Question

In a finite reactor, 10% of neutrons in a generation leaked out of the reactor while fast. Another 15% of the remaining neutrons leaked out of the system at thermal energies. The rest of the neutrons were absorbed in the reactor producing 1.5 neutrons per absorption. Calculate the multiplication factor for the reactor.

Answer 1

Multiplication factor = Neutrons produced in the present generation / Neutrons produced in the previous generation

Basis : Lets assume100 neutrons were produced in the first generation

It is said that 10% of these neutrons are leaked. This amounts to = 10% of 100 = 10 neutrons

This brings the neutron count to 100- 10 = 90 neutrons

Then, 15% of remaining neutrons are leaked out of the system at thermal energies . This amounts to = 15% of 90 = 13.5 neutrons.

Now, the neutron count in the system = 90 - 13.5 = 76.5

These neutrons were abosrbed producing 1.5 neutrons per absorption. Thus, neutrons produced in the second generation = 76.5*1.5 = 114.75 neutrons.

Multiplication factor = Neutrons produced in the present (second) generation / Neutrons produced in the previous (first) generation

Multiplication factor = 114.75/100 = 1.1475