Natural water contains a trace amount of tritium ( ³₁ H ). This isotope beta-decays with a half-life of 12.5 years . While ascending a difficult peak, a mountaineer discovers debris from a previous unsuccessful attempt, which includes a sealed bottle of whisky. Upon returning, the mountaineer analyses the whisky and determines that it contains merely 1.5 % of the ³₁ H radioactivity compared to a recently purchased bo

Step-by-step solution

Let the initial radioactivity of the natural water used to make the whisky be A₀ . For the recently purchased bottle marked '8 years old', the water was drawn 8 years ago. Its present radioactivity is: A₁ = A₀ e^ -8 Assuming the found bottle was also an '8 years old' whisky when it was left on the peak t years ago, the total time elapsed since its water was drawn is (t + 8) years. Its present radioactivity is: A₂ = A₀ e^ -(t+8) Given that the found bottle contains 1.5 % of the radioactivity of the recently purchase