Download Experiment 2-7. Planck constant measurement using photoelectric

Experiment 2-7.
Planck constant measurement
using photoelectric effect
Purpose of Experiment
Consider a situation where no circuitry is connected externally to the positive and negative
electrodes of the phototube. When the light is shined, the photoelectrons will be emitted with
kinetic energy from the metal of the anode. The emitted photoelectrons will be collected at
the opposite cathode to be charged negatively, and the anode will be positively charged due to
the electron escaping. The amount of charge charged increases gradually as the light is
continuously irradiated, so that a potential is formed between the cathode and the anode by
lowering the potential of the cathode. When the voltage (a kind of reverse voltage) reaches
the stop voltage value, the photo-electron eventually reaches an equilibrium state in which it
can no longer reach the cathode. At this time, it can be understood that the anode and the
cathode serve as capacitors. The voltage formed between the cathode and the anode when the
state equilibrium is the stop voltage. If this voltage is measured, it can theoretically be said
that the stop voltage is measured. However, in reality, a conventional voltmeter has an
internal resistance of several MΩ even if it is of a high-grade type, and if it is connected
between a cathode and an anode, a minute moving optoelectronic flows through the voltmeter
and will never reach the equilibrium state. Even if a voltmeter is connected after an early
stage, the equilibrium state is broken instantly and accurate measurement is impossible.
The recently developed OP-Amp has an input impedance of 1012Ω or more and can be used
to directly measure the blocking voltage with a normal voltmeter by amplifying it by one
time(buffer circuit). In this way, when the measurement is made, the electrons are collected
on the cathode and the equilibrium state can be obtained and the measurement of the stop
voltage can be performed.
Outline of Experiment

Measure Planck's constantusingphotoelectriceffect.
Experimental Method
These equipments are prepared in the laboratory.

