Download Department of Physical Sciences (Physics)

THE UNIVERSITY OF HULL
Department of Physical Sciences (Physics)
Level 4 Examination
May 2008
QUANTUM AND CLASSICAL PHYSICS: AN
INTRODUCTION
Friday 16 May 2008, 13.30 to 15.30
2 hours
Answer THREE questions, TWO from section A and ONE from section B.
Do not open or turn over this exam paper, or start to write anything until
told to by the Invigilator. Starting to write before permitted to do so may
be seen as an attempt to use Unfair Means.
Module 04175
CONTINUED
Page 1 of 6
SECTION A: QUANTUM PHYSICS I
1.
(i) Explain what is meant by the Photoelectric Effect.
[2 marks]
(ii) Describe briefly the apparatus used to study this effect and discuss the
main experimental observations making reference to appropriate graphs of
the results. Use these graphs to explain what is meant by:
(a) prompt emission
(b) the stopping potential
(c) the threshold frequency
[7 marks]
(iii) Very briefly indicate which features of these experimental observations
were difficult to explain using the classical wave theory of light. Discuss
Einstein’s quantum theory of light explaining what is meant by a photon.
Describe how a photon ejects a photoelectron with reference to an energy
level diagram for electrons in a metal, explaining what is meant by the work
function of a metal and stating Einstein’s photoelectric equation. Hence show
how the quantum theory of light can be used to account successfully for the
experimental observations in the graphs above.
[8 marks]
(iv) Orbiting satellites and spacecraft can become charged because the light
from the sun ejects electrons from their outer surface and they must be
designed to minimise this effect. If the skin is coated with Ni which has a work
function of 4.87eV, calculate the longest wavelength of the incident sunlight
which can eject a photoelectron. With this in mind comment on whether it
would it be preferable to use an alternative coating such as aluminium or
platinum which respectively have lower and higher work functions than Ni.
[3 marks]
[h = 6.63 x 10-34Js; c = 3 x 108 ms-1; charge on the electron,
e = 1.6 x 10-19C]
Module 04175
CONTINUED
Page 2 of 6
2.
(i) Einstein introduced the concept of the photon as a 'particle' of light.
Sketch the wave associated with the photon and after stating de Broglie's
hypothesis discuss and compare the photon wave and the de Broglie 'matter'
wave associated with a moving material particle. Referring to sketches of the
wave groups concerned explain the significance of the intensity of these
waves at any particular point and hence explain why the de Broglie wave is
called a probability wave. Give expressions for the energy and momentum of
a photon in terms of the frequency or wavelength of the wave and compare
these to de Broglie's hypothesis relating to a moving particle.
[6 marks]
(ii) Use de Broglie's hypothesis to calculate the wavelength associated with
the following particles:
(a) A meteorite particle of mass 1 x 10-5 kg moving with a speed of
10 km s-1.
(b) An electron moving with a speed of 107 ms-1.
Hence explain why de Broglie wave effects are only observable for
microscopic rather than macroscopic objects.
[6 marks]
(iii) In the domestic television tube the electrons are accelerated through a
potential of Vp. Ignoring any relativistic effects derive a suitable formula to
determine the de Broglie wavelength of such electrons and calculate this if
Vp = 25 kV0.
[4 marks]
(iv) Outline in very general terms the experiment of Davisson and Germer
which proved the validity of de Broglie’s hypothesis.
[4 marks]
[h = 6.63 x 10-34Js; charge on the electron e = 1.6 x 10-19 C ; electron mass
mo = 9.1 x 10-31 kg ; ]
Module 04175
CONTINUED
Page 3 of 6
3.
(i) Describe the Rutherford model of the atom giving the formula for the
balance of forces on the orbiting electron and discuss the experimental
evidence that led to this model replacing the earlier JJ Thomson ‘plum
pudding’ model.
[6 marks]
(ii) Explain the deficiencies of the Rutherford model which in turn made it
necessary to replace it with the Bohr model listing the main postulates on
which the Bohr model is based. Explain why both models apply to atoms with
only one electron or to atoms which effectively only have one electron.
[6 marks]
(iii) Given the equation for the balance of forces on the single orbital electron in
the Rutherford model for an atom of atomic number Z show that the
quantisation of the orbital angular momentum proposed in the Bohr model
results in the radius of the allowed orbits also being quantised according to:
r = oh2n2/mZe2
where n = 1,2,3….
[5 marks]
(iv) If the radius of the first Bohr orbit for hydrogen is 0.53 x 10-10 m determine
the corresponding orbital radius of the electron in the first Bohr orbit of singly
ionised helium.
[3 marks]
Module 04175
CONTINUED
Page 4 of 6
4.
(i) Define what is meant by the unified atomic mass unit (u). Given that
1u = 1.6605 x 10-27 kg, show that its energy equivalence is 931.5 MeV.
[3 marks]
(ii) Explain what is meant by the binding energy, EB, of a nucleus. Derive a
formula for EB by considering the energy equivalence of the nucleus on the one
hand and that of its constituent protons and neutrons on the other. Explain
briefly how the nucleus is held together against the Coulomb repulsion between
the positive charges on the protons contained within it discussing the role of the
strong nuclear force in this respect.
[6 marks]
(iii) Explain the significance of the three numbers A, Z, N used to characterise
a particular nuclide. Describe the four main radioactive decay processes which
occur by the emission of ,  and  radiation and by electron capture. Write
down the equations which show the relationship between the A, Z, N numbers
of the parent nuclide, the daughter nuclide and the particle emitted (or
absorbed) during these processes.
[7 marks]
.
(iv) A possible fuel for fusion power is deuterium-tritium. The deuteron-tritium
(d-t) reaction is given by the equation:
2H
+ 3H = 4He + n + Q where Q is the energy released in the reaction.
Calculate the magnitude of Q given the atomic masses below. Hence
show that this process does result in the release of energy.
2H
= 2.014102u; 3H = 3.016049u; 4He = 4.002603u;
Neutron Mass = 1.008665u
[4 marks]
[c =2.998 x 108 ms-1; charge on the electron, e = 1.6 x 10-19C]
Module 04175
CONTINUED
Page 5 of 6
SECTION B: MECHANICS, WAVES AND VIBRATIONS
5.
A batter hits a baseball so that it leaves the bat with an initial speed
vo = 37.0m/s at an angle  = 53.1º with respect to the horizontal . If
g = 9.80m/s2, find
(i) the position of the ball and the magnitude and direction of its velocity when
t = 2.0s;
[12 marks]
(ii) the time when the ball reaches the highest point of its path and the actual
height at this point;
[4 marks]
(iii) the range.
[4 marks]
6.
(i) A wave travelling along a string is described by an equation of the form
y = Asin(kx - t),
where A is the amplitude, k the wave number, and  the angular frequency. If
k = 72.1rad/m and  = 2.72rad/s, find the wavelength, period and frequency
of the wave.
[6 marks]
(ii) Define the phase velocity and the group velocity of a wave. Calculate the
phase velocity for the wave in (i) above.
[6 marks]
(iii) If the amplitude of the wave above is 3.27mm, show that the
displacement of a small segment of string located at x = 225mm at time
t = 18.9s is 1.92mm.
[8 marks]
Module 04175
END
Page 6 of 6