Question

The half-life of $40$K is $1.28\times {10}^9$ years. What mass of this nuclide has an activity of 1.00 $\mu Ci$?

• A. $w=0.143g$
• B. $w=0.343g$
• C. $w=0.443g$
• D. None of these

Answer 1

The correct option is A $w=0.143g$

$1.00\mu Ci=1.0\times {10}^{-6}Ci$
$=3.7\times {10}^{10}\times 1.0\times {10}^{-6}dps$

$\therefore \frac{-dN}{dt}=3.7\times {10}^{4}dps$

1 years $=3.1536\times {10}^{7}dps$

$\lambda =\frac{0.693}{t_{50}}=\frac{0.693}{1.28\times {10}^9\times 3.1536\times {10}^7}$
$=1.72\times {10}^{-17}{S}^{-1}$
$-\frac{dN}{dt}=\lambda N=\frac{\lambda w{N}_0}{40}$
$3.7\times {10}^4=\frac{1.72\times {10}^{-17}\times w\times 6.02\times {10}^{23}}{40}$

$\therefore w=0.143g$