Given:
Initial mass of Pu-240, N(0) = 24 g
Mass left after a certain time (Nt) = 20 g
To determine:
The decay time (t)
Explanation:
The radioactive decay is given by the following equation:-
N(t) = N(0)exp(-kt) -------(1)
where, the exponential decay constant k is given as:
k = 0.693/t1/2 ----(2)
Now, the half life t1/2 for a Pu-240 nucleus is 6560 years
k = 0.693/6560 = 1.056*10⁻⁴ year⁻¹
Substituting k in eq(1)
20 = 24 exp(-1.056*10⁻⁴t)
ln(20/24) = (-1.056*10⁻⁴t)lne
t = 1727 years
Ans: It will take 1727 years for the decay of Pu-240 from 24 to 20 g
