Question

The half-life of ${}_{92}^{238}U$ undergoing $\alpha -$decay is $4.5\times {10}^9$ years. What is true activity of the $1g$ sample of ${}_{92}^{238}U$? (Avogadro number$=6.022\times {10}^{23}$)

Answer 1

Given that,

Half life $T_{\frac{1}{2}}=4.5\times {10}^9=4.5\times {10}^9\times 3.156\times {10}^{7}s$

Avogadro number $N=6.023\times {10}^{23}$

Now, the number of atoms in 1g of uranium

$N=\frac{6.023\times {10}^{23}}{238}$

Now, the activity of the sample

$=\lambda N$

$=\frac{0.693}{T_{\frac{1}{2}}}\times N$

$=\frac{0.693}{4.5\times {10}^9\times 3.15\times {10}^7}\times \frac{6.023\times {10}^{23}}{238}$

$=1.237\times {10}^{4}d/s$

Hence, the activity of the sample is $1.237\times {10}^{4}d/s$