Question

The half-life period of a radioactive element is 14 hours. The fraction of the radioactive element that disintegrates in 56 hours is:

• A. 0.125
• B. 0.0625
• C. 0.9025
• D. 0.9375

Answer 1

The correct option is B 0.0625

The half-life period of a radioactive element is 14 hours. The fraction of the radioactive element that disintegrates in 56 hours is $0.0625$
The half-life period of a radioactive element is 14 hours.
The decay constant $\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{14}=0.0495$ /hour
$t=56$ hours

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

$56=\frac{2.303}{0.0495}log\frac{a}{a-x}$

$1.20=log\frac{a}{a-x}$

$15.98=\frac{a}{a-x}$

$\frac{a-x}{a}=\frac{1}{15.98}=0.0625$

The fraction of the radioactive element that disintegrates in 56 hours is 0.0625