Question

The half-life of a radioactive element is $10h$. How much will be left after $4h$ in $1g$ atom sample?

Answer 1

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{10}{hr}^{-1}$
$k=\frac{2.303}{4}\log \frac{1\times 6.023\times {10}^{23}}{N}$
$(\because 1gatom=6.023\times {10}^{23}atom)$
$\Rightarrow \frac{0.693}{10}=\frac{2.303}{4}\log \frac{6.023\times {10}^{23}}{N}$
or $\log \frac{6.023\times {10}^{23}}{N}=0.12036$
$\frac{6.023\times {10}^{23}}{N}=1.319$
$\therefore N=4.56\times {10}^{23}$ atom.