A radioactive element` X` converts into another stable elemnet `Y`. Half-life of `X` is `2h`. Initally, only `X` is present. After time `t`, the ratio of atoms of `X` and `Y` is found to be `1:4` Then `t` in hours is .

Options

A. 2
B. 4
C. between 4 and 6
D. 6

Answer

D

Explanation

Radioactivity at `T_(1) , R_(1) = lambda N_(1)`
Radioactivity at `T_(2) , R_(2) = lambda N_(2)`
`therefore` Number of atoms decayed in time
`(T_(1) - T_(2)) = (N_(1) - N_(2)) = ((R_(1) - R_(2)))/(lambda) = ((R_(1) - R_(2)) T)/(0.693) prop (R_(1) - R_(2) ) T `