384 7 Nuclear Physics – I
7.17 In the elastic scattering of deuterons of 11.8 MeV from 82 Pb^208 , the differen-
tial cross-section is observed to deviate from Rutherford’s classical prediction
at 52◦. Use the simplest classical model to calculate the closest distance of
approachdto which this angle of scattering corresponds. You are given that
for an angle of scatteringθ,disgivenby(d 0 /2) [1+cosec(θ/2)], whered 0
is the value ofdin a head-on collision.
[University of Manchester]
7.18 Given that the angle of scattering is 2 tan−^1 (a/ 2 b), where “a” is the least
possible distance of approach, andbis the impact parameter. Calculate what
fraction of a beam of 0.5 MeV deuterons will be scattered through more than
90 ◦by a foil of thickness 10−^5 cm of a metal of density 5 g cm−^3 atomic
weight 100 and atomic number 50.
[University of Liverpool]
7.19 An electron of energy 1.0 keV approaches a bare nucleus (Z=50) with an
impact parameter corresponding to an orbital momentum. Calculate the dis-
tance from the nucleus at which this has a minimum (take= 10 −^27 j-s,e=
- 6 × 10 −^19 Candm= 10 −^30 kg)
[University of Manchester]
7.20 A beam of protons of 5 MeV kinetic energy traverses a gold foil, one particle
in 5× 106 is scattered so as to hit a surface 0.5cm^2 in area at a distance 10 cm
from the foil and in a direction making an angle of 60◦with the initial direction
of the beam. What is the thickness of the foil?
[Saha Institute]
7.21 A narrow beam of alpha particles falls normally on a silver foil behind which
a counter is set to register the scattered particles. On substitution of platinum
foil of the same mass thickness for the silver foil, the number of alpha parti-
cles registered per unit time increases 1.52 times. Find the atomic number of
platinum, assuming the atomic number of silver and the atomic masses of both
platinum and silver to be known.
7.22 Derive an expression for the differential cross-section for energy transfer in
elastic collision between a heavy charged particle and an electron.
[University of London]
7.23 Ifσgis the geometrical cross-section (πR^2 ) for neutrons interaction with a
nucleus of charge Zand radiusR, then show that for positively charged
particles(+ze) the cross-section will decrease by a factor (1−R 0 /R), where
R 0 =zZe^2 / 4 πε 0 E 0 , andE 0 is the neutron energy.
7.24 Alphas of 4.5 MeV bombarded an aluminum foil and undergo Rutherford scat-
tering. Calculate the minimum distance of approach if the scattered alphas are
observed at 60◦with the beam direction.
7.25 If the radius of silver nucleus (Z=47), is 7× 10 −^15 m, what is the minimum
energy that the particle should have to just reach it? Give your answer in MeV.
[University of Manchester]