8.3 Solutions
447
8.92 Assuming that the elastic scattering of low energy neutrons is isotropic,
show that the mean energy of the neutron after each collision will be
E f = ( A
2
+ 1)E i /(A + 1)
2
where A is the mass number of the target nucleus. Determine the number of
collisions needed to thermalize fission neutrons (2 MeV) in graphite ( A = 12).
8.2.15 Fusion
8.93 Determine the range of neutrino energies in the solar fusion reaction, p + p →
d + e
+
+ ν. Assume the initial protons have negligible kinetic energy and that
the binding energy of the deuteron is 2.22 MeV, m p = 938.3 MeV/c
2 and
m d = 1875.7 MeV/c
2 and m e = 0.51 MeV/c
2 .
8.94 If the kinetic energy of the deuterons in the fusion reaction D + D →
3
2 He +
n + 3.2 MeV can be neglected, what is the kinetic energy of the neutron?
8.95 (a) It is estimated that the deutrons have to come within 100 fm of each other
for fusion to proceed. Calculate the energy that the deuterons must possess
to overcome the electrostatic repulsion.
(b) If the energy is supplied by the thermal energy of the deutrons, what is the
temperature of the deuteron?
[e
2
/4πε 0 = 1.44 MeV fm, Boltzmann constant k = 1.38 × 10
−23 J K
−1 ]
(c) In (b) the actual required temperature is lower than the estimated value.
Explain the mechanism by which the fusion reaction may proceed.
8.96 In a fusion reactor, the D-T reaction with Q value of 17.62 MeV is employed.
Assuming that the deuteron density is 7×10
18 m
−3 and the experimental value
< σ DT · v > = 10
−22 m
3 s
−1 and that equal number of deuterons and tritons
exist in the plasma at energy 10 keV, calculate the confinement time if the
Lawson criterion is just satisfied.
8.3 Solutions
8.3.1 Atomic Masses and Radii
8.1 An ion of charge q will pick up kinetic energy, T = qV in dropping through a
P.D of V volts. In a magnetic induction B perpendicular to its path, the ion of
momentum p will describe a circular path of radius r given by
p = qBr =
√
2MT =
2MqV
M =
q B
2 r
2
2V
(1)
For the first ion, q = 1.6 × 10
−19 C, B = 0.08, r = 0.0883 m and V =
400 V. Substituting these values in (1) we get
M 1 = 9.98 × 10
−27 kg
447
8.92 Assuming that the elastic scattering of low energy neutrons is isotropic,
show that the mean energy of the neutron after each collision will be
E f = ( A
2
+ 1)E i /(A + 1)
2
where A is the mass number of the target nucleus. Determine the number of
collisions needed to thermalize fission neutrons (2 MeV) in graphite ( A = 12).
8.2.15 Fusion
8.93 Determine the range of neutrino energies in the solar fusion reaction, p + p →
d + e
+
+ ν. Assume the initial protons have negligible kinetic energy and that
the binding energy of the deuteron is 2.22 MeV, m p = 938.3 MeV/c
2 and
m d = 1875.7 MeV/c
2 and m e = 0.51 MeV/c
2 .
8.94 If the kinetic energy of the deuterons in the fusion reaction D + D →
3
2 He +
n + 3.2 MeV can be neglected, what is the kinetic energy of the neutron?
8.95 (a) It is estimated that the deutrons have to come within 100 fm of each other
for fusion to proceed. Calculate the energy that the deuterons must possess
to overcome the electrostatic repulsion.
(b) If the energy is supplied by the thermal energy of the deutrons, what is the
temperature of the deuteron?
[e
2
/4πε 0 = 1.44 MeV fm, Boltzmann constant k = 1.38 × 10
−23 J K
−1 ]
(c) In (b) the actual required temperature is lower than the estimated value.
Explain the mechanism by which the fusion reaction may proceed.
8.96 In a fusion reactor, the D-T reaction with Q value of 17.62 MeV is employed.
Assuming that the deuteron density is 7×10
18 m
−3 and the experimental value
< σ DT · v > = 10
−22 m
3 s
−1 and that equal number of deuterons and tritons
exist in the plasma at energy 10 keV, calculate the confinement time if the
Lawson criterion is just satisfied.
8.3 Solutions
8.3.1 Atomic Masses and Radii
8.1 An ion of charge q will pick up kinetic energy, T = qV in dropping through a
P.D of V volts. In a magnetic induction B perpendicular to its path, the ion of
momentum p will describe a circular path of radius r given by
p = qBr =
√
2MT =
2MqV
M =
q B
2 r
2
2V
(1)
For the first ion, q = 1.6 × 10
−19 C, B = 0.08, r = 0.0883 m and V =
400 V. Substituting these values in (1) we get
M 1 = 9.98 × 10
−27 kg