A radioactive sample `S_(1)` having the activity `A_(1)` has twice the number of nucleic as another sample `S_(2)` of activity `A_(2)`. If `A_(2)=2A_(1)`, then the ratio of half-life of `S_(1)` to the half-life of `S_(2)` is

Options

A. 4
B. 2
C. 0.25
D. 0.75

Answer

C

Explanation

The initial momentum of the nucleus would be equal to `4u_(H)v`, where `u_(H)` is the unit mass of hydrogen. Since, the mass of hydrogen is 1, so the initial momentum can be given by 4. the final momentum of the nucleus would be equal to (A-4)V, where V is the final velocity. thus, we get from the conservation of momentum (A-4)V=4v, so `V=(4v)/((A-4))`.