8.2 Problems 441
8.51 Consider the reaction^27 Al(p,n)^27 Si. The positrons from the decay of^27 Si are
observed and their spectrum is found to have an end – point energy of 3.5 MeV.
Derive the Q value of the (p,n) reaction, and find the threshold proton energy
for the reaction given that the neutron – proton mass difference is 0.8 MeV.
[University of Manchester 1963]
8.52 The Q value of the^3 H(p,n)^3 He reaction is− 0 .764 MeV. Calculate (a) the
threshold energy for appearance of neutrons in the forward direction (b) the
threshold for the appearance of neutron in the 90◦direction.
[University of Liverpool 1960]
8.53 When^30 Si is bombarded with a deuteron,^31 Si is formed in its ground state
with the emission of a proton. Determine the energy released in this reaction
from the following information:-
(^31) Si→ (^31) p+β−+ 1 .51 MeV
(^30) Si+d→ (^31) p+n+ 5 .10 MeV
n→p+β−+ν+ 0 .78 MeV
[University of London 1960]
8.54 The nucleus^12 C has an excited state at 4.43 MeV. You wish to investigate
whether this state can be produced in inelastic scattering of protons through
90 ◦by a carbon target. If you have access to a beam of protons of kinetic
energy 15 MeV, what is the kinetic energy of the scattered protons for which
you must look?
[University of Bristol 1966]
8.55 A thin hydrogenous target is bombarded with 5 MeV neutrons, and a detec-
tor is arranged to collect those protons emitted in the same direction as the
neutron beam. The neutron beam is replaced by a beam ofγ-rays; calculate
the photon energy needed to produce protons of the same energy as with the
neutron beam.
[Osmania University]
8.56 Protons of energy 5 MeV scattering from^105 B at an angle of 45◦show a peak
in the energy spectrum of the scattered protons at an energy of 3.0 MeV
(a) To what excitation energy of^105 B does this correspond?
(b) What is the expected energy of the scattered protons if the scattering is
elastic?
8.57 Calculate the energy of protons detected at 90◦when 2.1 MeV deutrons are
incident on^27 Al to produce^28 Al with an energy differenceQ= 5 .5MeV.
[Royal Holloway University of London 1998]
8.58 The reaction^2 H+^1 H→^3 He+γ+ 5 .3 MeV occurs with the deuterons and
proton at rest. Estimate the energy of the helium nucleus.
If the reaction occurs in a region of the sun where the temperature is about
- 7 × 107 K, estimate how close the deuteron and proton must approach for
fusion to occur.
[Osmania University]