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# Exploring the decay of Plutonium 241

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Pu-241 is produced from neutron absorption by Pu-240 (which is produced by neutron absorption by Pu-239). Calculate the fractional in-growth of Am-241 from Pu-241 (i.e. number ratio Am-241/Pu-241) from time = 0 to 200 years. Pu-241 is the parent and Am-241 is the daughter.

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#### Solution Preview

The amount of 241Am in a plutonium sample arises from it's formation in the decay of 241Pu and it's destruction from it's own decay. The differential equation governing the number of atoms of 241Am in a sample is

dN(A) / dt = -Lamda(A)*N(A) + K(P)*Lamda(P)*N(P) (1)

where

N(A) = Number of atoms of 241Am at time t

N(P) = Number of atoms of 241Pu at time t

Lamda(A) = Decay constant of 241Am

Lamda(P) = Decay constant of 241Pu

Lamda(n) = rate at which 240Pu absorbs neutrons to form 241Pu

N(240) = Number of atoms of 240Pu in the original sample

K(P) = 0.9999754, fraction of 241Pu decays that lead to 241Am, accounting for 2.4 x 10-3 % that decay to 237U #

{We will assume this to be K(P) = 1 for the rest of the ...

#### Solution Summary

The decay of Plutonium 241 to Americium 241 is explored through its decay equations and the fractional growth in am-241 from Pu 241 is determined

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