PARTICLES |

Neutron
thermalization is important in the operation of nuclear reactors . A **collision**
may be **elastic** or **inelastic** between an incident neutron and
a target nucleus. An Inelastic collision results in the emission of gamma
rays.

**Q1)** __Explain__ why
gamma rays would be emitted in an **inelastic** collision.

Inelastic collisions that do not involve capture are important only for relatively fast neutrons

**Q2)** __Calculate__
the rest energy of a **neutron** . Hence determine the speed of a **1
MeV** neutron using (a) A **non - relativistic** formula for kinetic
energy.

(b) A **relativistic
**energy
formula.

Is it __necessary__ to use
relativistic
mechanics for analysing neutron scattering at this

energy ?

For the operation of nuclear reactors, slow moving neutrons in thermal equilibrium with their surroundings are required. This can be achieved by allowing neutrons to lose energy in elastic collisions. We now develop an analysis of this.

**Q3)** If a neutron of
mass **m _{1}** and incident speed

**(a)** **m _{1}
( u_{1} - v_{1} ) = m_{2} v_{2}**

**Q4) ^{ }**From
these two equations , show that

**Q5)** Hence show that
the **ratio** of __Kinetic Energy lost__ by object 1 in the collision
to its __initial kinetic energy__ is given by :

**Q6)** __Plot a graph__
of the kinetic energy ratio (y - axis) against the mass ratio (m_{2}
/ m_{1}) for mass ratios from 0 to 7.This should be a **SMOOTH**
curve with no discontinuities.

**Q7)** Letting the ratio
of masses be **R _{m}** and the ratio of energies as

**Q8)** If a neutron collides
with the following nuclei, what is the __% loss of KE__ for the neutron
in each case ?

It should now be clear that a neutron will lose energy most rapidly when scattered by lighter nuclei. 'Thermal' neutrons with an energy of just

**Q9)** Using your answer
from 8c , calculate how many head-on collisions with a ** ^{12}C**
nucleus are needed to 'thermalise' a

If **x ^{y} = z**
then

**Q10)** __Explain carefully__
why the **Moderator** in a nuclear reactor is made from 'light' water
, 'heavy' water (D_{2}0) or graphite .

**Q11)** If a moderator
was **NOT** used , how many collisions would be needed **per neutron**
to thermalise them if the target nuclei were ** ^{238}U** atoms
?

**Q12)** Explain q__ualitatively__
why your answers to Q8 are __maximum__ values and your answer to Q9
and Q11 are __minimum__ values.

Once thermal neutrons have been

**Q13)** If the **'Q' value**
of a nuclear reaction is defined as the difference between the rest energies
of the producs and the reactants, **( Q = ****Dmc ^{2}
)** , then

(i) Calculate the Q value of
the reaction shown in the diagram.

(ii) Calculate the *possible
*__range__ of **energies** and **frequencies** of the __gamma
rays__ produced.

Actually, in the fission of

**Q14)** If the **relativistic
kinetic energy**of a particle is given by the formula

then
**calculate**
the __kinetic energy__ of ONE of the emitted neutrons, the __speed__
at which it is travelling and the __number of head on collisions__ with
moderator atoms that would be needed to thermalise it.

**Q15)** A reactor is a
very efficient source of energy.

Calculate the number of ** ^{235}U**
atoms in a

Hence show that this mass of
uranium **per day** would
__produce energy__ at the rate of

1 MW - 1 000 000 joules per
second.

This is the __equivalent__
of 2600 kg (2 600 000 g )of coal !