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^(23)`, atomic weight of `.^(56)Mn=56 g mol^(-1)`).
At what constant rate P, `.^(56)Mn` nuclei are being produced in the cyclotron during the bombardment?

Options

A. ` 5xx 10^(11)`
B. ` 20 xx 10^(11)`
C. ` 1.2xx 10^(14)`
D. ` 1.8 xx 10^(15)`

Answer

d

Explanation

As rate of decay =Rate of production
`P=lambdaN rArr N=(P)/(lambda)=(Pt_(1//2))/(In2)=1.8xx10^(15)`.