Question

The number of disintegrations per second that will occur in $1$ gram of ${}_{92}^{238}U$ is:
(if its half-life against $\alpha$ decay is $1.42\times {10}^{17}s$)

• A. $1.2\times {10}^5{s}^{-1}$
• B. $1.5\times {10}^5{s}^{-1}$
• C. $2.1\times {10}^5{s}^{-1}$
• D. $0.1235\times {10}^5{s}^{-1}$

Answer 1

The correct option is D $0.1235\times {10}^5{s}^{-1}$

$t_{1/2}=1.42\times {10}^{17}s$
$1gm$ of U contains $=\frac{6\times {10}^{23}}{235}$
$=25.3\times {10}^{20}$ atoms
The decay rate:
$R=\lambda N$

$=\frac{ln2}{t_{1/2}}\times 25.3\times {10}^{20}$
$=\frac{.693}{1.42\times {10}^{17}}\times 25.3\times {10}^{20}$

$=0.1235\times {10}^5{s}^{-1}$