A small quantity of a solution containing `Na^(24)` radio-nuclide of half-life `T` and activity `R_(0)` is injected into blood of a person. `1 cm^(3)` of sample of blood taken from the blood of the person shows activity `R_(1)`. If the total volume of the blood in the body of the person is `V`, find the timer after which sample is taken.

Options

A. `(T)/(ln (2))[1n"" (R_(0))/(VR_(1))]`
B. `(T)/(ln(2))[ln ""(VR_(0))/(R _(1))]`
C. `(T)/( ln (2))[ ln "" (VR_(1))/(R _(0))]`
D. `(T)/( ln (2))[ ln "" (R_(1))/(VR _(0))]`

Answer

A

Explanation

Total volume of blood.
`V = ("Total activity R")/("Activity per"cm^(3) (R_(1))`
`= (R_(0)e ^(- lamda t ))/(R _(1)) , (or) (V R _(1))/(R _(0)) = e ^(- lamda t)`
`-ln ((VR_(1))/(R _(0))) = lamda t = (ln (2) t)/(T), t = (T)/(ln (2))ln ((R_(0))/( VR_(1)))`