Determining Planck’s Constant
Purpose:
To experimentally determine Planck’s constant h by measuring the kinetic energy of photons propagating at different
frequencies and to confirm the independence of intensity on the energy of the emitted photoelectrons.
Introduction:
As the century came to a close in the late 1800s, physicists discovered inconsistencies that could not be easily explained
with classical physics. One such problem resulted from unexplained observations of the blackbody radiation spectrum.
In 1901, Max Planck proposed a law of radiation making the assumption that a light wave of frequency f is due to
oscillating molecules whose energy can only take on discrete values. He claimed that these allowed energy levels are
separated by the amount
E = hf
(1)
−34
In this equation h refers to a constant called Planck’s constant and has the value of 6.626×10 J s. This assumption
represents a radical departure from classical physics in which any energy is allowed for oscillating molecules. When
Planck put forth his theory, his estimate of h was considered a mathematical value contrived to fit an explanation
to observation rather than a discovery of a fundamental constant in its own right. It was not until later that
the significance of Planck’s constant was further fortified with experimental results, particularly from Einstein’s
theoretical explanation of the photoelectric effect. In this experiment we will verify Planck’s constant using our own
quantitative measurements of the photoelectric effect.
In the photoelectric effect, light strikes a material, causing electrons to be emitted. The classical model predicted
that as the intensity of incident light was increased, the amplitude and thus the energy of the wave would increase.
This would then cause more energetic photoelectrons to be emitted. The new quantum model, however, predicted
that higher frequency light would produce higher energy photoelectrons, independent of intensity, while increased
intensity would only increase the number of electrons emitted (i.e. higher current called the photoelectric current).
In the early 1900’s it was found that the kinetic energy of the electrons emitted in the photoelectric effect
was dependent on the wavelength, or frequency, and independent of intensity, while the magnitude
of the photoelectric current was dependent on the intensity as predicted by the quantum model.
Albert Einstein proposed the quantum model of light and explained the key experimental features of the photoelectric
effect using his famous equation for which he received the Nobel prize in 1921:
E = hf = KEmax + Wo
(2)
where KEmax is the maximum kinetic energy of the emitted photoelectrons, and Wo , the work function, is the energy
needed to remove them from the surface of the material. E is the energy supplied by the quantum of light known as
a photon.
We will be able to test the independence of intensity
on the energy of the emitted photoelectrons as well as
experimentally determine Planck’s constant in this laboratory. In this apparatus a light photon with energy hf
is incident upon an electron in the cathode of a vacuum
tube. The electron uses a minimum of its energy, Wo , to
escape the cathode, leaving it with a maximum energy
of KEmax in the form of kinetic energy. The emitted
photoelectrons can reach the anode of the tube and be
measured as electric current. However, by applying a reverse potential Vo between the anode and cathode, the
current can be stopped. KEmax can be determined by
measuring the minimum reverse potential needed to stop
the electrons and reduce the current to zero. Relating
kinetic energy to the stopping potential gives the equation:
1
KEmax = eVo
(3)
hf = eVo + Wo
(4)
h
Wo
Vo =
f−
e
e
(5)
Using Einstein’s equation,
When solved for Vo the equation becomes:
If we plot Vo vs f for different frequencies of light the slope is equal to h/e. Thus using the accepted value for e, of
1.602 ×10−19 coulombs, we can determine Planck’s constant h.
Laboratory Procedure:
Part I.I - Taking Direct Measurements
1. Make a table in your notebook of values to be measured.
2. The equipment should be set up as shown in the diagram below. Turn on the h/e apparatus.
As a source of monochromatic light it is customary to use a mercury bulb. The most readily available lines
are:
Color
Frequency (Hz)
Wavelength (nm)
5.187 x 1014
578.0
Green
14
5.490 x 10
546.1
Blue
6.879 x 1014
435.8
14
Yellow
Violet
7.409 x 10
404.6
Ultraviolet
8.203 x 10 14
365.5
2
Although invisible, the ultraviolet light can be seen on the white reflective mask of the h/e apparatus, which
is made of a special fluorescent material. The ultraviolet line will appear as blue and the violet line will also
appear bluish.
3. You can see these five colors in two orders of the mercury light spectrum as shown in the diagram below. Focus
the light from the mercury light source onto the slot in the white reflective mask on the h/e apparatus so that
only yellow spectral line from the first order falls on the opening of the mask. Notice that the grating is blazed
to produce a brighter spectrum on one side, make sure you have aligned the correct side. Your instructor can
give further details on this step.
4. Tilt the light shield of the apparatus out of the way to reveal the white photodiode mask inside the apparatus.
Align the system by rotating the h/e apparatus on its support base so that the same color light that falls on
the opening of the light screen falls on the window in the photodiode mask with no overlap of color from the
other spectral bands.
5. Adjust the lens/grating assembly on the mercury lamp until you achieve the sharpest image of the aperture
centered on the hole in the photodiode mask. Return the light shield to its closed position.
