7.2 Problems 387
7.47 The range of 5 MeVα’s in air at NTP is 3.8 cm. Calculate the range of 10 MeV
α’s using the Geiger–Nuttal law.
7.48 Mean range ofα-particles in air under standard conditions is given by the
formulaR(cm)= 0. 98 × 10 −^27 v 03 , wherev 0 (cm s−^1 ) is the initial velocity
of anα-particle of 5.0 MeV, find (a) its mean range (b) the average number of
ion pairs formed by theα-particle over the whole path as well as over its first
half, given that the ion pair formation energy of an ion pair is 34 eV.
7.49 Protons and deuterons are accelerated to the same energy and passed through
a thin sheet of material. Compare their energy losses.
7.50 Protons and deuterons lose the same amount of energy in passing through a
thin sheet of material. How are their energies related?
7.51 Determine the average radiative energy loss of electrons ofp= 2 .7GeV/c
crossing one radiation length of lead.
7.52 A beam of electrons of energy 500 MeV traverses normally a foil of lead
1/10th of a radiation length thick. Show that the angular distribution of
bremsstrahlung photons of energy 400 MeV is determined more by multiple
scattering of the electrons than by the angular distribution in the basic radiation
process.
7.2.4 ComptonScattering................................
7.53 In the Compton scattering, the photon of energyE 0 =hν 0 and momentum
P 0 =hν 0 /cis scattered from a free electron of rest massm. Show that
(a) the scattered photon will have energyE=E 0 /[1+α(1−cosθ)], where
θis the angle through which the photon is scattered andα=hν 0 /mc^2
(b) the kinetic energy acquired by the electron is
T=αE 0 (1−cosθ)/[1+α(1−cosθ)]
(c) tan (θ/2)=(1+α)tanφ, whereφis the recoil angle of the electron.
7.54 Calculate the maximum fractional frequency shift for an incident photon of
wavelengthλ= 1 A scattering off a proton initially at rest (Compton scatter- ̊
ing analogue with proton instead of electron)
[adopted from the University College, Dublin, Ireland 1967]
7.55 A 30 keV x-ray photon strikes the electron initially at rest and the photon is
scattered through an angle of 30◦, what is the recoil velocity of electron?
[University of New Castle 1966]
7.56 A collimated beam of 1.5 MeV gamma rays strikes a thin tantalum foil. Elec-
trons of 0.7 MeV energy are observed to emerge from the foil. Are these due
to the photoelectric effect, Compton scattering or pair production? Assume
that any electrons produced in the initial interaction with the material of the
tantalum foil do not undergo a second interaction.
[University of Manchester 1972]