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Sph 202: Modern Physics Question Paper

Sph 202: Modern Physics

Course:Bachelor Of Education Science In Physics And Chemistry

Institution: Kenyatta University question papers

Exam Year:2012

KENYATTA UNIVERSITY

UNIVERSITY EXAMINATIONS 2010/2011
MAY INTAKE SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE

SPH 202: MODERN PHYSICS

DATE: WEDNESDAY 10TH AUGUST 2011 TIME: 2.00 P.M. – 4.00 P.M.

INSTRUCTIONS
Answer Question ONE and any THREE other questions.
Question One carries 28 marks while the other questions have 14 marks each.
Constants:
h = 6.6 x 10-34 js, c = 3.0 x 108 m/s, leV = 1.6 x 10-19 J, me = 9.1 x 10-31 kg,
e = 1.6 x 10-19 C
Question One (28 marks)
a) What is an inertial frame of reference. (1 mark)
b) Discuss the postulates of the special theory of relativity (4 marks)
c) What is Photoelectric effect (2 marks)
d) Describe a black body. (2 marks)
e) An Electron in a hydrogen atom jumps from the n = 5 to n = 3 level
i) Is a photon absorbed or emitted in this process? (2 marks)
ii) Calculate the energy of the photon. State whether it is in the visible
region
f)Calcium has a work function of 2.7eV, what is the maximum wavelength that will
cause emission from calcium. (3 marks)
g) Calculate
i) The speed
ii) The de Broglie wavelength of an electron which has been accelerated from
rest through a p.d. of 250V. (4 marks)
h) An alien spaceship streaks past FSU football stadium along the direction of play at
0.6c (as measured by the players on the field). A football field is 120 yards long and
55 yards wide. Eager to learn about Earth games, an alien on the spaceship makes
some measurements. Conveniently, the alien has already studied Earth units of
measurement
i) What is the length of the field according to the alien? (2 marks)
ii) What is the width of the field according to the alien? (2 marks)
iii) The alien has a television and watches the game which begins at 1:30 p.m.
EST and ends at 4:30 p.m. EST. How much time has elapsed according to the
alien? (3 marks)

Question Two (14 marks)
(a) Cosmic ray photons from space are bombarding your laboratory and smashing
massive objects to pieces! Your detectors indicate that two fragments, each of mass
m0, depart such a collision moving at 0.6c at 60o to the photon’s original direction of
motion.
(i) In terms of m0 and c, what is the energy of the cosmic ray photon? (4 marks)
(ii) In terms of m0, what is the mass m of the particle being struck (assumed
initially stationary) (2 marks)
(b) (i) The solar spectrum has the approximate shape of a black body. The peak
intensity is found at a wavelength of 4700Ao. Calculate the surface
temperature of the sun (1 mark)
(ii) Show that the energy of an electron is given by 8 n h
Where n = 1, 2, 3 (7 marks)

Question Three (14 marks)
(a) Sodium has a work function of 2.3eV. Calculate
(i) Its threshold frequency
(ii) The maximum velocity of photoelectrons produced when the sodium is
illuminated by light of wavelength 5 x 10-7m
(iii) The stopping potential with light of this wavelength. (4 marks)
(b) (i) Sketch the Zeeman Effect, the energy level diagram that shows the expected
splitting of 3s and 2p state in the presence of an external magnetic field.
Ignore spin. (3 marks)
(ii) What are the selection rules for transitions governing the l and m quantum
numbers. (2 marks)
(iii) Indicate all allowed transitions from each ml states of 3s level to the 2p level
(2 marks)
(iv) How many different energies are emitted? (3 marks)

Question Four (14 marks) whose origins coincide at
time t = 0s and whose Cartesian coordinate axes are parallel. Suppose that the
origin of the frame moving with velocity v ciˆ

relative to the origin of S.
(i) Write the Galilean transformations that relate (x, y, z, t)
(2 marks)
(ii) Write the Lorentz transformations that relate (x, y, z, t)
(2 marks)
(iii) Suppose an event 1 E occurs at (2 ,3 ,4 ,0 ) 1 1 1 1 x y z t m m m s and another event 2 E occurs at ( , , , ) (3 ,4 ,5 ,1 ) 2 2 2 2 x y z t m m m s . Using both Galilean and Lorentz transformations determine the coordinates of these two events
in (8 marks)
(iv) How far apart (both spatially and temporally were these two events as
measured by an observer stationary in S. (2 marks)

v) Using both Galilean and Lorentz transformations, determine how far apart)
both spatially and temporally) these two events were, as measured by an
observer stationary in S’ (2 marks)

Question Five (14marks)
a) A photon and a particle have the same wavelength, compare
i) Their linear momenta (1 mark)
ii) The photon’s energy and the particle’s total energy (1 mark)
iii) The photon’s energy and the particle’s kinetic energy (1 mark)
b) Show that the de Broglie wavelength of a particle of rest mass m0 and kinetic energy
K is given by (2 marks)
c) Show that if the total energy of a moving particle greatly exceeds its rest energy, its
de Broglie wavelength is nearly the same as the wavelength of a photon with the
same total energy. (2 marks]
d) A proton and electron have the same kinetic energy. Compare the wavelength and
phase and group velocities of their de Broglie wave (2 marks)
e) i) Show that the phase group velocities is a particle of rest mass mo and de Broglie wavelength(2 marks)
ii) Compare the group and phase velocities of an electron with the de Broglie
wavelength 1 x 10-13m (2 marks)
iii) Verify the statement that, is the phase velocity is the same for all wavelengths
of a certain wave phenomenon, the group and phase velocities are the same.
(1 mark)

Sph 202: Modern Physics Question Paper

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