6. Place the yellow filter onto the mask then again rotate the h/e apparatus to maximize the voltage. The filters
have frames with magnetic strips that mount on the outside of the reflective mask and prevent the ambient
room lighth/efrom
interfering with the lower frequency green and yellow lines from the mercury
spectrum. Only
Apparatus and h/e Apparatus Accessory Kit
012-04049J
use the respective filters on the green and yellow spectral lines.
White
1s
t
O
rd
er
2n
d
Ultraviolet
O
rd
er
Violet
Blue
3r
d
Green
Yellow
O
rd
e
r
2nd and 3rd Order Overlap
Green & Yellow Spectral lines
in 3rd Order are not Visible.
Color
7.
8.
Frequency (Hz)
Wavelength (nm)
All values except wavelength for yellow line are
Yellow
578
Record the stopping
potential,
Vo , with
the DVM
yellow line5.18672E+14
in your notebook.
from Handbook
of Chemistry
and Physics,
46th ed. for the
Green
5.48996E+14
546.074
The wavelength of the yellow was determined exDetermine δVoperimentally
based onusing
thea 600
precision
of the DVM. If this
value is6.87858E+14
not stable, consider
line/mm grating.
Blue
435.835
varies in determining
NOTE: δV
Theo .yellow line is actually a doublet
with wavelengths of 578 and 580mm.
δVo
9. Determine the fractional uncertainty (
Vo
) for this
Violet
Ultraviolet
measurement
7.40858E+14
how much the value
404.656
8.20264E+14
365.483
and
record this in
your
data table.
Figure 10. The Three Orders of Light Gradients
10. Repeat steps 3–9 for each color for a total of five different stopping potentials for the first order.
Using the Filters
14. Press the “PUSH TO ZERO” button on the side panel
11. Using the values
forApparatus
the frequencies
ofaccumulated
each spectral
line given in the table above, plot a graph of Vo vs f .
of the h/e
to discharge any
poThe (AP-9368) h/e Apparatus includes three filters: one
Determine the
slope
and
calculate
Planck’s
constant.
tential in the unit's electronics. This will assure the ApGreen and one Yellow, plus a Variable Transmission Filter.
paratus records only the potential of the light you are
The filter frames have magnetic strips and mount to the out-
12. Compare your
experimental
value
h and
theoretical
value of 6.626 ×10−34 J s.
measuring.
Note that the
outputof
voltage
will the
drift with
side of the White Reflective Mask of the h/e Apparatus.
the absence of light on the photodiode.
15. Read the output voltage on your digital voltmeter. It is
Part I.II - Taking
Direct Measurements
a direct measurement of the stopping potential for the
photoelectrons. (See Theory of Operation in the Technical Information section of the manual for an explanation of the measurement.)
➤ NOTE: For some apparatus, the stopping potential will temporarily read high and then drop down
to the actual stopping potential voltage.
3
Use the green and yellow filters when you're using the
green and yellow spectral lines. These filters limit higher
frequencies of light from entering the h/e Apparatus. This
prevents ambient room light from interfering with the
lower energy yellow and green light and masking the true
results. It also blocks the higher frequency ultraviolet light
from the higher order spectra which may overlap with
lower orders of yellow and green.
The Variable Transmission Filter consists of computergenerated patterns of dots and lines that vary the intensity
1. Adjust the h/e apparatus as in Part I.I so that the first order green spectral line is focused on the photodiode
mask. Remember again to use the green filter.
2. Now place the variable transmission filter on the white reflective mask (and over the colored filter) such that
the light passes through the 100% transmission window and reaches the photodiode. This filter does not affect
the frequency of the incident light, but only its intensity.
3. Record the stopping potential Vo .
4. Determine δVo based on the precision of the DVM. If this value is not stable, consider how much the value
varies in determining δVo .
o
5. Determine the fractional uncertainty ( δV
Vo ) for this measurement and record this in your data table.
6. Repeat steps 2–5 with the light passing through the 80%, 60%, 40%, and 20% transmission windows.
7. Adjust the h/e apparatus as in Part I.I so that the first order ultraviolet spectral line is focused on the
photodiode mask.
8. Record the stopping potential Vo of the ultraviolet first order spectral line for the 100% transmission percentage.
9. Determine δVo based on the precision of the DVM. If this value is not stable, consider how much the value
varies in determining δVo .
o
10. Determine the fractional uncertainty ( δV
Vo ) for this measurement and record this in your data table.
11. Repeat steps 8–10 with the light passing through the 80%, 60%, 40%, and 20% transmission windows for the
ultraviolet first order spectral line.
Part II - Determining Uncertainties in Your Final Values
In the results section of your notebook, state the results of part I.I of your experiment in the form h±δh. Note,
δh should be equal to the largest fractional uncertainty from your values of voltage.
δVo
δh = h ∗
Vo
You should also address the following questions with regards to Part I.I and Part I.II:
1. Do different colors of light affect the maximum energy of the photoelectrons?
2. Does this experiment support the quantum model of light?
3. Does your result for h in part I.I agree within the uncertainties to the theoretical value? Be sure to clearly
state the quantitative values you are comparing. If there are any large discrepancies, quantitatively comment
on their possible origin.
4