Consider `x overset(-alpha)toyoverset(-alpha)toz`, where half-lives of x andy are z year and one month, the ratio of atoms of x and y when transient equilibrium `[T_(1//2)(x)gtT_(1//2)(y)]` has ben established is

Options

A. `1:2`
B. `1:26`
C. `26:1`
D. `23:1`

Answer

D

Explanation

`N_(2) = (lambda_(1)N_(1)^(0))/(lambda_(2)-lambda_(1))(e^(-lambda_(1)t)-e^(-lambda_(2)t))`
When `(T_(1//2))_(1) gt (T_(1//2))_(2)` at transient equilibrium
`lambda_(1) lt lambda_(2)`
`e^(-lambda_(2^(t)))lt lt e^(-lambda_(1^(t)))`
`N_(2) = (lambda_(1)N_(1)^(0)e^(-lambda_(1^(t)))`
`therefore` `N_(1)/N_(2) = (lambda_(2)-lambda_(1))/lambda_(1) = (0.693/1)-(0.693/(2 xx 12))/((0.693)/(2 xx 12)) = 23/1`