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. $45.6×10^{21}$ atoms
• B. $45.6×10^{23}$ atoms
• C. $45.6×10^{24}$ atoms
• D. $45.6×10^{20}$ atoms

Answer 1

Answer: (B)

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{10}h{r}^{−1}$
$k=\frac{2.303}{4}\log \frac{1×6.023×10^{23}}{N}$
$(âˆ\mu 1g$ atom $=6.023×10^{23}$ atom $)$
$⇒\frac{0.693}{10}=\frac{2.303}{4}\log \frac{6.023×10^{23}}{N}$
or $\log \frac{6.023×10^{23}}{N}=0.12036$
$\frac{6.023×10^{23}}{N}=1.319$
$∴N=4.56×10^{23}$ atom.