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