# Question #f18b2

Dec 21, 2016

An exponential decay which describes nuclear disintegration can be described in terms of half-life as below

$N \left(t\right) = {N}_{0} {\left(\frac{1}{2}\right)}^{\setminus \frac{t}{{t}_{1 / 2}}}$ .....(1)
where ${N}_{0}$ is the initial quantity of the disintegrating sample,
$N \left(t\right)$ is the quantity of sample that still remains after a time $t$,
${t}_{1 / 2}$ is the half-life of the sample.

1. the quantity ${N}_{0}$ may be measured in grams, moles, number of atoms etc.
2. It is statistical probability that half of the sample would decay in a time equal to one Half life.

Inserting given values in the equation (1) we get
$N \left(t\right) = {N}_{0} {\left(\frac{1}{2}\right)}^{\setminus \frac{10}{5}}$
$\implies N \left(t\right) = {N}_{0} \left(\frac{1}{4}\right)$
$\implies$ Quantity of sample disintegrated is $\frac{3}{4} {N}_{0}$

From definition of half life, probability of nuclear disintegration in $10$ years is $0.75$.