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.
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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.
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 ?
Q3) If a neutron of
mass m1 and incident speed u1 collides
with a stationary nucleus, mass m2, show that for an
elastic , head - on collision:
(a) m1
( u1 - v1 ) = m2 v2
.
(b) m1
( u1 + v1 ) ( u1 - v1 ) = m2
v22
Q4) From
these two equations , show that u1 + v1 = v2
and hence 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 (m2
/ m1) for mass ratios from 0 to 7.This should be a SMOOTH
curve with no discontinuities.
Q7) Letting the ratio
of masses be Rm and the ratio of energies as Re
, and writing
Re = f ( Rm)
, prove by differentiating with the product or quotient rule
that Re is a Maximum when Rm
equals 1 .Hence deduce that the
most effective interchange
of energy occurs when incident and target particle have equal mass.Now
examine your graph again - is it correct ?
Q8) If a neutron collides with the following nuclei, what is the % loss of KE for the neutron in each case ?
Q9) Using your answer
from 8c , calculate how many head-on collisions with a 12C
nucleus are needed to 'thermalise' a 1 MeV neutron. You
may find the result
If xy = z then y log10 x = log10 z useful here.
Q10) Explain carefully
why the Moderator in a nuclear reactor is made from 'light' water
, 'heavy' water (D20) 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 238U atoms
?
Q12) Explain qualitatively
why your answers to Q8 are maximum values and your answer to Q9
and Q11 are minimum values.
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 = Dmc2
) , 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.
Q14) If the relativistic
kinetic energyof 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 235U atoms in a 1g sample.
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 !