Question

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

• A. $4.231\times 10^{4}dps$
• B. $1.721\times 10^{3}dps$
• C. $1.235\times 10^{4}dps$
• D. $5.167\times 10^{3}dps$

Answer 1

Answer: (C)

Given, $T_{1/2}=4.5\times 10^{9}years=4.5\times 10^9\times 3.156\times 10^{7}s$
Number of atoms in $1g$ Uranium,
$N=\frac{6.023\times 10^{23}}{238}$ atoms
The activity of the sample is $\lambda N$
$=\frac{0.693}{T_{\frac{1}{2}}}\times N$
$=\frac{0.693\times 6.023\times 10^{23}}{4.5\times 3.156\times 10^{16}\times 238}$
$=1.235\times 10^4\text{ dps}.$