Question

Write the relationship between the half life and average life of a radioactive substance

Answer 1

• The half-life of a radioactive elementis the amount of time it takes for half of a sample of the element to decay away.

• It is smaller than the mean lifetime by a factor of ln(2), the natural logarithm of 2. The half-life units are time units such as seconds or years

Answer 2

$\bf \: Radioactive \: decay \: is \: a \: statistical \\ \bf process, \: that \: is, \: it \: can \: not \: be \: \\ \bf \: said \: that \: which \: particle \: of \: \\ \bf radioactive \: substance \: will \\ \bf \: release \: the \: particle \: by \: decay \: and \: \\ \bf \: d ecay. \: Thus, \: the \: time \: of \: decay \\ \bf\: of \: the \: nucleus \: can \: be \: anything \: between \: zero \: and \: \\ \bf \: infinite, \: hence \: the \: average \: age \: of \: \\ \bf all \: nuclei \: is \: called \: median \: \\ \bf \: age. \: Display \: it \: from \: ( \tau ) \\ \\ \underline {\bf Middle \: of \: the \: radioactive} \\ \underline{ \bf substance \: is \: equal \: to \: the} \\ \underline{ \bf \: \: inversion \: of \: decay \: determines} \\ \\ mens \: \boxed{ \tau = \frac{1}{ \lambda} }$

$\bold{\huge{\underline{Relation\:Between\:Half\:Life\:and\:Average\:life}}}$

The half life of Radioactive substance

$T \: = \frac{0.6931}{ \lambda} \\ \\ \implies0.6931 \times \frac{1}{ \lambda}$

But,

$\bf \: Average \: life \implies \tau = \frac{1}{ \lambda} \\ \\ so \: \: \: \: \: \bf \: T = 0.6931 \tau$

Means- Half life (T) = 0.6931 × Average life

$Or \: \: \: \: \: \: \: \: \tau = ( \frac{1}{0.6931} ) \times T$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \implies1.443 \: T \:$

$\boxed{ \bf \: Average \: life = 1.443 \times Half-life }$