Question

It is estimated that the Chernobyl disaster released 6.0 MCi (activity of 2.22 x 10¹⁷ s^-1) of ¹³⁷Cs into the environment. The half-life of ¹³⁷Cs is 30.2 years. (a) Calculate the decay time of ¹³⁷Cs. (b) Calculate the number of nuclei N released. (c) Calculate the mass of ¹³⁷Cs released. (d) What is the activity of the Cs after 20 days?

Answer 1

a) decay time :

mean life of Cs=1/decay constant =half life/ln(2)

T=30.2/ln(2)

T=30.2/0.693

T=43.57 years

b) decay constant = ln(2)/ half life

Activity= decay constant*Number of nuclei

N=(2.22*10^17*30.2*365*24*3600)/0.693

N=3.050937350*10^26 nuclei

c) mass of Cs released = number of nuclei released* mass of one nuclei

M=3.050937350*10^26*137

M=4.18*10^37 amu

d) activity after 20 days:

A=decay constant * exp(-decay constant*t)

A=(0.693/30.2)*exp(-(0.693*20)/(30.2*365))

A=0.02294/exp(0.00125)

A=1.045697 year^-1

A=329.77 sec^-1