Physics Group: Mei Mei Chan,
Travis Christolear, David Lao,
Alex Pearson, Chris Perez,
Luke Singleton, Colin Smith,
Faculty Advisors: Vladimir
Gasparyan, Thomas Meyer
OF PLANCKS CONSTANT
Plancks constant h is fundamental to the quantum theory of matter and radiation. This constant, introduced by Planck in 1900, revolutionized the world of modern
physics. It appears in Einsteins explanation of the photoelectric effect, in Bohrs model for the hydrogen atom, and Schrdingers equation among others. We
performed four experiments in which we obtain experimental values for h.
electrons are emitted when light is incident
on a metal surface. This is known as the
photoelectric effect 1).
In 1905 Albert Einstein applied Planck's
theory of the quantization of light and
explained the photoelectric effect in terms
of the quantum model using:
E h f = KEmax + .
E is the energy supplied by the quantum of
light or a photon, KEmax is the maximum
photoelectrons, and is the energy
needed to remove them from the surface of
the material (the work function).
Electrons can be emitted from the surface
of a material, in this case a metal, when
they are bombarded by photons with an
energy greater than the work function of
the metal. In the h/e experiment, photons
with energy hf are incident on the cathode
of a vacuum tube.
The electrons in the cathode use a
minimum of their energy to escape,
leaving the surface with a maximum energy
of KEmax. By applying a reverse potential V
between the anode and cathode, the
stopped. KEmax can then be determined by
measuring the minimum reverse potential
needed to bring the photoelectric current to
Thus, Einstein's relationship becomes hf =
Ve + , or
V = (h/e) f - ( /e)
A plot of V versus f for different frequencies
of light will yield a linear plot with a slope
(h/e) and a V intercept of (- /e). Since
intensity of the light does not affect the
kinetic energy of the photoelectrons, the
stopping potential remains constant for
frequency, it is confirmed that the photon
The Balmer Series
S t o p p in g P o t e n t ia l ( V )
Theory: Hertz discovered in 1887 that
Theory: In the 19th century it was discovered that
hot materials and gases emit light of characteristic
wavelengths. It was not until 1885 that a Swiss high
school teacher, Johann Balmer, found an empirical
relationship, called the Balmer formula for hydrogen
, for the wavelength
= RH ( - )
Stopping Potential vs. Frequency
f(x) = 0.4 x 0.4
where n = 3, 4, 5 ... and the Rydberg constant RH has
the value 1.097 107 m-1.
Nils Bohr gave a theoretical explanation for this
formula in 1913, based on the earlier discovery by
Max Planck, that light is quantized. The Bohr model of
the hydrogen atom2) yields a formula for RH
f(x) = 0.41 x 1.33
RH = 2 m k2 e4 2 / h3 c
f(x) = 0.44 x 1.49
Frequency ( 1014 Hz)Fig.
Fig. 2 LED experiment
Experimental Methods and Results: In the design of photoelectric
effect experiments we need a source of light of various wavelengths. In two of
these experiments performed, we utilized color filters to eradiate a metallic
surface with monochromatic light (Fig. 1). We should point out that the two filter
experiments differ only in the equipment used.
Alternatively, in a third
experiment, we use light emitting diodes (LEDs) to provide a source of
monochromatic photons (Fig. 2). In all three experiments we apply an electric
potential between the anode and cathode, as shown in Fig. 3. The resulting
electric field between the anode and cathode opposes the energy of the emitted
photoelectrons. The voltage required to stop the current flow is proportional to
the energy of the photoelectrons.
In Fig. 4 we have plotted the stopping potential for various sources of light vs. the
frequency of the incident light. We fitted the data to Eq. 1. In the case of the
two filter experiments we arbitrarily set to zero, which allows for a more
optically pleasing comparison of the three curves. Using the value of e = 1.602 x
C, we obtain the three values of h from the slopes of the three lines.
hfilter1 = 6.49 x 10-34 Jsec;
hfilter2 = 6.98 x 10-34 Jsec;
hLED = 6.52 x 10-34 Jsec
where m is the mass of the electron, e is its electric
charge, c is the speed of light and h is Planck's
constant. k is the Coulomb constant . We have
measured e and c in separate experiments during this
year's REVS-UP program. In this experiment we
measure RH, which allows us to compute h.
Experiment and Results.: We used a standard
optical spectroscope (see Fig. 5), in which light from a
hydrogen lamp is passed through a 300 lines/mm
grating. The wavelengths of the characteristic lines of
hydrogen (see. Fig. 6) are measured by determining
the angle of diffraction for each line with a telescope.
The relationship between wavelength and the
angle is given by d sin = m, where d is the
spacing between the lines of the grating and m = 1,
2, 3 ... We obtain
1 = 647 nm (red); 2 = 475.5 nm (green); 3 = 424
where the subscript of refers to the value of n in the
Balmer formula (Eq. 1). These results yield an average
value of RH = 1.124 107 m-1. Substituting the
values for m, k, e, and c into Eq. 2 we determine the
value of h = 6.57 10-34 J sec, in good agreement
with measurements of h obtained using the
photoelectric effect and the accepted value of h.
photoelectric effect to determine h in three different
experiments, each with different equipment, and,
using a totally different method, we also measure h in
a spectroscopic experiment. All experiment are in
good agreement with the accepted value of h = 6.626
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