CHEM 332
Physical Chemistry
Spring 2014
Problem Set 1
1.
Find the wavelength of an electromagnetic wave used to broadcast radio in the FM whose
frequency is 106.7 MHz.
2.
The Radiant Energy Density of a Blackbody in the interval  to  + d is denoted as:
f(,T) d
Using classical theory, Rayleigh & Jeans predicted f(,T) should be given by:
f(,T) =
As we discussed in class, the Rayleigh-Jeans Law led to the Ultraviolet Catastrophe.
Planck's solution to the problem gives:
f(,T) =
a) Show that when  is large, Planck's Law reduces to the Rayleigh-Jeans Law. Recall:
b) Show that f(,T) approaches zero as  approaches zero.
3.
Convert Planck's Law for Blackbody Radiation f(,T) into a function of frequency, R().
Show that max, the frequency at which the blackbody radiation is a maximum, is:
max
= kTx/h
where x is the non-zero solution of:
x + 3e-x = 3
This implies max increases linearly with T.
4.
Find the energy of photons with wavelengths at the extremes of the visible spectrum;
400nm (violet) and 700 nm (red).
5.
Data for the Stopping Potential (Vo) versus Wavelength () for the Photoelectric Effect
using Sodium are:
 [nm]
200
300
400
500
600
Vo [volts]
4.20
2.06
1.05
0.41
0.03
The Stopping Potential is the potential below which no electrons can reach the anode in a
photoelectric apparatus. This is related to the maximum Kinetic Energy of the emitted
electrons by:
KEmax = (1/2 mv2)max = eVo
Plot these data so as to obtain a straight line and from your plot find the Work Function, the
Threshold Frequency, and the ration h/e.
6.
Let's assume the wave model for light is correct and estimate lag time required for the
Photoelectric Effect to kick in. Let the intensity of the incident radiation be 0.01 W/m2.
Assuming that the area of an atom on a metal's surface is 1 Å2, find the energy per second
falling on an atom. If the Work Function for the metal is 2 eV, how long will it take for
this much energy to fall on one atom and eject an electron?
7.
Find the wavelength of a 2 ton truck traveling at 65 mph.
8.
Use Balmer’s formula to determine the wavelengths of the three spectral lines beyond the
4th Balmer line (violet) in the Balmer Series.
9.
Use Rydberg’s formula to determine the wavelengths for the first three lines Brackett
Series (nf = 4) of the spectrum of the Hydrogen atom. Determine the Series Limit for the
Brackett Series. Compare this with the wavelength of the first Paschen Line (nf = 3) .
10.
The Ritz Combination of Principle can be considered to be a statement of energy
conservation. Explain.
12.
The Bohr model of the Hydrogen atom predicts the radii of the electron's orbit is given by:
r = ao n2
where ao equals 0.529 Angstrom.
Determine the circumference of the second Bohr orbit of the Hydrogen atom. Use this to
determine the wavelength of the electron in this orbit. Finally, determine the velocity of
the electron in this orbit. What percentage of the speed of light is this velocity?
13.
Calculate the wavelength of the ni = 2 to nf = 1 transition for Positronium. In the Bohr
Model of Positronium, the mass of the electron must be replaced by the reduced mass of
the system. Why?
14.
Some general questions:
a) Show that 1/i = -i.
b) True or False: if z = z*, then z must be a real number.