A radioactive nuclide X decays at the rate of `1.00 xx 10^(5)` disintegration `S^(-1) g^(-1)`. Radium decays at the rate of `3.70 xx 10^(10)` disintegration `s^(-1) g^(-1)`. The activity of X in millicurie `g^(-1) (mci g^(-1))` is

Options

A. 0.027
B. `0.270 xx 10^(-5)`
C. 0.0027
D. 0.00027

Answer

B

Explanation

`(dx_(1))/(dt) = lamda N_(1), 1 xx 10^(5) = lamda N_(1)`
`(dx_(2))/(dt) = lamda N_(2), 3.7 xx 10^(10) = lamda N_(2)`
`(N_(1))/(N_(2)) = (1 xx 10^(5))/(3.7 xx 10^(10)) = (1 xx 10^(-5))/(3.7) = 0.27 xx 10^(-5)`