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The work
by Planck on black-body radiation showed that light of frequency f
occurred in quanta , termed photons, the energy of a photon being
E
= hf where h is a constant.
Q1)
Give a typical wavelength, frequency and energy for
photons in each part of the Electromagnetic spectrum. State the energies
in electronvolts as well as joules.
Q2)
Which famous experiment confimed the equation E = hf ? What
else did it show ?
Q3)
If the energy of a photon obeys the relativistically invariant
energy equation
E2 = c2(p2 + M2c2)
then
show that if the momentum of a photon is given by
p = E/c that the
rest
mass M of a photon must be zero.
(a) Photons may be created and destroyed in arbitrary numbers in Eg: Bremsstrahlung.
(b) Black body radiation shows that photons are 'Bosons' which means they do not have to obey the exclusion principle. In the language of quantum mechanics this means that the wave functiony of a system of photons must be symmetric if any two are interchanged.
(c)
The Spin of the photon is 1. The square of its angular momentum
is given by
2h2 = 1(1+1)h2
In general spin is given by s(s+1)h2. There are two spins which correspond to the two types of circularly polarised light.
Q4)
Explain what is meant by bremsstrahlung .
Q5)
What is the exclusion principle?
Q6) Explain what is meant by
(a) Unpolarised light.
(b) Plane polarised light.
(c)
Circularly polarised light .
Include a labelled diagram for each of your answers.
How can there be two types of circularly polarised light ?
ELECTRONS:
The electron
was the first elementary particle to be discovered. It has negative charge
'e'
which is (-1.6x10-19 C) and a low rest mass
(Me
= 9.1x10-31 kg).The mass of the electron may be measured
in terms of its rest energy (0.511 MeV).
Q7)Briefly
outline the experiment which determined the ratio e/Me
for an electron. Why does the value measured not give consistent results
?
(Hint:
SpecialRelativity).
Which
experiment
determined the value of 'e'
?
The study
of atomic spectra showed that the electron has two spin states.
The number of spin states for a particle of non-zero rest mass is 2s
+ 1 so the electron has spin 1/2. This means that the electron
is a Fermion - it obeys the exclusion principle and its wave
function is antisymmetric
Q8)
If the wave function of two electrons in different states is given
by
Y(1,2) = y(1)f(2) - f(1)y(2)
then
show that the two electrons cannot occupy the same state.
Electric
charge is conserved and so electrons cannot be arbitrarily created
or destroyed. The creation or annihilation of an electron must always be
accompanied by creation or destruction of some other particle.
Q9)
If the de Broglie wavelength is given by l
= h / p then show that if
kinetic
energy is denoted by T , that the relativistic invariance of
total
energy leads to
You may like to refer
to Special Relativity Equations
page.
Q10)Show
that the de Broglie wavelength of an electron with kinetic energy 10eV
is 3.9 x 10-10 m.
Q11)Calculate
the de Broglie wavelength for an electron that has kinetic energy equal
to its rest energy.
Q12)Briefly
describe one simple situation in which electrons are modelled as waves
and one where they are modelled as particles.