Download Photoelectric Effect

Date :
Photoelectric effect
1. Photoelectric effect
Background
Photoelectric effect
Planck’s constant
Work function
Photocell
Aim of the experiment
To determine Planck‟s quantum of action from the photoelectric voltages
measured at different wavelengths.
Apparatus required
Photocell
Interference filter set
Spectral lamp Hg
Power supply for spectral lamps
Mounting plate
Electrometer amplifier
Digital multimeter
Connecting cords
Theory
Inside of the photocell there is a metal coated cathode. The annular anode is opposite
the cathode. When a photon of frequency  strikes the cathode, then an electron can
be ejected from the metal (external photoelectric effect) provided the photon has
sufficient energy.
Some of these ejected electrons reach the (unilluminated) anode so that a potential
difference is set up between anode and cathode, which reaches the limiting value V
after a short (charging) time. The electrons flow against the electric field set up by the
voltage V. The kinetic energy of the electrons, determined by the light frequency,  ,
h  W 
1
m v 2 (Einstein equation)
2
where, h = Planck’s constant, W = work function of the cathode surface, v = electron
velocity and m = rest mass of the electron.
Electrons will thus only reach the anode as long as their energy in the electric field is
equal to the kinetic energy:
eV 
1
mv2
2
with, e = electron charge.
15
Photoelectric effect
An additional contact potential  occurs, because the surfaces of the anode and
cathode are different:
eV   
1
mv2
2
If we assume that W and „  ‟ are independent of frequency, then there will be a linear
relationship between the voltage V (to be measured at high impedance) and the light
frequency  ,
V 
W  h
 
e
e
Next, by measuring the voltages at different wavelength (i.e., at different frequencies)
one plots the voltage vs frequency graph. A straight line is drawn through the
experimental points (i.e. V = a + b ). One can determine the value of Planck‟s
constant from the slope of the straight line, the literature value of which is
h  6.63  10 34 Js.
16
Photoelectric effect
G
Procedure
Supply
Power (12 V~)
Electrometer
Amplifier
Multimeter
V
Lamp
Photocell
C
G
Fig. 1 Experimental set up for determining Planck‟s quantum of action
1.Make the electrical connections as per diagram 1. Keep the lamp and filter in the
same line. Connect the ground of the photocell to the ground of the electrometer
amplifier. Note the ground terminal of the amplifier and connect correctly (you
may connect it to the base plate).
2. Set the digital voltmeter range to 2V DC. Measure the voltage without any
filter. Hold the terminal G in hand while taking the readings, if the voltage
fluctuates too much in the multimeter.
3. Close the photocell slit. Place one filter in front of the photocell and discharge
the electrometer by short-circuiting the ground terminal with the positive
electrometer amplifier entrance before measuring any voltage. Open the photocell
slit and measure the voltage. Wait until the voltage reading is steady.
4. Measure voltages for various filters by repeating the procedure 3.
5. Repeat the experiment for different lamp – filter separations.
6. Plot frequency vs. voltage and find h from the slope of the graph.
17
Photoelectric effect
Observations
Voltage for closed slit………..V
Voltage without any filter (open slit) …………… V
Separation
between lamp
and filter
Table 1
Determination of h
Wavelength
Frequency
()
( = c/)
(nm)
(sec-1)
366
405
436
546
578
366
405
436
546
578
366
405
436
546
578
Results and Calculations
Value of h from the plot …………………………J. sec.
18
Voltage
(V)
(volt)
Photoelectric effect
Error Calculation: If the slope is calculated using voltages V1 and V2 from the
graph, then
h V1  V2

h
V1  V2
Discussion
i.
ii.
The view that the light propagates as a series of little packets of energy
(photons) is directly opposed to the wave theory of light. According to the
wave theory, which provides the sole mean of explaining the optical
effects like interference and diffraction, the energy carried out by the light
is distributed continuously through out the wave pattern. According to the
quantum theory, which is strikingly successful in explaining photoelectric
effect, light spreads out from the source as a series of localized
concentration of energy.
In a specific event light exhibits either a wave or a particle nature, never
both simultaneously. The wave theory of light and the quantum theory of
light are complement to each other.
Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
What is the value of Planck‟s constant?
What are the sources of error in this experiment?
What is photoelectric effect?
Define “work-function”.
What is the time lag between the arrival of light at a metal surface and the
emission of photoelectron?
What do you mean by stopping potential/extinction voltage/cut off
voltage?
What type of material should be chosen for photoelectron emission?
What is photoelectric cell?
What do you know about the structure of photovoltaic cell?
Can you name a recent method of a very accurate determination of
Planck‟s constant?
Interpret thermionic emission in light of photoelectric effect.
In which phenomenon do you see the inverse photoelectric effect?
References
1. PHYWE, LEP 5.1.04 Planck‟s “quantum of action” from photoelectric effect
2. Prospective of Modern Physics by A. Beiser 539 BEI/P N69
3. The Feynman Lectures on Physics (Vol III) by R.P. Feynman 530 FEY/L
19
Photoelectric effect
Graph : Photoelectric effect
20
Photoelectric effect
Detail of the Electrometer amplifier
Charges that have resulted from static electricity can be determined by transferring the
charge to a capacitor of known capacitance and measuring the electrical potential of
this. It is difficult to measure this potential with customary measuring instruments, as
a current flows through the measuring instrument and this leads to decay of the
applied charge. The smaller the internal resistance of the measuring instrument, the
quicker the potential reduced. Customary measuring instruments have an internal
resistance of about 10 M ohms.
The electrometer amplifier has a voltage input with a very high internal resistance
(>1013 ohm) and can be used to measure such charges.
Functional and operating elements
1. Amplifier input
2. Auxiliary input.
3. Amplifier output
4. Trimmer for offset voltage
5. LED for display of operating voltage (12 V~)
6. For alternating voltage supply (12 V~)
7. Connecting socket for plug-in power supply unit with hollow plug.
8. For external connection
9. Reference potential (earth)
21