One microgram of radioactie sodium `Na^(24)` with a half life of 15 h was injected fin to a living system for a bio assay .How long will iot take for the radioactivity to fall to 25% of the initial value?

Options

A. 60 h
B. 22.5 h
C. 375 h
D. 30h

Answer

D

Explanation

`t_(1//2)` of `_(11)Na^(24)=15h`
`[R]_(0)=1.0 mug`
`[R]=1.0xx(25)/(100)=(25)/(100)=0.25 mug`
`K=(06932)/(t_(1//2))=(0.6932)/(15)h^(-1)`
`k=(2.303)/(t)log[R]/([R])`
`(0.6932)/(15)=(2.303)/(t)log(100)/(25)=(2.303)/(t)log4`
`(0.6932)/(15)=(2.303)/(t)xx0.6020`
`t=(15xx2.303xx0.6020)/(0.6932)`
=`(20.7995)/(0.6932)`
=30.00h