August 2010 PH110
UNIVERSITY OF ZIMBABWE
DEPARTMENT OF PHYSICS
BSc Part I
PH 110:ATOMIC AND NUCLEAR PHYSICS
Second Semester Examination: August 2010
Duration: Two Hours
Charge of an electron, e = 1.60×10-19 C
Rest mass of an electron m = 9.11×10-31 kg
Mass of a proton, mp = 1.007825 u
Mass of an alpha particle = 4.002603 u
Mass of a lithium atom = 7.016003 u
Rydberg constant, R = 1.097×107 m-1
Speed of light, c = 3×108 m s-1
Planck’s constant, h = 6.63×10-34 J s
Atomic mass unit, u = 1.66 × 10-27 kg
Mass-energy conversion factor, 1u = 931.5 MeV
1 eV = 1.602 × 10-19 J
Answer ALL parts of Section A and any THREE Questions from Section B. Section A
carries 40 marks and each question of Section B carries 20 marks.
1. (a) Describe an experiment which demonstrates that:-
(i) cathode rays travel in straight lines. [3]
(ii) cathode rays carry energy. [3]
(b) A beam of electrons passes undeflected through crossed electric and
magnetic fields of magnitude 3.8×103 W m-1 and 2.5 ×10-3 T, respectively.
(i) Calculate the velocity of the electrons. [3]
(ii) What is the radius of their path if the electric field is switched off? [3]
(c) When monochromatic light of wavelength 230 mm is incident on a metal
surface, the current in the photoelectric circuit falls to zero when a reverse
voltage of 1.64 V is applied. Calculate work function of the metal. [5]
(d) (i) Briefly discuss the Compton effect experiment [2]
. (ii) X-rays of wavelength 0.50 nm are scattered from a block of carbon.
The scattered x-rays are observed at an angle of 65° to the incident beam.
Calculate the wavelength and energy of the scattered beam. [4]
(e) Draw a well labeled energy level diagram of the hydrogen atom and on it
show the first three lines in the:
(i) Lyman series.
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August 2010 PH110
(ii) Balmer series.
(iii) Paschen series [5]
(f) In a Davisson and Germer electron diffraction experiment the electrons are
accelerated by a voltage of 54 V from rest. The first intensity maxima
occurs at an angle of 50° using a nickel crystal. If the rows of the atoms
of crystal are 2.5×10-10 m apart, calculate
(i) the wavelength of the electrons. [3]
(ii) the wavelength of the same electrons using de Broglie relationship.[3]
(g) Briefly discuss the Franck-Hertz experiment and explain why it is important.
In this experiment, mercury vapor emitted uv-light of wavelength 0.25 µm.
Calculate the corresponding energy emitted. [2]
SECTION B
2. (a) Describe the Rutherford model of the atom. [4]
(b) Discuss the results from Rutherford’s alpha scattering experiment and
explain how these results support his atomic model. [8]
(c) An alpha particle of energy 8.68 MeV approaches directly a gold nucleus
(atomic number = 79).
(i) Calculate the distance of closest approach. [4]
(ii) What is the impact parameter of another alpha particle of the same
energy which is deflected through 70°? [4]
3. (a) Define the terms
(i) endothermic reaction and [2]
(ii) exothermic reaction [2]
(b) (i) Explain what is meant by the binding energy of the nucleus. [4]
(ii) Determine the binding energy of the helium nucleus. [4]
(c) When Lithium is bombarded by a proton, two alpha particles are produced
as follows:-
1 1 7 3
H + Li → 4He2 + 4He2
Determine the Q-value of the reaction and state whether the reaction is
endothermic or exothermic. [3]
(d) (i) Define the three particles emitted in a radioactive decay. [3]
A freshly prepareed sample of a radioactive isotope has an activity of
10 mCi. After 4 hrs its activity is 8 mCi.
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August 2010 PH110
(ii) Find the decay constant and half life. [1]
(iii) How many atoms of the isotope were contained in a fresh sample? [1]
4. (a) Discuss the statement “x-ray emission is the inverse of photoelectric effect.”[6]
(b) Explain how a continuous x-ray spectrum is produced and deduce the
expression for the short wavelength limit. [6]
(c) X-rays of wavelength 8.2×10-11m are scattered from the atoms of a crystal.
The second order maximum in the Bragg reflection occurs when the angle
between the x-ray beam and the plane of the crystal is 23.5°. Calculate
(i) the spacing between adjacent planes. [4]
(ii) the total number of interference maxima obtained. [4]
5. (a) State the assumptions made by Bohr in formulating the theory of the
hydrogen line spectra. [4]
(b) Show that the permitted energies of an electron around the hydrogen
nucleus are given by:
13.6 eV
En = −
n2
Define all symbols used. [8]
(c) Calculate the frequency and the energy of the K α x-ray emitted from
the sulphur atom (Z =16). [8]
6. (a) State Heisenberg uncertainty principle for
(i) position and momentum. [2]
(ii) energy and time interval. [2]
(b) Discuss Heisenberg uncertainty principle for energy and time with
reference to the excited state and the ground state of an atom. [7]
(c) An electron is confined within a region with ∆x = 1 × 10-10m.
(i) Estimate the minimum uncertainty in the x-component of the
electron’s momentum. [4]
(ii) If another electron has a momentum equal to the uncertainty found
in (i) above, calculate the kinetic energy of the electron. [5]
END OF PAPER
