The radionuclide `.^(56)Mn` is being produced in a cyclontron at a constant rate `P` by bombarding a manganese target with deutrons. `.^(56)Mn` has a half-life of `2.5 h` and the target contains large numbers of only the stable manganese isotopes `.^(56)Mn`. The reaction that produces `.^(56)Mn` is
`.^(56)Mn +d rarr .^(56)Mn +p`
After being bombarded for a long time, the activity of `.^(56)Mn` becomes constant, equal to `13.86 xx 10^(10) s^(-1)`. (Use `1 n2=0.693`, Avagardo number `=6 xx 10^(2)`, atomic weight of `.^(56)Mn=56 g mol^(-1)`).
At what constant rate P, `.^(56)Mn` nuclei are being produced in the cyclontron during the bombardment?

Options

A. `2xx10^(11)"nuclei"//s1`
B. `13.86xx10^(10)"nuclei"//s`
C. `9.6xx10^(10)"nuclei"//s`
D. `6.93xx10^(10)"nuclei"//s`

Answer

B

Explanation

In equilibrium, rate of decay=Rate of production