Radioactive decay is expressed by the following formula:
[tex] N_{t} = N_{0} e^{-lambda * t} [/tex]
N₀ is the initial number of undecayed atoms.
Nt is the number of undecayed atoms remaining after time t
λ is the decay constant.
The relationship between λ and the half life time t1/2 is:
λ = [tex] \frac{0.693}{ t_{1/2} } [/tex] = 0.693 / 5.27 = 0.1315 [tex] y^{-1} [/tex]
Taking natural logs for both sides of the decay expression:
ln Nt = ln N₀ - λ t
ln Nt = ln 199 - (0.1315 x 20)
= 5.293 - 2.63 = 2.66
From which:
Nt = 14.29 g
