Question

The radioactive isotope ${}^{32}P$ decays by first order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a given sample of ${}^{32}P$ to decay?

• A. 21 days
• B. 42 days
• C. 62 days
• D. 80 days

Answer 1

The correct option is C 62 days

For the given first order reaction, $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{14.3}.$

But $k=\frac{2.303}{t}log\frac{a}{a-x}$

Substitute values in the above expression.

$\frac{0.693}{14.3}=\frac{2.303}{t}log\frac{100}{5}$

$t=61.82days\simeq 62days.$

Option C is correct.