Question

A sample of a radioactive substance has 10^(6) radioactive nuclei. Its half life time is 20 s How many nuclei will remain after 10 s ?

Answer 1

Answer:

$7.0 7\times {10}^{5}$

Explanation:

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Answer 2

Given:

• nuclei number $N_{0}=10^{6}$
• half life, T = 20 s

To find: number of nuclei remaining after in 10 s = ?

Solution:

We know that, decay constant,

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

$\quad\quad\quad =\frac{0.693}{20}$

$\quad\quad\quad =0.03465$

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

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

$\to N=10^{6}\times e^{-0.03465\times 10}$

$\to \bold{N=0.7\times 10^{6}}$