Question

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

• A. $45.6\times10^{21}$ atoms
• B. $45.6\times10^{23}$ atoms
• C. $45.6\times10^{24}$ atoms
• D. $45.6\times10^{20}$ atoms

Answer 1

Answer: (B)

$k=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{10} hr ^{-1}$
$k=\frac{2.303}{4} \log \frac{1 \times 6.023 \times 10^{23}}{N}$
$\left(\because 1 g\right.$ atom $=6.023 \times 10^{23}$ 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.