7.2 Problems 385
7.26 The following counting rates (in arbitrary units) were obtained whenαparti-
cles were scattered through 180◦from a thin gold (Z=79) target. Deduce a
value for the radius of a gold nucleus from these results.
Energy ofα
particle
(MeV)8 12182226273034
Counting rate 91,000 40,300 18,000 12,000 8,400 100 12 1.1
[University of Manchester]7.27 If a silver foil is bombarded by 5.0 MeV alpha particles, calculate the deflec-
tion of the alpha particles when the impact parameter is equal to the distance
of closest approach.
7.28 Calculate the minimum distance of approach of an alpha particle of energy
0.5 MeV from stationary^7 Li nucleus in a head-on collision. Take the nuclear
recoil into account.
7.29 A narrow beam of alpha particles with kinetic energyT=500 keV falls nor-
mally on a golden foil incorporating 1. 0 × 1019 nuclei cm−^3. Calculate the
fraction of alpha particles scattered through the anglesθ<θ 0 = 30 ◦
7.30 A narrow beam of protons with kinetic energyT= 1 .5 MeV falls normally
on a brass foil whose mass thicknessρt= 2 .0mgcm−^2. The weight ratio
of copper and zinc in the foil is equal to 7:3. Find the fraction of the protons
scattered through the angles exceedingθ = 45 ◦. For copper,Z =29 and
A= 63 .55 and for zincZ=30 andA= 65. 38
7.31 The effective cross-section of a gold nucleus corresponding to the scattering
of monoergic alpha particles at angles exceeding 90◦is equal toΔσ= 0 .6kb.
Find (a) the energy of alpha particles (b) the differential cross-sectionσ(θ)at
θ= 90 ◦
7.32 Derive Darwin’s formula for scattering (modified Rutherford’s formula which
takes into account the recoil of the nucleus).
7.2.3 Ionization, Range and Straggling .....................
7.33 Show that the order of magnitude of the ratio of the rate of loss of kinetic
energy by radiation for a 10-MeV deuteron and a 10-MeV electron passing
through lead is 10−^7.
7.34 Suppose at the sea level the central core of an extensive shower consists
of a narrow vertical beam of muons of energy 60 GeV which penetrate the
interior of the earth. Assuming that the ionization loss in rock is constant at
2MeVg−^1 cm^2 , and the rock density is 3.0gcm−^3 , find the depth of the rock
through which the muons can penetrate.
7.35 Show that deuteron of energyEhas twice the range of proton of energyE/2.