Question

Natural water contains a small amount of tritium (H31). This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the H31 radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.

Answer 1

Explanation:

It is given:

Tritium has the half-life time, $T 12=12.5$ years

Constant of disintegration, $\lambda=0.69312 .5$ per year

When there is bottle manufacturing, let $A_{0}$ be the activity.

After 8 years, the activity A is shown as

$A=A O e-0.69312 .5 \times 8$     …(1)

Let us assume that t years ago, the mountaineering had taken place.

Then, the bottle’s activity on the mountain, A’ is shown as

$A^{\prime}=A O e-\lambda t$

where,$A^{\prime}=(\text { Bottle's activity } 8 \text { years ago }) \times 1.5 \%$

$A^{\prime}=A O e-0.69312 .5 \times 0.015 \times 8$    …(2)

When (1) is compared with (2),

$0.69312 .5 \pm=\times 812.5-0.6931+\ln [0.015]$

$\Rightarrow-0.69312 .5 \mathrm{t}=-0.69312 .5 \times 8-4.1997$

$\Rightarrow t=83.75 \text { years }$