Question

A sample of a radioactive element whose half-life is
30 s contains a million nuclei at a certain instant of
time. How many nuclei will be left after 10 s?
(a) 3.33 x 10
(b) 3.78 x 10
(c) 7.94 x 100
(d) 1.26 x 10
​

Answer 1

Given:

• nuclei number $N_{0}=10^{6}$
• half life, T = 30 s

To find: number of nuclei left after 10 s = ?

Solution:

We know that, decay constant,

$\quad\quad\lambda = \frac{0.693}{T}$

$\quad\quad\quad =\frac{0.693}{30}$

$\quad\quad\quad =0.0231$

∴ the number of nuclei left after 10 s is given by

$\quad N=N_{0}e^{-\lambda t}$

$\to N=10^{6}\times e^{-0.0231\times 10}$

$\to N=7.94\times 10^{5}$

So, option (c) is correct.