`Na^(22)` has half life of 2.68 years . It decays both by positron emission and electron capture with a ratio of 86% of the former to 14% of the later . The half life for positron emission in years (nearly) is ……….

Answer

3

Explanation

`t_(1//2) = (0.693)/(lambda_(1)) = (0.693)/(0.2224) = 3.116 -= 3 , Y_(A) = (lambda_(1))/(lambda) xx 100 = 86 l lambda = (0.693)/(2.68) ………. (2)`
`Y_(B) = (lambda_(2))/(lambda) xx 100 = 14 , lambda = (lambda_(1) + lambda_(2)) ……... (3) implies (lambda_(1))/(lambda_(2)) = (86)/(14) ...... (1)` From (1) , (2) and (3)
`lambda = (lambda_(1)+ lambda_(2)) = (0.693)/(2.68) , (lambda_(1) + (14 lambda_(1))/(80) ) = 0.2586 , lambda_(1) (1 + (14)/(80)) = 0.2586`
`lambda_(1) = (0.2586 xx 86)/(100) = 0.2244 , t_(1//2) = (0.693)/(lambda_(1)) = (0.693)/(0.2224) = 3.116 -=3`