Calculate the hife life of a radioactive substance if its activity drops to 1/16 th of its intial value in 30 years?

We know that the activity of a radioactive substance at any time, t is given by
A=A0e-λt  ---1
Where
A = Activity of radioactive material remaining after time t
A0 = Initial activity of material
λ = Decay constant

Given
AA0=116t = 30 years
Putting these values in (1) we get
116=e-30λe30λ=1630λ=ln 16=2 ln 2λ=ln 215
Also
Half life of a radioactive substance is given by
T1/2=ln2λPutting the value of λ we getT1/2=ln2ln215=15 years

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