Unit 6 Photoelectric Effect Keywords: Photoelectric Effect, Work Function Objective: The black body radiation experiment launches the research of quantization model. Through several famous experiments, consolidates the importance of quantum mechanics. Among them, photoelectric effect is one of the most famous experiments, and is the start of the understanding toward quantum physics. This experiment observes the electron emitted when different energy of light strikes the Cs3Sb metal slab to explain the principle of photoelectric effect and derive the Plank’s constant h.

Apparatus: Photoelectric effect experiment instrument, Mercury vapor light source, one yellow and green filters, digital voltmeter, variable transmission filter

Mercury vapor light source Photoelectric effect experiment instrument

Digital voltmeter

Filter Fig. 1

Principle: If a light strikes the surface of the metal and the wavelength of the light is longer than a specified amount, there would be no electron emitted from the surface of the metal to induce the photo current whatever the strength of the light is. This is the phenomenon that the classical wave model can't explain. Einstein announced the theory of photoelectric effect in 19th century, that is, explained the photoelectric effect in terms of the quantum model of light. Assume there is a light wave with frequency ν. Einstein assumed that the wave light is in quantum condition. Each photon has energy E= hν, and the total energy of the wave light is Etotal = nhν. Where n is the number of the photons. If the intensity of the light is higher, it means the number of the photons is larger. When the energy of the photon is higher enough, light strikes the surface of the metal, and then the photon would collide with the electrons in the atom, so that the electrons would emit from the surface into the air. The kinetic energy of the emitted electron is equal to the energy of the photon minus the electron attracted energy ψ from the surface of the metal. This energy is also called as work function. At the same time, we can imagine that the metal slab as the emitter in the vacuum tube in Fig 2, so that the emitted electrons have kinetic energy. Then the electrons can move towards the collector and form the current, and we call it as photo-current. However, when we add a voltage between the emitter and the collector of the vacuum tube, the voltage would form an electric field between the emitter and the collector, stop the electrons from moving towards collectors and decrease the photo-current. Therefore, if the energy that the electrons received from the electric field is equal to the maximum kinetic energy of the emitted electrons, the electrons can't arrive at the collectors, and then the photo-current would become zero. At this time the reverse voltage V 0 is called as stopping potential. In a word, the energy of the photon is hν , the work function is φ , the stopping potential is eV 0 , and the charge of the electron is e. Therefore, the variables have the following relationship:

eV0 = hν − φ In the experiment, through measuring the relationship between the stopping potential and the frequency of the light, we can derive the work function of the metal slab and explain the photoelectric effect.

Photons

_

+

i G

V

Fig 2. Vacuum tube

Instructions: 1. Set up the equipment as shown in Fig 1. 2. To check the batteries, use a voltmeter to measure between the OUTPUT ground terminal and each BATTERY TEST terminal (-6V MIN and +6V MIN). If either battery tests below its minimum rating, it should be replaced before running the experiments.

Fig 3.

Photoelectric effect instrument

★ Keep the experiment in the darkness in order to avoid influence from other light sources.

A. Change the frequency of the light, and then measure the stopping potential. 1. Adjust the photoelectric effect instrument, open the mercury vapor light source and wait for several minutes. At this time, we can see several orders of diffraction, and each order of diffraction contains five spectral colors. The wavelength is shown in Table 1. Select the first order of diffraction as the light source. Q1: What do we use to split the light? Is there any other method to do this? 2. Roll the light shield of the apparatus out of the way so that only one of the yellow colored bands falls upon the opening of the mask of the photodiode. 3. Begin with the yellow colored band. Place the yellow colored filter over the white reflective mask on the photoelectric effect instrument. Be sure that the light incident into the vacuum tube before returning the light shield to closed position, which is to avoid the incidence of ambient light into the vacuum tube. 4. Press the button of Reset, and the internal circuit of the instrument would calculate the stopping potential and then show in the digital voltmeter. Record the digital voltmeter reading, which is the stopping potential. 5. Repeat step 2~4 to measure the stopping potential of each light. Be sure to use the green colored filter when the light source is green colored band, but others don't need the filters. 6. Plot the figure of stopping potential V0 versus the frequency of incident light v. Extend the line to make the line intersects with the v axis. (Fig 4.)

Fig. 4 Q2: How can we get h from the figure of stopping potential V0 versus the frequency of incident light v? Q3: How can we get the work function from the intercepts of x and y axes in the figure of stopping potential V0 versus the frequency of incident light v? Please use the data to compare the work function derived from two different ways?

B. Change the intensity of the light source Observe the relationship between the stopping potential and the intensity of the light source. 1. Place the Variable Transmission Filter in front of the White Reflective Mask as in Fig. 5 so that the light passes through the section marked 100% and reaches the photodiode. Record the digital voltmeter voltage reading. (The digital voltmeter voltage reading should hold the same value over 2 minutes.) 2. Move the Variable Transmission Filter and record the digital voltmeter voltage reading when the light passes through the section marked 80% and 60%. 3. Select another light source, and repeat step 1~3.

20

40

60

80

100

Relative Transmission (%) Fig. 5 Q4: What could we conclude when comparing the stopping potential with three different intensities of the light sources? Does it conform to the theory? Why? Q5: In this experiment we don’t need to measure the stopping potential of red colored band. Do you know why? Q6: Why do we place the filter only when the light sources are yellow and green colored bands? Q7: Is the Plank’s constant h you derive the same as it from the text book? Q8: Is the work function you derive the same as the work function of Cs3Sb metal slab (1.36± 0.08 eV)? If it is not the same, please explain it. Q9: What kind of research did Einstein do to win the Nobel Prize?

Remark: 1. The light spectrum of the Mercury vapor light source contains ultraviolet spectrum. Don’t stare at the Mercury vapor light source directly.

Color

Frequency (Hz)

Wavelength (nm)

Yellow Green Blue Violet Ultraviolet

5.18672E+14 5.48996E+14 6.87858E+14 7.40858E+14 8.20264E+14

578 546.074 435.835 404.656 365.483

Table 1 Wavelength of different light sources

material

Work function(eV)

material

Work Function(eV)

material

Work Function(eV)

Ag

4.26

Al

4.28

As

4.79

Au

5.1

Ba

2.52

Bi

4.34

Ca

2.87

Co

4.97

Cr

4.44

Cs

1.95

Cu

4.65

Fe

4.6

Ga

4.35

Ge

5.15

In

4.08

K

2.3

Mn

4.08

Mo

4.49

Na

2.36

Ni

5.15

Pb

4.25

Pd

5.4

Pt

5.63

Rb

2.05

Ru

4.71

Sb

4.56

Si

4.95

Sn

4.28

Ta

4.3

Ti

4.33

U

4.33

W

4.55

Zn

3.63

Table 2 Work function of different materials