Planck constant measuring device

6 kinds of LED light source, photo tube device, low noise amplifier, polarizer for brightness
control
Fig.1 Planck constant measuring device
a)LIGHT SELECT : Light source selection button, from left, Infrared(850nm) Red(640nm), Orange(585nm),
Green(520nm), Blue(465nm), Dark Blue(420nm). Operate in a pressed state with operation indicator LED
b) ZERO ADJ. : Ammeter Zero Control Terminal
c) GAIN : Current amplifying terminal
d) COLLECTOR : Phototube reverse voltage regulating terminal
e) INT./EXT. : Internal meter / external meter selection terminal
f) Brightness control device : Two polarizers rotate 0 to 90 degrees to adjust the brightness
Fig.2 Phototube
1) Planck constant measurement
① Adjusting the brightness Turn the polarizer to 0 °(parallel plate).
② When LIGHT SELECT is used when there is no pressed button, turns on the power with the COLLEC- TOR set to
the minimum value in the middle of the ZERO ADJ. without the pressed button. When measuring with an internal meter,
place it at the INT terminal.
③ Push the RED button of LIGHT SELECT, and adjust GAIN so that the current value is 80 ~ 120 (or maximum)
(current amplification for more accurate measurement, maximum amplification for RED & YELLOW)
④ Press the RED button again to turn OFF and adjust the ZERO ADJ. to adjust the zero point so that the ammeter reading
is zero.
⑤ Activate the light source by pressing the RED button and adjust the COLLECTOR to measure the stopping voltage ( )
at which the ammeter's current value is zero.
⑥ Similarly, measure the stop voltage for the ORANGE, GREEN, BLUE, and Dark Blue sources.
⑦ Draw the relationship graph of the stop voltage according to the frequency of the light source with the measured data.
Obtain The Planck constant through the slope of the graph, and determine the work function through the intercept.
At previous experimental equation
,
and , is Planck constant
⑧ Turn the polarizer about 30 °and repeat the above steps ① to ⑦.
⑨ Turn the polarizer about 60°and repeat the above steps ① to ⑦.
Fig.3 Schematic diagram of Planck constant measuring device
Cf. It can be seen that the photoelectric effect is not generated below the minimum frequency through the infrared light source (850 nm).
Whetherthe infraredLEDisoperatingcan be checked with a mobilephone camera.
Fig.4 Relationship betweenblockingvoltage and frequencyofincidentlight
2) Relationship between intensity of light and photocurrent
① Adjusting the brightness Turn the polarizer to 0 °(parallel plate).
② When LIGHT SELECT is used when there is no pressed button, turns on the power with the COLLEC- TOR set to
the minimum value in the middle of the ZERO ADJ. without the pressed button. When measuring with an internal meter,
place it at the INT terminal.
③ Push the RED button of LIGHT SELECT, and adjust GAIN so that the current value is 80 ~ 120 (or maximum)
(current amplification for more accurate measurement, maximum amplification for RED & YELLOW), and fix the gain
to this state.
④ Press the selected button again to turn OFF and adjust ZERO ADJ. to adjust the zero point so that the current value of the
ammeter is zero.
⑤ Press the selected button to activate the light source and measure the amount of photocurrent at this time.
⑥ Adjusting the light intensity Turn the polarizer to 5 °and measure the photocurrent at this time. Similarly, the amount of
photocurrent at that time is measured while changing the angle of the polarizing plate by 5 degrees and changing it to 90
degrees.
⑦ Change the light source from Yellow to Dark Blue and repeat the above steps ① ~ ⑥.
⑧ Check the relationship between the intensity of light and photocurrent.
Cf. Theintensityofthelight withthepolarization angle ( ) ofthepolarizingplate decreasesin proportionto
.
3) Relationship between light intensity and blocking voltage
① Adjusting the brightness Turn the polarizer to 0 °(parallel plate).
② When LIGHT SELECT is used when there is no pressed button, turns on the power with the COLLEC- TOR set to
the minimum value in the middle of the ZERO ADJ. without the pressed button. When measuring with an internal meter,
place it at the INT terminal.
③ Select one of the five light sources of the LIGHT SELECT and press to adjust GAIN to adjust the current value to 60 ~
80. (It is advantageous to select one of Green to Dark Blue). Fix the gain to this state.
④ Press the selected button again to turn OFF and adjust ZERO ADJ. to adjust the zero point so that the current value of the
ammeter is zero.
⑤ Activate the light source by pressing the selected button and adjust the COLLECTOR to measure the blocking voltage
( ) at which the ammeter's current value becomes zero.
⑥ Turn the brightness control polarizer to 5 °and repeat the above steps ② ~ ⑤ for the selected light source (1).
⑦ Repeat the above steps ② ~ ⑤ for the selective light source (1) with the light intensity control flat plate at 10 °. Measure
in the same way up to 80 °.
⑧ Check the relationship between the intensity of light and the blocking voltage.
It is recommended to write experiment notes in the following way.
1) Planck constant measurement
Measurement stop voltage (V)
light source
Wavelength(nm)
Frequency (Hz)
Polarization
angle 0°
Polarization
angle 30°
Polarization
angle 60°
Red
Yellow
Green
Blue
Dark Blue
• Measurement result
• Graph of relationship between blocking voltage (corresponding energy) and incident light frequency
2) Relationship between intensity of light and photocurrent
• Measurement result (For convenience, set I0=1.)
Intensity
photocurrent ( )
Angle (°)
Red
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Yellow
Green
Blue
Dark Blue
• Graph of relationship between intensity of light and photocurrent
3) Relationship between light intensity and blocking voltage
•Light source :
Polarization
angle (°)
Intensity
Stop voltage (V)
Polarization
angle (°)
0
45
5
50
10
55
15
60
20
65
25
70
30
85
35
80
40
Intensity
Stop voltage (V)
• Graph of relationship between light intensity and blocking voltage
Background Theory
The emission and absorption of light was an early topic investigated by Marx Franck, a German physicist. Franck has
encountered considerable difficulty when attempting to formulate a theory that explains the spectral distribution of light
emitted using classical models. Classical theory (Rayleigh-Jeans law) predicts that the amount of light emitted from the
black body increases sharply as the wavelength decreases. On the other hand, it shows that the experiment approaches the
spirit. This discrepancy is known as ultraviolet catastrophe. Measurements taken from the emission of light from a hot
emitting body show that the maximum intensityof the emitted light is radically deviated from the classically predicted value.
(Wein’s theory). To create a theory that is consistent with experimental results, Franck has to think of a new light model
called a quantum model. In this model, the light is emitted as a very small, quantum bundle with a low (non-continuous)
value.
1) Planck's Quantum Theory
In the late 1800s many physicists were able to explain all the laws of the universe and thought that they had discovered all
the laws of nature. However, as scientists became more involved in research, inconsistencies that could not be explained
easily appeared in many areas of research.
In 1901, Frank published his theory of radiation. Here he said that oscillators and many similar physical structures have
possible discontinuous values or levels. The energy value between these discontinuous values can never be obtained. Franck
continues to argue that emissions and absorptions in radiation are related to the transfer or migration between energy levels.
The energy lost or obtained by the oscillator is in the form of a quantum of energy to be copied. The sizes of these quantities
are expressed as follows.
Where
constant
is the radiation energy,
is the frequency of the radiation, and is the natural fundamental constant. This
is the Planck constant. The Planck constant has a meaning beyond the relationship between light energy and
frequency. This is the cornerstone of a quantum mechanics view in the subatomic world. In 1918, Planck won the Nobel
Prize for Physics for quantum theory of light.
2) Photoelectric effect
When high energy electromagnetic waves (light) are incident on the solid surface, photoelectrons are emitted from the
solid surface. This is called photoelectric effect. The classic wave theory predicts that as the intensity of light increases, the
amplitude and energy of the wave will increase, so that when the light is incident on the solid surface, it will emit a larger
energy photoelectron. However, the new quantum model predicts that light at higher frequencies will produce
photoelectrons with higher energy regardless of intensity. On the other hand, increasing the intensity of incident light only
increases the number of photoelectrons. In the early 1900s, several researchers found that the kinetic energy of
optoelectronics depends on wavelength and frequency, and it is independent of amplitude. On the other hand, the magnitude
of the photocurrent or the number of electrons depends on the intensity as predicted by the quantum model. Einstein adopted
the quantum model and described the photoelectric effect with a quantum model using the famous formula that received the
Nobel Prize for Physics in 1921.
Where
is the maximum kinetic energy of the emitted photoelectron and
electrons to come off the surface of the material. This is called a work function.
photon.
is the energy required for the
is the energy given as light in the form of a