Question

How long will it take for the radioisotope Rn-222 to decay to 54.2 g if the half-life of Rn-222 is 3.8235 days, starting with the following. (Isotopic mass of Rn-222 is 222.017570 g/mol.)

(

(a) 80.6 g Rn-222

(b) 10.6 mol Rn-222

Answer 1

Radioactive decay is an example for first order kinetics and for I order kinetics

K=0.693/t1/2

K= 0.693/3.8235= 0.181 day^-1

A. And for I order kinetics, K= (2.303/t)log(Ao/A)

t=(2.303/K)log(Ao/A)= (2.303/0.181)log(80.6/54.2)

=12.7log(1.48)= 12.7(0.170)= 2.16 days

B. Mass = no of moles X MW= 10.6x222.01757=2353.38 g

t= (2.303/0.181)log(2353.38/54.2)

= 12.7log(43.72)

=12.7(1.63)

t= 20.79 days