Question

Half-life of Ra is 1600 years if initial mass of radium is 400 g. The time after which it decays 100 gm, will be:

• A. 6400 years
• B. 4800 years
• C. 3200 years
• D. 1600 years

Answer 1

Answer: (B)

For the relation $N=N_0{e}^{-\lambda t}$ where $\lambda =\frac{0.693}{T_{1/2}}$ Hence $T_{1/2}=1600$ years, $N_0=400g,$ $N=400-100=300g$ so, $-\frac{0.693t}{T_{1/2}}=\frac{300}{400}$ or $\frac{0.693}{T_{1/2}}t=\ln \frac{3}{4}$ so $t=\frac{T_{1/2}\ln \frac{3}{4}}{0.693}=\frac{1600\ln \frac{3}{4}}{0.693}$ $=4800years$