Natural water contains a small amount of tritium `(`_1^3H)`. 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 bottle of whisky.On returm he analyses the whisky and finds that it contains only 1.5 per cent of hte ``_1^3H` radioactivity as compared to a recently purchased bottle marked '8 years old' .Estimate the time of that unsuccessful attempt.

Answer

A, B, C

Explanation

The activity when the bottle was manufaciured `= A_(0)`
Activity after 8 year
` = A _( 0) e^((-0.689)/(12.5) xx8)`
Let the time of the mountineering
= t year from the present
` A = A_(0) e^((-0.653)/(128) xxt) ……. (1) `
A = Activity of the bottle found on
the mountain
`A_0` = (Activity of the bottle
manufactured 8 years before)
xx 1.5 %
` A = A_(0) e^((-0.6931)/(12.5)) xx 8) xx (1.5 / 100) `
`= A_0e^(-0.693/12.5 xx8) xx 0.015`........(2)
Comparing (1) and (2)
` (-0.693)/(12.5) t = (-0.6931 xx 8)/(12.5) + In [0.015]`
` rArr (-0.693)/(12.5)t = (-0.693)/(12.5) xx 8 + 4.1997`
` rArr 0.055441 = 0.44352 + 4.1997`
`rArr t = 83.75 year`