OBJECTIVES

    The following objectives are carried out in this experiment:
1. We measure the kinetic energy of light as a function of wavelength
2. We determine Plancks constant
3. We study the effects of intensity of photoelectrons on photoelectric energy

INTRODUCTION

     Previous exercises in class on the subject of optics had covered the phenomena of diffraction and interference. These two phenomena can be explained by the wave theory of light. However, the photoelectric effect cannot be explained by the same theory. To explain the wave theory of light, we must make use of photo " particles " or photons. That is to say, the photoelectric effect (the phenomena whereby light of around a certain energy strikes a cathode and liberates electrons), can be explained by the paricle nature of light.
    When light (or photons) strike a metal surface, the photons liberate electrons from the metal surface. Each electron liberated is known as a photoelectron and each photoelectron has a certain kinetic energy.

PROCEDURE

    The following is the apparatus for this experiment

    A high intensity mercury lamp was shone onto the cathode (photodiode) through select filters of different wavelengths. The electrometer in the circuit was used to measure the voltage produced and the digital voltmeter recorded this measurement digitally. The photocurrent produced by the phototube is very small, hence it is very difficult to measure the voltage with a conventional voltmeter. The electrometer consumes zero current, whereas the conventional voltmeter consumes about 0.1µa at 1.0volt.
    The phototube was also set up with the anode shielded from the light. This prevented photoelectrons from being emitted from the cathode and cancelling out the photoelectrons of the cathode.
    It was observed that electrometers tend to drift. Thus, for each measurement of photovoltage, the capacitor must be shorted, and the output voltage for zero-input voltage measured. The photovoltage then is the difference between the raw DVM (digital volt-meter) value and the zero value.
    Care was taken to avoid light leaks around the edges of each filter.
    The data obtained for this experiment was then used to plot a graph of net voltage vs. frequency. The frequency of each wavelength was calculated in order to determine Plancks constant based on the formula: E = hf. The frequency was calculated using  . The energy was the voltage generated at the terminals of the phototube. The slope of this graph was h/e i.e. plancks constant per electron measured in Vnsec. The data is shown below.

DATA
 
 

FILTER NUMBER	WAVELENGTH (nm)	DIGITAL VOLT READING	ZERO VOLTAGE READING	NET  VOLTAGE	AVERAGE NET VOLTAGE
22	577	-3.18 -3.02 -2.95 -2.82	-2.54 -2.37 -2.29 -2.20	0.640 0.650 0.660 0.620	0.643
74	546	-2.76 -2.72 -2.70 -2.66	-2.06 -2.03 -1.99 -1.96	0.700 0.690 0.710 0.700	0.700
50	436	-2.88 -2.83 -2.77 -2.68	-1.90 -1.84 -1.76 -1.68	0.980 0.990 1.01 1.00	0.995
18A	365	-3.05 -3.00 -2.95 -2.89	-1.20 -1.13 -1.08 -1.02	1.85 1.87 1.87 1.87	1.87

SAMPLE CALCULATIONS

Frequency of each wavelength
using 

1. 577nm

Slope

1eV = 1.6 * 10^-19J

Literature Value = 6.63 * 10^-34 J.S

error = ( 6.63 * 10 ^-34 - 6.30 * 10^-34) J.S = 0.33 * 10^-34 J.S

       In the next part of the experiment, the relationship between photocurrent and intensity was investigated. Logger-Pro was used in the output of the electrometer, and the voltage vs. time on the capacitor was measured. According to the wave theory of light, when the intensity of the light is increased, an increase in the energy (voltage) of the photoelectrons will follow as well as the current. The data and graph of this experiment are shown below.
 

RESULTS

    The value obtained experimentally for plancks constant was 6.30 * 10^-34 J.S. The literature value for Plancks constant is 6.63 *10^-34J.S. Thus, the final experiment was off by 5%.
    In the second part of the lab, it was observed that within the same frequency, the same amount of energy was produced by lights of different intensites. It was also observed that more intense lights obtained the high energies before the less intense lights. Lights of different frequencies were observed to produce photoelectrons of different energies.

CONCLUSION

    From this lab it can be concluded that the energy obtained by photoelectrons is dependent on the frequency and wavelength of the incident light and is independent of the intensity of the light.
    This is in contrast to the wave theory of light. The wave theory predicts that the photoelectric energy is directly proportional to the intensity i.e. larger energy field = larger photoelectric energy. Since our data shows otherwise, it can be stated that the wave theory is not compatible with the photoelectric phenomenom.
    The resolution is that light is quantized. A "Photon" is one quantum of light. The energy of a photon can be described by the following equation:

                            E photo = hf = hc/wavelength
    Albert Einstein won the nobel prize in 1921 for his work on the particle nature of light.