Question

What is the half life of a radioactive substance if 87.5% of
any given amount of the substance disintegrates in 40
minutes ?
(a) 20 minutes (b) 10 minutes
(c) 13 minutes 32 sec (d) 160 minutes

Answer 1

The half life of the radioactive substance is 13.32 minutes.

Given:

Amount of substance = 87.5%

Time = t = 40 minutes

To find:

Half life of the radioactive substance = ?

Formula:

The half life is given by the formula:

$t_{50 \%}=\frac{0.693}{K}$

Solution:

From question, we can understand that the reaction follows order one.

Now, the formula used is:

$K t=2.303 \log \frac{[R]_{0}}{[R]_{t}}$

$[R]_0 = 100\% -87.5\% = 12.5\% [R]_0$

On substituting the known values, we get,

$K \times 40=2.303 \log \frac{[R]_{0}}{12.5 [R]_{0}} \times 100$

$\therefore K=0.052 \ \mathrm{min}^{-1}$

Now, the half life is given as:

$t_{50 \%}=\frac{0.693}{0.052}$

Thus, the half life of the substance is:

$\therefore t_{50 \%}=13.32 \ \mathrm{min}$