1000 Solved Problems in Modern Physics

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]