Download The Photoelectric Effect

PHOTOELECTRIC EFFECT
The Photoelectric Effect
In 1887 German physicist Heinrich Hertz discovered that electric charge is emitted from the
surface of a metal body when illuminated with ultraviolet light. More careful investigation showed
that electromagnetic radiation is able to release electrons from the surface of a metal. This
phenomenon is now known as the photoelectric effect. Electron emission occurs only if the
frequency of incident light exceeds the characteristic cut-off frequency of the particular metal.
Importantly, the photoelectric effect cannot be explained in terms of classical physics with light
modeled as a wave.
Electric charge and discharge
Here we explore the electric charging and discharging of an aluminium can, using ultraviolet light.
Follow the steps and record your observations in the table below.
Remove any dirt or build up of aluminium oxide on the can using the sandpaper provided.
Place the aluminium can on the electroscope and transfer electric charge to the can using an
ebonite rod.
What type of electric charge is generated in this way?
Illuminate the cleaned surface of the can with light from a torch. What do you notice?
Using goggles, illuminate the same surface with ultraviolet (UV) light. What do you notice?
Now use a glass rod to transfer electric charge to the aluminium can.
What type of electric charge is generated in this way?
Illuminate the cleaned surface of the can with light from a torch. What do you notice?
Illuminate the same surface with ultraviolet light. What do you notice?
Type of light
Negative charge
Positive charge
Bright white light
Dim white light
Bright UV light
Dim UV light
Which particles of the metal do you think are being emitted as the can discharges?
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PHOTOELECTRIC EFFECT
An electric charge can be interpreted as an excess or a deficit of electrons. Charging with an
ebonite rod causes an excess of electrons thereby producing a negative electric charge. When
illuminated with ultraviolet light the aluminium can discharges, but this is not the case with torch light.
It is apparent that ultraviolet light has a particular feature that the torch light lacks, or that ultraviolet
light has more of ‘something’ than the torch light.
When using the glass rod for the assignment a positive charge is produced due to a deficit of
electrons. In this case no change in the electric charge of the can is detected with either the torch light
or ultraviolet light.
The negative charge on the can decreases as excess electrons are emitted. The UV light is therefore
able to remove some of the electrons from the surface of the metal. Light intensity (which is the
amount of light) and the colour of light both effect the ability of light to remove electrons in this way.
The photoelectric effect: experimental equipment
1) Protective cover for the photocell
2) Light conducting tube: for LEDs
3) Nano-ammeter for photocurrent
4) Voltmeter for control voltage
5) Dial for adjustment of control voltage
6) Dial for fine adjustment of control voltage
7) Dial for setting light source intensity
8) Socket for the light source
9) Socket for the power supply
10) LEDs with cables
• Connect the red light source to the equipment. What do you notice?
What is the cause of the electric current generation?
What is the source of the electrical power required to maintain the energy of the current?
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PHOTOELECTRIC EFFECT
The main part of the equipment is the photocell, whose light sensitive electrode (the
cathode) is made of caesium. This cathode (the negative electrode) corresponds to the metal
body within the equipment from which electrons are emitted.
In the photoelectric effect, emitted electrons are called photoelectrons. When the cathode is
illuminated using LED lights of different colours, a weak current can be observed passing
through the photocell. This is called the photocurrent. The observation can be interpreted as the
light removing electrons from the metal cathode, which then travel to the anode.
(1)
where is current,
is charge and is time. Since maintaining an electrical current requires
energy the energy of the incident light must transfer kinetic energy,
, to the electrons
(2)
where
is mass and
is velocity.
Adjust the control voltage in both the forward direction and the reverse direction. What do
you notice?
What factors affect the magnitude of the current?
What does the magnitude of the current indicate about the photoelectrons?
Why does the magnitude of the current decrease as the voltage is increased?
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PHOTOELECTRIC EFFECT
What does the control voltage produce in the vacuum tube between the electrodes?
Where is the kinetic energy of the emitted electrons transferred to?
The photoelectric cell is placed between the electrodes of an external variable voltage, the
control voltage. It can be observed that this external voltage affects the magnitude of the
photocurrent. If the voltage is positive (the cathode is negative) the photocurrent flows. If the
voltage is negative (the cathode is positive) the photocurrent is decreased and for a certain
voltage stops completely.
The magnitude of electric current in the circuit (i.e. the photoelectrons flowing through the
vacuum tube) can be regulated by the control voltage. Adjusting the control voltage changes the
electric field opposing the motion of photoelectrons, and is found to decrease the current. As the
reverse voltage, , increases the circuit current, , decreases.
