Irodov – Problems in General Physics

6.6. Nuclear Reactions

• Binding energy of a nucleus:
  Eb = ZmH ± (A Z) mn — M, (6.6a)

where Z is the charge of the nucleus (in units of e), A is the mass number, mil,

mn, and M are the masses of a hydrogen atom, a neutron, and an atom corres-

ponding to the given nucleus.

In calculations the following formula is more convenient to use:

Eb = ZAH -F (A — Z)A, — A, (6.6b)

where AH, An , and A are the mass surpluses of a hydrogen atom, a neutron,

and an atom corresponding to the given nucleus.

• Energy diagram of a nuclear reaction
  m M M m' M' Q (6.6c)
  is illustrated in Fig. 6.12, where m--+M and m'+M' are the sums of rest masses
  of particles before and after the reaction, -f• and f- are the total kinetic ener-
  gies of particles before and after the reaction
  (in the frame of the centre of inertia), E is
  the excitation energy of the transitional
  nucleus, Q is the energy of the reaction, E^ A 2
  and E' are the binding energies of the par-
  ticles m and m' in the transitional nucleus,

T

1, 2, 3 are the energy levels of the transi-

tional nucleus. filtM

• Threshold (minimum) kinetic energy
  of an incoming particle at which an endoer-
  gic nuclear reaction^ /77W11

Tth—

m+M

IQI (6.6d)

becomes possible; here m and M are the
masses of the incoming particle and the
target nucleus.
6.249. An alpha-particle with kinetic energy T = a 7.0 MeV is
scattered elastically by an initially stationary Li 6 nucleus. Find
the kinetic energy of the recoil nucleus if the angle of divergence
of the two particles is 0 = 60°.
6.250. A neutron collides elastically with an initially stationary
deuteron. Find the fraction of the kinetic energy lost by the neutron
(a) in a head-on collision;
(b) in scattering at right angles.
6.251. Find the greatest possible angle through which a deuteron
is scattered as a result of elastic collision with an initially stationary
proton.
6.252. Assuming the radius of a nucleus to be equal to R =
= 0.13 VA pm, where A is its mass number, evaluate the density
of nuclei and the number of nucleons per unit volume of the nucleus.
6.253. Write missing symbols, denoted by x, in the following
nuclear reactions:
(a) 13 1 ° (x, a) Be;

Fig. 6.12.