A radiochemical generator is freshly purified at to contain only ( )

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 radiochemical generator is freshly purified at

t=0

to contain only

^{225}\mathrm{Ra}

(

T_{1/2}=14.9\,\mathrm{d}

), no

^{225}\mathrm{Ac}

present.

^{225}\mathrm{Ra}

decays entirely to

^{225}\mathrm{Ac}

(

T_{1/2}=9.9\,\mathrm{d}

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

t_{\max}

at which the activity of

^{225}\mathrm{Ac}

is largest, and state the ratio of the

^{225}\mathrm{Ac}

activity to the

^{225}\mathrm{Ra}

activity at that instant. ((b)) Under the chapter's 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

^{225}\mathrm{Ac}

T_{1/2}^{\rm calc}=1.13\,\mathrm{d}

. Find the preformation factor

P_\alpha

for

^{225}\mathrm{Ac}