Page 269 - Essentials of physical chemistry

Early Experiments in Quantum Physics 231

in the blackbody derivation. This added tremendous credibility to Planck’s blackbody
12, 398
proved to be useful.

DE (eV)
equation. Once again, the formula l (A ) ¼
4. In 1923, De Broglie proposed the seemingly strange concept that there is some sort of
mathematical pilot wave that can be used to describe the behavior of particles as given by
h h
. The matter wavelength of electrons was found to be similar in
the formula l ¼ ¼
p mv
size to chemical bonds leading to the idea that we need to learn ‘‘wave mechanics’’ to
understand the behavior of small particles such as electrons and nuclei.
5. In 1927, a key experiment by Davisson and Germer at Bell Laboratories in the United
States showed that a beam of electrons (particles) were diffracted from an annealed crystal
lattice of Ni atoms. The property of diffraction is a key characteristic of waves. This set the
stage to use ‘‘wave mechanics’’ to describe phenomena at the small scale of atoms and
molecules. In addition, a new technique of ‘‘low-energy electron diffraction’’ (LEED) was
developed to study material surfaces at the atomic level.

PROBLEMS
5 4
8p k
and compare the result to the
10.1 Insert the values of the constants into the formula for a ¼ 3 3
15h c
numerical value given in the text.
10.2 To show how the maximum of the Planck formula shifts with temperature set the first
x

derivative of r(l) with respect to l to zero and rearrange it to y(x) ¼ e x þ 1 ¼ 0
5

hc dy x 1
where ¼ x. Then ¼ e þ , which can be used in a Newton–Raphson iteration
l m kT dx 5

e x g þ 0:2x g 1
. Start with a good guess of
to find x from guessed values. x better ¼ x guess
0:2 e x g
½ Š
hc
where W is
x ¼ 5.0 and in a few iterations you will obtain Wein’s constant for l max T ¼
Wk B
the converged constant from the iteration. This problem ‘‘explains’’ why the color of a hot
object changes with the temperature as the maximum of the blackbody shifts with tempera-
ture. This effect and the constant value were known before Planck solved the problem so it is
important to show that Planck’s law agrees with previously known data.
10.3 On an Internet site called the ‘‘Physics Forum’’ at http:==www.physicsforums.com, a student
with the identification of ‘‘georgeh’’ and the topic title of ‘‘Stopping Voltage’’ says he has a
problem to find Planck’s constant and the work function, W f , from two data points for sodium
metal. He cites two points: a stopping potential of 1.85 V at 300 nm and another stopping
potential of 0.82 V at 400 nm. Convert the wavelengths to frequencies and plot the stopping
potential on the vertical axis and the frequencies on the horizontal axis. Extrapolate the line
between the two points to 0.0 Stopping Potential and calculate the W f value for sodium in
electron volts. Calculate the effective value of the slope of the two points and convert the units
to J s=frequency to compare the value to Planck’s constant.
10.4 Calculate the De Broglie wavelength of a baseball with a mass equal to 5.25 oz avoirdupois
traveling at 90 mph. compare that to the De Broglie wavelength of an electron traveling at
10% of the speed of light in vacuum which is comparable to the speed of a 1s electron in a
heavy atom.
10.5 Davisson and Germer also reported a strong diffraction intensity peak for 65 eV electrons
at an angle of 448 from the incident beam striking the face of their Ni crystal perpendicular
to the surface, which they assigned to the {1, 0, 0} plane of the Ni crystal structure.