Question

The radioactive isotope of cerium-$137$ of weight $8g$ was collected on $1$st Feb 2006 and kept in a sealed tube. On $1$st July 2006, it was found that only $0.25g$ of it remained. The half-life period of the isotope is:

• A. $37.5$ days
• B. $30$ days
• C. $25$ days
• D. $50$ days
• E. $60$ days

Answer 1

The correct option is B $30$ days

$A=A_o{e}^{-kt}\ln \left(\frac{A_o}{A}\right)=kt\ln \left(\frac{8}{0.25}\right).\frac{1}{150}=kk=0.0231\therefore t_{1/2}=\frac{0.693}{k}=30days.$