`Cu^(64)(" half life" =12.8 "hours" )` decay by `beta^(c-)-` emission `(38%), beta^(o+)-` emission(19%), and electron capture `(43%)`. Write the decay products and calculate partial half lives for each of the decay processes.

Explanation

The nuclear reactions are `:`
`._(29)Cu^(64) rarr ._(30)Zn^(64)+._(-1)e^(0)(._(-1)beta^(0))`
`._(29)Cu^(64) rarr ._(28)Ni^(64)+._(+1)e^(0)(._(+1)beta^(0))`
`._(29)Cu^(64)+._(-1)e^(0) rarr ._(28)Ni^(64)`
Given, `lambda_(avg)=(0.693)/(12.8)hr^(-1)`
`:. lambda_(1)+lambda_(2)+lambda_(3)=lambda_(avg)=(0.693)/(12.8)=5.41xx10^(-2)hr^(-1)......(i)`
Also for parallel path decay
`lambda_(1)=` Fractional yield of `._(30)Zn^(64)xxlambda_(avg)`
`lambda_(2)=` Fractional yield of `._(28)Ni^(64)xxlambda_(avg)`
`lambda_(3)=` Fractional yield of `_(28)Ni^(64^(**))xxlambda_(avg)`
`(lambda_(1))/(lambda_(2))=(38)/(19) ....(ii)`
and `(lambda_(1))/(lambda_(3))=(38)/(43) ....(iii)`
From Eqs. `(i), (ii),` and `(iii), lambda_(1)=2.056xx10^(-2)hr^(-1)`
`lambda_(2)=1.028xx10^(-2)hr^(-1),lambda_(3)=2.327xx10^(-2)hr^(-1)`
`t_(1//2)` for `beta^(c-)-` emission `=(0.693)/(2.056xx10^(-2))=33.70hr`
`t_(1//2)` for `beta^(o+)-` emission`=(0.693)/(1.028xx10^(-2)0=67.41hr`
`t_(1//2)` for electron capture `=(0.693)/(2.327xx10^(-2))=29.78hr`