Download Determination of Planck`s Constant

14 Sep 07
Planck.1
DETERMINATION OF PLANCK’S CONSTANT
This experiment deals with the quantization of electromagnetic radiation (in this case, light)
as demonstrated by the photoelectric effect. By determining the maximum energy of the
electrons emitted from a phototube for various frequencies of light, an attempt will be made to
verify the predicted relationship between maximum photo-electron energy and light frequency,
and values for Planck’s constant and the work function of the emitter of the phototube will be
determined.
Theory: The Photoelectric Effect
Late in the nineteenth century a series of experiments revealed that electrons are emitted
from a metal surface when it is illuminated with light of sufficiently high frequency. This
phenomenon is known as the photoelectric effect. It was found that the energy distribution of the
emitted electrons (called photo-electrons) is independent of the intensity of the light. A strong
light beam yields more photoelectrons than a weak one of the same frequency, but the average
electron energy is the same. The maximum photoelectron energy was found to depend on the
frequency of the light. At frequencies below a certain critical frequency characteristic of the
metal surface being illuminated, no electrons are emitted. Above this frequency the maximum
photoelectron energy, KEmax, increases linearly with increasing frequency.
i.e.
KEmax = h(ν – νo) = hν – hνo
where νo is the threshold frequency below which no photoemission occurs, and h is a constant.
The value of h, Planck’s constant, (6.626 × 10–34 J·s = 4.136 × 10–15 eV·s), is always the same,
whereas νo varies with the particular metal being illuminated. Also, within the limits of
experimental accuracy, there is no time lag between the arrival of light at the metal surface and
the emission of photoelectrons. These observations cannot be explained by the electromagnetic
theory of light.
In 1905 Einstein explained the photoelectric effect by assuming that light propagates as
individual packets of energy called quanta or photons. This was an extension of the quantum
theory developed by Max Planck. In order to explain the spectrum of radiation emitted by
bodies hot enough to be luminous, Planck assumed that the radiation is emitted discontinuously
as bursts of energy called quanta. Planck found that the quanta associated with a particular
frequency ν of light all have the same energy, E = hν, where h = 6.626 × 10–34 J·s
= 4.136 × 10–15 eV·s (Planck’s constant). Although he had to assume that the electromagnetic
energy radiated by a hot object emerges intermittently, Planck did not doubt that it propagated
continuously through space as electromagnetic waves. Einstein, in his explanation of the
photoelectric effect, proposed that light not only is emitted a quantum at a time, but also
propagates as individual quanta.
According to Einstein’s proposal, the empirical equation KEmax = hν – hνo is interpreted as
follows:
KEmax = the maximum photo-electron energy
hν
= the energy content of each quantum of the incident light
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hνo
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= the work function, ϕ, the minimum energy required to remove an electron from
the metal surface being illuminated
Thus Einstein’s explanation of the photoelectric effect is that it is a result of collisions
between photons (light quanta) of the incident light beam and electrons in the metal surface. In
the collision, the photon energy hν is absorbed by the electron. Some of this energy is then used
to overcome the binding energy of the electron to the metal, and the remainder appears as kinetic
energy of the freed electron. This quantum theory of light is totally contrary to the wave theory,
which predicts that light energy is distributed continuously throughout the wave pattern, and
which provides the sole means of explaining many optical effects such as diffraction and
interference. This wave-particle duality cannot be avoided; both theories are required to account
for the observed behaviour of electromagnetic radiation. The ‘true’ nature of light cannot be
described in terms of everyday experience, and both wave and quantum theories must be
accepted, contradictions included, as being closest to a complete description of light.
Apparatus:
The equipment consists of a high-intensity mercury vapour light source, a diffraction grating,
a set of interference filters, a phototube, an ultrahigh impedance amplifier and its associated
electronics, and a voltmeter. The diffraction grating and interference filters enable separation of
the light from the mercury source into prominent spectral lines of discrete wavelength (and hence
frequency), the phototube contains the metal surface to be illuminated, and the rest of the
equipment is used to determine the maximum kinetic energy of the photo-electrons emitted in the
phototube. Figure 1 is a picture of the equipment.
Figure 1
The phototube consists of two electrodes enclosed in an evacuated tube. One electrode (the
cathode) has a large photosensitive surface and is called the emitter. The other electrode (the
anode) is a wire and is called the collector. When the emitter is exposed to light, electrons are
ejected from its surface. Some of the emitted electrons strike the anode, causing the anode to
become negatively charged with respect to the cathode. When the anode potential (Vo) becomes
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sufficiently large, subsequent photoelectrons have insufficient kinetic energy to overcome the
potential difference, so no more electrons reach the anode and the anode potential stabilizes.
This occurs when KEmax = eVo. Vo is measured by the built-in high impedance amplifier and
displayed on the multimeter. Figure 2 is a schematic diagram of the phototube/amplifier.
Figure 2
Measuring Vo for various known discrete frequencies of light allows analysis of the relation
between KEmax and ν.
Procedure and Experiment:
NOTE:
For best results, this experiment should be done with the room lights off. Also, avoid
bumping the equipment, as proper alignment is crucial.
Turn on the mercury light source, the phototube/amplifier, and the digital voltmeter.
Set the digital multimeter to the 2 or 20 DCV setting, as necessary. (You will probably need to
use the 20 V setting for the violet lines.)
The six spectral lines to be measured are:
violet
violet
blue
green
yellow
red
365.0 nm
404.7 nm
435.8 nm
546.1 nm
578.0 nm (ave. of 577.0 nm and 579.1 nm)
623.4 nm
Filters are available for all but the 365.0 nm line. Using the provided holder the desired filter
should be positioned as close as possible to the aperture of the mercury light source.
For each of the first order spectral lines, measure Vo. Be sure to make a reasonable estimate of
the experimental error in each of your Vo values.
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Prior to taking each measurement, press the ‘push to zero’ button on the phototube/amplifier and
be sure to allow sufficient time for the voltmeter reading to stabilize.
Analysis:
Plot maximum photoelectron energy (KEmax = eVo) vs. light frequency. Remember to calculate
and include error bars for the energy values.
Does your graph agree with Einstein's equation
KEmax = hν – ϕ ?
Draw the best-fit line and the maximum-fit line through your data. Assuming the Einstein
equation is correct, determine values for h, Planck's constant, and ϕ, the work function, from
your graph. Compare your value of h (and its error range) with the accepted value of
6.626 × 10–34 J·s or 4.136 × 10–15 eV·s.