390 7 Nuclear Physics – I
7.2.6 Pair Production ....................................
7.75 Calculate the maximum wavelength ofγ-rays which in passing through matter,
can lead to the creation of electrons.
[University of Bristol 1967]
7.76 A positron and an electron with negligible kinetic energy meet and annihilate
one another, producing twoγ-rays of equal energy. What is the wavelength of
theseγ-rays?
[University of Dublin 1969]
7.77 Show that electron–positron pair cannot be created by an isolated photon.
7.2.7 CerenkovRadiation ................................
7.78 Pions and muons each of 150 MeV/c momentum pass through a transparent
material. Find the range of the index of refraction of this material over which
the muons alone give Cerenkov light. Assumemπc^2 =140 MeV;mμc^2 =
106 MeV.
7.79 A beam of protons moves through a material whose refractive index is 1.8.
Cerenkov light is emitted at an angle of 11◦to the beam. Find the kinetic
energy of the proton in MeV.
[University of Manchester]
7.80 The rate of loss of energy by production of Cerenkov radiation is given by
the relation−dW/dl=(z^2 e^2 /c^2 )∫(
1 −β (^21) μ 2
)
ωdωerg cm−^1 whereβcis
the velocity, ze is the charge,μis the refractive index of the medium and
ω/ 2 πis the frequency of radiation. Make an order of magnitude estimate of
the number of photons emitted in the visible region, per cm of track, by a
particle havingβ= 0 .9 passing through water. The fine structure constant
α=e^2 /c= 1 / 137
[University of Durham]7.2.8 Nuclear Resonance ................................
7.81 The 129 keV gamma ray transition in^191 IrwasusedinaM ̈osbauer experiment
in which a line shift equivalent to the full width at half maximum (Γ)was
observed for a source speed of 1 cm s−^1. Estimate the value ofΓand the mean
lifetime of the excited state in^191 Ir.
7.82 An excited atom of total massMat rest with respect to a certain inertial system
emits a photon, thus going over into a lower state with an energy smaller by
Δw. Calculate the frequency of the photon emitted.
[University of Durham 1961]