upon irradiation californium with neutron, a radio chemist discovered a new nuclide having mass number of 250 and a half life of 30 minutes. Three hours after the irradiation, the observed radioactivity due to the nuclide was 10 dis/minute. How many atoms of the nuclide were prepared initially ?

Options

A. `2.8 xx 10^(2)`
B. `2.8 xx 10^(4)`
C. `2.8 xx 10^(3)`
D. `2.8`

Answer

B

Explanation

`A = A_(0)e^(-lambdat), " "2.303 log ""(A)/(A_(0)) = -lambdat`
`2.303 log ""(10)/(A_(0)) = (-0.693)/(t_(0.5)) xx 3.0 = (-0.693)/(0.5) xx 3.0 " " therefore (10)/(A_(0)) = 0.0156`
`A_(0) = 640 min^(-1) " "N_(0) = (A_(0))/(lambda) = (640 x 30)/(0.693) = 2.8 xx 10^(4)`