The half life of a radioactive isotope 25 days . After what time it will disintegrate 75%

Options

A. 50 days
B. 48 days
C. 24 days
D. 125 days

Answer

A

Explanation

Initial amount of the surface`=N_(0)`
Amount left after time, `t=N_(t)`
Now, `N_(t)=N_(0)((1)/(2))^(n)`
`N_(t)=(N_(0))/(4)` (given)
[`because` After 75% disintegration only 1/4th amount will be left]
`therefore (N_(0))/(4)=N_(0)((1)/(2))^(2)`
Total time `=t_(1//2)xxn=25xx2=50` days.