390
7 Nuclear Physics – I
7.2.6 Pair Production
7.75 Calculate the maximum wavelength of γ-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 two γ-rays of equal energy. What is the wavelength of
these γ-rays?
[University of Dublin 1969]
7.77 Show that electron–positron pair cannot be created by an isolated photon.
7.2.7 Cerenkov Radiation
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. Assume m π c
2
= 140 MeV; m μ c
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 −
1
β 2 μ 2
ωdω erg cm
−1 where βc is
the velocity, ze is the charge, μ is the refractive index of the medium and
ω/2π is 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 having β = 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 Ir was used in a M¨ 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 of Γ and the mean
lifetime of the excited state in
191 Ir.
7.82 An excited atom of total mass M at 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]
7 Nuclear Physics – I
7.2.6 Pair Production
7.75 Calculate the maximum wavelength of γ-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 two γ-rays of equal energy. What is the wavelength of
these γ-rays?
[University of Dublin 1969]
7.77 Show that electron–positron pair cannot be created by an isolated photon.
7.2.7 Cerenkov Radiation
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. Assume m π c
2
= 140 MeV; m μ c
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 −
1
β 2 μ 2
ωdω erg cm
−1 where βc is
the velocity, ze is the charge, μ is the refractive index of the medium and
ω/2π is 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 having β = 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 Ir was used in a M¨ 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 of Γ and the mean
lifetime of the excited state in
191 Ir.
7.82 An excited atom of total mass M at 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]