Physics 215
Winter 2002
Introduction to Modern Physics
Prof. Ioan Kosztin
March 21, 2001
Midterm Exam
This is a closed book exam. During the exam, you may only use a simple pocket
calculator. The duration of the exam is 1hour 15min.
Provide (at least) a one paragraph answer to the following questions:
1. [10pt] What is the special theory of relativity, and what are two principles on which
is based on?
2. [10pt] What is the photoelectric effect, and what are the laws which govern this
effect?
3. [10pt] What is the Compton effect, and how does it differ from the photoelectric
effect?
4. [10pt] What is the meaning of the particle-wave duality? How does this concept
apply to (a) light and (b) electrons?
5. [10pt] What is the Heisenberg uncertainty principle, and what is its physical
meaning?
6. [10pt] What is the Schrödinger equation, and what is the difference between (a)
the time-dependent and (b) the time-independent version of this equation?
Solve the following problems:
7. [20pt] An electron is trapped at a defect in a crystal. The defect may be modeled as
a one-dimensional, rigid-walled box (i.e., 1D infinite potential well) of width d=1.00 nm.
(a) By solving the corresponding time-independent Schrödinger equation, determine the
stationary states (i.e., energy eigenvalues and eigenfunctions) of the trapped electron.
(b) Sketch the wavefunctions and probability densities for the n=1 and n=2 states (i.e.,
for the ground state and the first excited state). (c) For the ground state (n=1), find
the probability that the electron is located between x1=0.15 nm and x2=0.35 nm, where
x=0 is the left side of the box. (d) Calculate the energies in electron volts of the n=1
and n=2 states. The electron mass is m=9.1x10-31 kg, and 1 eV=1.6x10-19 J.
Physics 215
Midterm Exam
8. [20pt] A 0.100 mA electron beam with kinetic energy 54.0 eV enters a sharply
defined region of lower potential where the kinetic energy of the electrons is increased
by 10.0 eV. What current is reflected at the boundary? (This simulates electron
scattering at normal incidence from a metal surface, as in the Davisson-Germer
experiment). The electron mass is m=9.1x10-31 kg, and 1 eV=1.6x10-19 J.
Hint: The reflection coefficient R for the scattering of an electron from a
potential step (i.e., U1 for x<0 and U2 for x>0) is given by R=[(k1-k2)/ (k1+k2)]2, where k1
(k2) is the wave vector of the incoming (transmitted) electron.
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