A sample 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 sample contains

1.000\,\mathrm{g}

of pure

^{237}\mathrm{Np}

(

T_{1/2}=2.14\times10^{6}\,\mathrm{y}

) at

t=0

, with no

^{233}\mathrm{Pa}

present.

^{237}\mathrm{Np}

decays by

\alpha

emission entirely to

^{233}\mathrm{Pa}

(

T_{1/2}=27.0\,\mathrm{d}

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

^{233}\mathrm{Pa}

t=200\,\mathrm{d}

, and state whether secular equilibrium has been reached by then. ((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

^{237}\mathrm{Np}

T_{1/2}^{\rm calc}=1.07\times10^{5}\,\mathrm{y}

. Find

P_\alpha

for

^{237}\mathrm{Np}