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)`).
After a long time bombardment, number `.^(56)Mn` nuclei present in the target depends upon.

Options

A. All (i), (ii), and (iii) are correct.
B. Only (i) and (ii) are correct.
C. Only (ii) and (iii) are correct.
D. Only (i) and (iii) are correct.

Answer

c

Explanation

As `N =(Pt_(1//2))/(In2)`
It is dependent upon `P` and `t_(1//2)`. Initial number of `.^(56)Mn` nuclei will make no differnce as in equilibrum, rate of production equals rate of decay. Large intial number will only make equilibrium come sooner.