Question

0.1 mg of ${}^{239}Pu$ emits $1.4\times {10}^7$ particles per minute. What is its half-life?

• A. 2.372 years
• B. 3.372 years
• C. 4.472 years
• D. None of these

Answer 1

The correct option is A 2.372 years

$-\frac{dN}{dt}=\lambda N$

$0.1mg$ ${}^{239}Pu$ = $0.1\times {10}^{-3}g=\frac{0.1\times {10}^{-3}}{239}mol$

$\therefore N=\frac{0.1\times {10}^{-3}\times 6.02\times {10}^{23}}{239}$atoms

$\therefore 1.4\times {10}^7=\frac{\lambda \times 0.1\times {10}^{-3}\times 6.02\times {10}^{23}}{239}$

$\therefore \lambda =5.56\times {10}^{-11}mi{n}^{-1}$

$\therefore t_{50}=\frac{0.698}{\lambda }=7.481\times {10}^{11}s$

$=2.372years$