Which sample contains greater number of nuclei ?
a `5.00 -mu Ci` sample of `.^240 Pu` (half-life `6560 y`)
or `a 4.45-mu Ci` sample of `.^243 Am` (half-life `7370 y`).

Options

A. `.^240 Pu`
B. `.^243 Am`
C. Equal in both
D. None of these

Answer

C

Explanation

( c) The activity `(-(dN)/(dt)) = lamda N rArr N =(-(dN)/(dt))((T_(1//2))/(log_e 2))`
Taking the ratio of this expression for `.^240 Pu` to this same expression for `.^243 Am`,
`(N_(Pu))/(N_(Am)) = ((-(dN_Pu)/(dt))(T_(1//2))_(Pu))/(-(dN_(Am)/(dt))(T_(1//2))_(Am))`
`=((5 muci) xx (6560 y))/((4.45 mu ci) xx(7370 y)) = 1`
i.e., the two samples contains equal number of nuclei.