ${\mathrm{T}}_{1/2}=4.47\times 10^8\mathrm{yr}$ $\frac{\mathrm{N}}{{\mathrm{N}}_0}=\frac{60}{100}={\left(\frac{1}{2}\right)}^{\mathrm{n}}\Rightarrow 2^{\mathrm{n}}=\frac{10}{6}$ Apply logarithm on both sides $\begin{array}{rl}& \mathrm{n}\log 2=\log 10-\log 6\\ \Rightarrow & \mathrm{n}\times 0.3=1-0.778=0.22\\ \Rightarrow & \mathrm{n}=\frac{0.222}{0.3}=0.74\end{array}$ So, $\mathrm{t}={\mathrm{nT}}_{1/2}=0.74\times 4.47\times 10^8$ or, $\mathrm{t}=3.3\times 10^8\mathrm{yr}$