The ratio of half-life times of two elements `A` and `B` is `(T_(A))/(T_(B))`. The ratio of respective decay constant `(lambda_(A))/(lambda_(B))`,is

Options

A. `(T_(B))/(T_(A))`
B. `(T_(A))/(T_(B))`
C. `(T_(A)+T_(B))/(T_(A))`
D. `(T_(A)-T_(B))/(T_(A))`

Answer

A

Explanation

Activity, `R=R_(0)e^(-lamdat)`
`implies ((1)/(3))=e^(-lamdaxx3)=e^(-3lamda)` . .. . (i)
Again, `(R')/(R_(0))=e^(-lamdaxx9)=e^(-9lamda)=(e^(-3lamda))^(3)`
`=((1)/(3))^(3)` [from eq. (i)]
`=(1)/(27)implies R'=(R_(0))/(27)`
Hence, in 9 days activity will become `(1)/(27)` of the original value.