Question

A vessel of $125cc$ contains ${}_1^{3}H$ ( $t_{1/2}=$2.3 y ) at $500KPa$ and $300K$. The activity of the gas is

• A. $0.754Ci$
• B. $7.24Ci$
• C. $72.4Ci$
• D. $724Ci$

Answer 1

Answer: (D)

$724Ci$

$t_{\frac{1}{2}}=2.3years$

$\lambda =\frac{ln2}{2.3}\times (years{)}^{-1}$

$1Ci=3.7\times {10}^{10}decayspersecond$ and

$\frac{dN}{dt}=\lambda N$ where N is number of atoms.

Now, using gas law $PV=nRT$
$\frac{{10}^3\times 125m^3\times {10}^{-3}}{8.314\times 300}=n$

$\Rightarrow n=0.025058moles$

$1$ mole contains $6.024\times {10}^{23}molecules$
$0.02$ moles contain $1.50899molecules\times {10}^{22}$

Activity $=\frac{ln2\times 1.50899\times {10}^{22}}{2.3\times 365\times 24\times 3600}dps$ $=724curie.$