A radioactive substance has a half-life period of 40 days. Calculate the time taken for 3/4th of original atoms to disintegrate.

Explanation

T=40 days
Number of atoms disintegrated `=3/4 N_(0)`
Number of atoms disintegrated `=3/4 N_(0)`
Number of atoms left after time `t=N_(0)-3/4N_(0)`
`=1/4N_(0)`
Number of half-lives in time `t=n=t/T`
`rArr n=t/40`
Number of nuclei left after n-half-lives `=N=N_(0)(1/2)^(n)`
`1/4N_(0) = N_(0)(1/2)^(n)`
`1/4=(1/2)^(n)`
`rArr t/40 2`
t=80 days.