The control voltage generates an electric field in the equipment which affects the flow of
photoelectrons. With a negative voltage between the electrodes the electric field acts as a
‘brake’, decelerating the electrons flowing from the cathode to the anode. When moving in an
electric circuit against an electric field photoelectrons will do an amount of work
(3)
where
is the reverse or ‘braking’ voltage and
is the charge on an electron.
• Search, by adjusting the control the voltage, for the value of
at which the current is zero.
What can we say about the motion of photoelectrons in this situation?
Where is the kinetic energy of the emitted electrons transferred to?
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PHOTOELECTRIC EFFECT
When the voltage of the circuit is adjusted such that the electric current is zero, we can
conclude that all (even the fastest) photoelectrons have been stopped. The kinetic energy of the
photoelectrons,
, is then matched by the work done,
, against the electric field. We can show
the calculation as:
(4)
(5)
(6)
where
is the work done on a photoelectron by the electric field with control voltage
elementary charge .
is the final kinetic energy of the photoelectron and
and
is the initial
kinetic energy of the photoelectron.
The voltage at which the current is stopped is called the stopping voltage,
. By measuring
the stopping voltage we can determine the maximum kinetic energy of the photoelectrons,
.
The relationship between stopping potential and maximum kinetic energy of photoelectrons is
(7)
The interpretation of these results is that light striking the cathode gives the photoelectrons
kinetic energy, this energy is sufficient to bring the electrons to the anode only if their kinetic
energy is greater than the energy needed to work against the electric field. The stopping voltage
of the emitted electrons with maximal kinetic energy is therefore equal to work done by the
electron against the opposing electric field.
Does the stopping potential depend on the light intensity?
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PHOTOELECTRIC EFFECT
When the current is reduced to zero, electrons are no longer arriving at the anode. By adjusting
the intensity of light incident on the cathode we find that the magnitude of the current varies,
however the voltage at which all the electrons can be stopped remains the same.
Consider what your findings indicate about the interaction of light with the cathode material.
• Repeat your measurements with other light sources, and record the results below.
Wavelength of light
(nm)
Frequency of light
(
Hz)
Stopping voltage
(V)
Maximum kinetic
energy of electrons
(
J)
What factors influence the value of the stopping voltages?
What does this say about the energy of the photoelectrons? Where does this energy come from?
What can we conclude about light on the basis of these results?
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PHOTOELECTRIC EFFECT
Varying the color of light (by changing the frequency of the radiation) produces similar results for
all frequencies, with the exception that the value of the stopping voltage is different for each frequency.
The stopping voltage depends on the frequency of light incident on the cathode and therefore the
maximum kinetic energy received by the electrons also depends on the frequency of the incident light.
It is evident that the energy of light is proportional to its frequency.
• Plot the data obtained from measurements on a graph with
on the y-axis and
The maximum kinetic energy of the electrons can be calculated from equation (7).
on the x-axis.
What type of graph is produced by plotting these data points?
What does this say about the relationship between the maximum kinetic energy of the
photoelectrons and light frequency?
• If possible, draw a line of best fit
What does the value of the slope determine and what are the units?
What is the physical meaning of the x-coordinate at the intercept on the x-axis?
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PHOTOELECTRIC EFFECT
From the graph, the frequency intercept can be interpreted as a threshold point below which the
lower frequency radiation does not contain enough energy to eject an electron from the metal. This
interpretation is supported by the earlier observations whereby the light from a torch was unable to
remove electric charge from the charged can, while the UV light could.
The intercept on the energy axis can be interpreted as the amount of energy an electron requires to
escape from the sea of electrons.
Compare the value of your gradient with the accepted value from the book of natural constants.
Which natural constant have you determined?
In explaining this phenomenon Albert Einstein introduced a new theory of light behaviour, the photon
model, according to which
Radiation consists of individual quanta of light called photons.
Photons are absorbed and emitted completely or not at all.
When a photon is absorbed by a metal, the energy is transferred to a single electron.
The speed of a photon is the speed of light, .
Each individual photon has energy such that
, where
is the frequency of light, and h
is a universal constant called Planck’s constant.
According to Einstein's model, the photoelectric phenomenon is due to a single photon being
absorbed by a single electron, which receives the entire frequency-dependent energy,
. Some of this
‘photon energy’ is used in removing the electron from the metal; this is given by the symbol
called the work function. The remaining energy is transferred to kinetic energy of the electron,
and is
. We
can now deduce that the maximum kinetic energy of a photoelectron as
(8)
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