How long will it take 24 g of plutonium 240 to decay 20 grams

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

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