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TUTORIAL QUESTIONS – THURSDAY 15th MAY 2014

COMPLETE SOLUTIONS TO THE TUTORIAL QUESTIONS SET ARE BELOW.

1. A beam of photons is partially attenuated in passing through

a brick wall, which is thick. If the linear absorption coefficient is

and the incident photon flux is calculate

the energy deposition rate in Watts for each of wall.

Energy deposition rate ( ) is

To find the change in photon flux

We can use the linear absorption equation

And therefore

( )

Putting these back into the energy deposition rate equation gives

( )

( ) ( ) ⁄

To put into appropriate units

⁄

2.

i) If a person has a mass of and presents a total area of , calculate the maximum permissible incident radiation intensity for photons if the allowed dose rate is ⁄ . Data: Average absorption length for humans

Human linear absorption coefficient

We know the energy deposition rate equation

( )

However, we need the equation in terms of incident radiation intensity

( )

We are given the energy deposition rate in terms of allowed dose rate

⁄

To convert to appropriate units

⁄

Knowing the mass of a person is and the total area is we can find the

energy deposition rate

⁄

Putting this back into the rearranged equation we get

( )

( )

⁄

ii) If the above photon flux is present on the outside of the 1.5 m thick concrete shielding of a reactor core, calculate the photon flux at the inside of the shield if the linear absorption coefficient of concrete is

. We know the linear absorption equation

However, what was previously the incident radiation intensity is now the latter radiation intensity so we need to rearrange the above equation in terms of incident radiation intensity

Putting in the values

⁄

3.

A concrete wall thick reduces the intensity of a parallel beam of rays to an intensity . What is the total thickness of a concrete wall required to reduce the beam to 1% of ?

Data: Absorption coefficient of concrete

First of all we calculate the thickness of a concrete wall required to reduce the beam from to 1% of . We know the linear absorption equation

Rearranging into terms of and exchanging for

( ⁄ )

Knowing that

( )

We now need to add this value to the original thickness of a concrete wall required to reduce the beam from to .

4.

A fuelled fast reactor contains of

and has a maximum output of 600 MW (thermal). Calcualte the doubling time in years Data: Breeding ratio ( )

Energy release per fission ( ) Fission cross-section ( )

Absorption cross-section ( )

We know that the doubling time equation is

( )

Using Avagadros Constant we can find

⁄

, , , and are all given in the question. To calculate

⁄

⁄

Putting all the values back into the original equation

( )

( )( )( )

( )( )( )

Converting to appropriate units

5.

Fissile is to be used in combination with fertile

in a breeding

programme in which the atom ratio of

is 0.15. Determine the minimum breeding ratio for the process to ensure full consumption of

the .

We know the equation for the breeding ratio

We also know that in this combination we have

And in this ratio we have

is in terms of mass and we have the atom ratio. However, because the molar masses of these two isotopes are very close we can make the assumption that the atom ratio is the same as the mass ratio and thus

6.

Fissile is to be used in combination with fertile

in a breeding

programme which consumes all of the . If the breeding ratio is

0.92, calculate the mass ratio in which the two elements should be combined.

We use the same equation as in question 5

However, we now have the breeding ratio and are required to calculate the mass ratio

We know that in this combination of isotopes we have

If we take the mass of to be 1 we can find the mass ratio of thorium

0.087