Question

6- A 400-μg sample of pure ²²⁶Ra (1600 years) is encapsulated. How long will it take for the activity of ²²²Rn (3.824 days) to build up to 100 µCi?

7- The decay chain of ¹³⁹Cs to ¹³⁹Ba to stable ¹³⁹La is observed from an initially pure sample of 1mCi of ¹³⁹Cs. The half-lives of ¹³⁹Cs to ¹³⁹Ba are 9.5 min. and 82.9 min. What is ¹³⁹Ba activity after 33.5 min?

8-In non-equilibrium state, the decay constant of the parent should be ……….the decay constant of the daughter.

9-The neutron absorbance cross section of control rods is…….. its value for the moderator.

10-The abundance of……….decreased in the enrichment process of uranium.

Answer 1

Decay reactions of 226-Ra and 222-Rn are given below

half life of 226Ra is 1600 years , half life of 222Rn is 3.824 days

For a series of Radioactive decay, number of atoms of Rn present at time t is given by

......................(1)

where 1 is decay constant of 226Ra

1 = ln2 / T1/2 = ln2/(1600 365 ) = 1.187 10-6 (day)-1

2 is decay constant of 222Rn

2 = ln2 / T1/2 = ln2/ 3.824 = 0.181 (day)-1

From the magnitude of decay constants , we get, ( 2 - 1 ) 2 and

Hence we rewrite eqn.(1) as

....................(2)

No = number of atoms in 400 g sample of 226Ra

No = ( 400 10-6 6.02 1023 ) /226 = 1.065 1018

N2 = number of 222Rn atoms required for 100 activity

dN/dt = 2 N2   , i..e., N2 = ( 100 3.7 104 24 3600) / 0.181 = 1.766 1012

Hence from eqn.(2) , we get .

By substituting valuesin above equation , we solve for t.

we can get t as , t = 1.73 day or 1 day 17 hours 30 min