Question

The half life of ${}_{92}^{238}U$ undergoing $\alpha$ decay is $4.5\times {10}^9$ years. What is the activity of 4 $g$ sample of ${}_{92}^{238}U$ ?

• A. $4.9\times {10}^4$ per second
• B. $3.6\times {10}^4$ per second
• C. $1.2\times {10}^4$ per second
• D. $5.6\times {10}^4$ per second

Answer 1

The correct option is A $4.9\times {10}^4$ per second

$A=\lambda N=\frac{0.693}{t\frac{1}{2}}\times \left(\frac{m}{M}\right)\times N_{av}$
$=\frac{0.693}{4.5\times {10}^9\times 365\times 86400}\times \frac{4}{238}\times 6.02\times {10}^{23}$
$=4.9\times {10}^4$ per second