## Transcribed Text

Problem 1: If electromagnetic radiation with a photon energy of 20 meV impinges
on two slits spaced 0.1 mm apart, find the angle 0 between the center line and the 1st
minimum and 1st maximum of the resulting interference pattern.
Problem 2: A non-relativistic beam of electrons travels at 5% the speed of light and
impinges on a slit that is 0.05 um wide. Use modern units (e.g. eV, etc) to find the
angle 0 between the center line and 1st minimum of the resulting diffraction
pattern. How far away would you locate a detector so that the 1st minimum is
spaced 2 mm from the center line?
Problem 3: If a Cu Ka x-ray diffracts from a periodic crystal and the first maximum
is detected by a Geiger counter at 20 = 40°, then find the crystal spacing d of the
crystal.
Problem 4: The wave function for a free electron is given by y (x) = Acos(3x-t)
where the units of X are in nanometers. Find the wavenumber k (nm-¹), de Broglie
wavelength A, momentum term pc (in eV), and kinetic energy Ek (eV) of the electron
(use "modern" units).
Problem 5: Use the de Broglie relation to find A and k for electrons with kinetic
energy of 300eV.
Problem 6: If an electron moves between two barriers located 0.1 nm apart, find its
minimum energy (eV) due to the Heisenberg Uncertainty principle. To increase this
energy by a factor of 9, what should the new barrier distance be?
Problem 7: When a beam of electrons travels through a slit, there is an uncertainty
in the lateral position of the beam (i.e.slit width 4y) and an accompanying minimum
uncertainty in the transverse momentum Apy due to Uncertainty Principle. This
momentum uncertainty results in a spreading of the beam AY, where the spread
depends on the distance from the slit. Find the spread width of a beam traveling at
Vx = 106 m/s through a 100-m wide slit when it hits a plate located D = 50 m past
the slit.
Problem 8: A proton is known to be within an interval 6 fm (the radius of a large
nucleus). Roughly what is the minimum uncertainty in its velocity? (Treat this problem
as 1 -dimensional, and express your answer as a fraction of c.
Problem 9: An excited state of a certain nucleus has a lifetime of 5 X 10-18 S. Find the
minimum possible uncertainty in its energy.
Problem 10: Use Excel (or similar program) to graph the energy VS. momentum (E
VS.
pc)
relationship
for
a
photon
and
a
He
atom
(3728
MeV/c2).
Include
the
formula
for E VS. pc on each graph and use pc values from 0 to 1000 eV. Next, derive
the phase and group velocities of each particle. Which particle shows no dispersion?

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