Question

In a sample of a radioisotope, $\frac{3}{4}$ of the atoms had disintegrated in $60$ minutes. What is the half-life of the radioisotope?

Answer 1

$\because \ln \frac{A_t}{A_o}=-kt\ln \left(\frac{3}{4}\frac{A_o}{A_o}\right)=-k\times 60k=\frac{1}{60}\ln \frac{4}{3}{t}_{1/2}=\frac{\ln 2}{k}=\ln 2\times \frac{60}{\ln \frac{4}{3}}=\frac{60\ln 2}{(\ln 4-\ln 3)}$