Question

A 1 Ci source of radiation is a significant source. ^(238) U is an alpha emitter.

What mass of ^(238)U has an activity of 3 Ci?

Express your answer to two significant figures and include the appropriate units.

Answer 1

we know, half life time of U-238, T12 = 4.5 billion years

= 4.5*10^9 years

= 4.5*10^9*365*24*60*60 s

= 1.42*10^17 s

Activity, R = 3 Ci

= 3*3.7*1^10 Bq

= 10.11*10^10 Bq

we know, decay constant lamda = 0.693/T1/2

= 0.693/(1.42*10^17)

= 4.88*10^-18 s^-1

let N is the no of atoms present at the instant.

we know, R = lamda*N

N = R/lamda

= 10.11*10^10/(4.88*10^-18)

= 2.07*10^28

mass of uranium required, m = N*mas of uranium atom

= 2.07*10^28*3.983*10^-25

= 8.24*10^3 kg <<<<<<--------------Answer