Question

Radium has a half-life of $ 5 \,years$ . The probability of decay of a radium nucleus in $ 10\, years$ is

• A. $50\%$
• B. $75\%$
• C. $100\%$
• D. $60\%$
• E. $25\%$

Answer 1

Answer: (B)

$ \frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{t/T}}={{\left( \frac{1}{2} \right)}^{\frac{10}{5}}}={{\left( \frac{1}{2} \right)}^{2}}=\frac{1}{4}=25% $
This is probability of remaining portion of radium. So, probability of decay
$ =(100-25)%=75% $