Question

A $U^{236}$ sample of mass 1.0 g emits alpha particles at the rate $1.24\times {10}^4$ particles per second. (NA = $6.023\times {10}^{23}$)

• A. The half life of this nuclide is $4.5\times {10}^9$ years
• B. The half life of this nuclide is $9\times 10^9$ years
• C. The activity of the prepared sample is $2.48\times {10}^4$ particles/sec
• D. The activity of the prepared sample is $1.24\times {10}^4$ particles/sec.

Answer 1

Answer: (A), (D)

The correct options are
A The half life of this nuclide is $4.5\times {10}^9$ years
D The activity of the prepared sample is $1.24\times {10}^4$ particles/sec.

$\begin{array}{c}\text{No. of nucleus initially present is}\\ N_0=\frac{1}{238}\times 6.023\times {10}^{23}\\ N_0=2.531\times {10}^{21}\\ \text{Activity is}A=1.24\times {10}^4\end{array}$

$\begin{array}{c}\lambda =\frac{A}{N_0}=4.90\times {10}^{-18}\\ \therefore T_{1/2}=\frac{\ln 2}{x}=4.49\times {10}^9\text{years}\end{array}$

Hence, option $A$ and $D$ are correct.