Question

It is desired to sample a nuclear power plant coolant system. The coolant contains N-16 radioactivity of 3 mCi/ml . It is desired to put a piping system that will delay the sample to allow the N-16 to decay to a level of 1 microcurie per ml. The velocity of the fluid in the pipe is 3 ft/s.

What is the minimum length of pipe required?

Answer 1

The half life of N16 = 7.13 s

now calculate the number of half life

assume initial concentration is C_A0 = 3 mCi /ml=

3*10^-3 Ci/ml

assume there is after n half life concentration is C_A = 1 micro curi / ml = 10^-6 Ci/ ml

C_A =( C_A0/2)ⁿ

substitute all the values in above expression

10^-6 Ci/ml = ( 3*10^-3 Ci/ml )ⁿ

take the ln of above expression and solve

n = 2.38

half life of N16 = 7.13 s

total time = 7.13 s * 2.38 = 16.9694 s

length of the pipe = velocity * time = 3 ft/s *16.9694 s = 50.9 ft

length of pipe= 50.9 ft