A source contains of pure ( ) at

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radioactivity and decay modes

The Nucleus Resolved, Ch Decay rates from the golden rule: kinetics closed and alpha decay finished

Problem

A source contains

1.000\,\mathrm{g}

of pure

^{238}\mathrm{Pu}

(

T_{1/2}=87.7\,\mathrm{y}

) at

t=0

, with no

^{234}\mathrm{U}

present.

^{238}\mathrm{Pu}

decays entirely by

\alpha

emission to

^{234}\mathrm{U}

, which itself decays with

T_{1/2}=2.455\times10^{5}\,\mathrm{y}

. ((a)) Using the two-member Bateman solution, find the activity of

^{234}\mathrm{U}

present at

t=350\,\mathrm{y}

. ((b)) Under a stated WKB prescription (

R=1.2(A_d^{1/3}+4^{1/3})\,\mathrm{fm}

, point-charge Coulomb barrier,

\ell=0

), the calculated (preformation-factor-one) alpha half-life of

^{238}\mathrm{Pu}

T_{1/2}^{\rm calc}=37.0\,\mathrm{y}

. Using the measured half-life above, find the preformation factor

P_\alpha