`.^(64)Cu` (hlaf lifre `= 12.8h`) deacays by `beta^(-)` emission `(38%), beta^(+)-` emission `(19%)` and electron capute `(43%)`. Write the decay products and calculate partial half-live for each of the decay processes.

Explanation

We know,

Given `lambda_(av) = (0.693)/(12.8) hr^(-1)`
`:. lambda_(1) + lambda_(2) + lambda_(3) = lambda_(av) = (0.693)/(12.8) = 5.41xx10^(-2) hr^(-1)` .....(1)
Also for parallel path decay
`lambda_(1)` = Fractionlal yield of `._(30)^(64)Zn xx lambda_(av)`
`lambda_(2)` = Fractional yeild of `._(28)^(64) Ni xx lambda_(av)`
`lambda_(3)` = Fractionlal yield of `._(28)^(64) Ni xx lambda_(av)`
`:. (lambda_(1))/(lambda_(2)) = (38)/(19)` ....(2)
`(lambda_(1))/(lambda_(3)) = (38)/(43)` ....(3)
From eqs. (1), (2) and (3)
`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^(-)` emission
`= (0.693)/(2.056xx10^(-2)) = 33.70 hr`
`t_(1//2)` for `beta^(+)` emission
`= (0.693)/(1.028xx10^(-2)) = 67.41 hr`
`t_(1//2)` for electron capture
`= (0.693)/(2.327xx10^(-2)) = 29.28 hr`