If a 100 g sample of an isotope with a half-life of 10 years decays for 20 years, the remaining mass will be

To solve this, we can use two equations.

t1/2 = ln 2 / λ = 0.693 / λ       -      (1)

where, t1/2 is half-life and λ is the decay constant.

Nt = Nοe∧(-λt)                         -    (2)

Nt = amount of atoms at t =t time
Nο = initial amount of atom 
t = time taken

From (1),
10 yr = 0.693 / λ
λ = 0.693 / 10 yr

From (2)
Nt = 100 g eΛ(-(0.693 / 10 yr) x 20 yr)
Nt = 25.00 g. 

Hence, remaining mass will be 25.00 g

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