Photoelectric effect

Transcription

1 Photoelectric effect Objective Study photoelectric effect. Measuring and Calculating Planck s constant, h. Measuring Current-Voltage Characteristics of photoelectric Spectral Lines. Theory Experiments showed that, when light is incident on certain metallic surfaces, electrons are emitted from the surfaces. This phenomenon is known as photoelectric effect, and emitted electrons are called photoelectrons. The first discovery of this phenomenon was Hertz. This figure represents an apparatus in which the photoelectric effect can occurs. An evacuated glass tube contains a metal plate K connected to the negative terminal of battery and metal plate A connected to the positive terminal. When tube is kept in dark the ammeter reads zero, indicated no current. When monochromatic light of appropriate wavelength shines on the cathode (K) a current is detected by ammeter; photoelectrons can be emitted and transferred to the anode (A). This constitutes a photocurrent. By changing the voltage between the anode and cathode, and measuring the photocurrent, you can determine the characteristic current-voltage curves of the photoelectric tube. Several features of photoelectric effect could not explained by classical wave theory of light: 1- No electron emitted if the incident frequency below cut off frequency v c. 2- Number of photoelectron emitted is proportional to the light intensity. And the maximum kinetic energy of the photoelectron is independent of light intensity. 3- Maximum kinetic energy of the photoelectron increase with increasing frequency. The classical wave model predicted that as the intensity of incident light was increased, the amplitude and thus the energy of the wave would increase. This would then cause more energetic photoelectrons to be emitted. The new quantum model, however, predicted that - Higher frequency light would produce higher energy emitted electrons (photoelectrons), independent of intensity. - Increased intensity would only increase the number of electrons emitted (or photoelectric current).

2 - In the early 1900s several investigators found that the kinetic energy of the photoelectrons was dependent on the wavelength, or frequency, and independent of intensity, while the magnitude of the photoelectric current, or number of electrons (photoeectron) was dependent on the intensity as predicted by the quantum model. Einstein applied Planck's theory and explained the photoelectric effect in terms of the quantum model using his famous equation for which he received the Nobel Prize in 1921: E hv = KE max +W 0 Where KE max is the maximum kinetic energy of the emitted photoelectron, and W 0 (the work function) is the minimum energy needed to remove them from the surface of the material. A light photon with energy hv is incident upon an electron in the cathode of a vacuum tube. The electron uses a minimum W O of its energy to escape the cathode, leaving it with a maximum energy of KE max in the form of kinetic energy. Normally the emitted electrons reach the anode of the tube, and can be measured as a photoelectric current. However, by applying a reverse potential V between the anode and the cathode, the photoelectric current can be stopped. KE max can be determined by measuring the minimum reverse potential needed to stop the photoelectrons and reduce the photoelectric current to zero. Relating kinetic energy to stopping potential gives the equation: KEmax = ev s Therefore, using Einstein's equation, h = e V s + W O When solved for V s, the equation becomes: ev s = hv -W 0 V s = h e v - W 0 e If we plot V s vs v for different frequencies of light, the graph will look like Figure. The vertical intercept is equal to W O /e and the slope is h/e. coupling our experimental determination of the ratio h/e with the accepted value for e, x coulombs, we can determine Planck's constant, h.

3 The basic facts of the photoelectric effect experiments are as follows: Photoelectric effect is not observed below a certain cutoff frequency because the energy of photon must equal or grater than the work function W 0. KE max is independent of intensity but it is depends only on the frequency. If the intensity is doubled, the number of photon is doubled, which double the number of photoelectron emitted. KE max Maximum kinetic energy of the photoelectron increase with increasing frequency because (KE max = hv -W 0 ) dependent only on light frequency and the work function. For a given frequency (color) of light, if the voltage between the cathode and anode, V, is equal to the stopping potential, V s, the photocurrent is zero. When the voltage between the cathode and anode is greater than the stopping voltage, the photocurrent will increase quickly and eventually reach saturation. The saturated current is proportional to the intensity of the incident light. Light of different frequencies (colors) has different stopping potentials. The slope of a plot of stopping potential versus frequency is the value of the ratio, h/e. The photoelectric effect is almost instantaneous. Once the light shines on the cathode, photoelectrons will be emitted in less than a nanosecond. Apparatus Included Equipment 1. Optical Filters, Apertures, Caps, and Screws 2. Mercury Light Source Enclosure 3. Photodiode Enclosure 4. Power Supply 5. Photoelectric Effect Apparatus

4 Experiment 1: Measuring and Calculating Planck s constant, h Preparation before measurement 1. Cover the window of the Mercury Light Source enclosure with the Mercury Lamp Cap from the Optical Filters box. Cover the window of the Photodiode enclosure with the Photodiode Cap from the Optical Filters box. 2. on the h/e Power Supply, turn on POWER and MERCURY LAMP. On the Photoelectric Effect Apparatus, push in the POWER button to the ON position. 3. Allow the light source and the apparatus to warm up for 20 minutes. 4. On the apparatus, set the VOLTAGE Range switch to V. Turn the CURRENT RANGES switch to To set the current amplifier to zero, first disconnect the A, K, and down arrow (GROUND) cables from the back panel of the apparatus. 6. Press the PHOTOTUBE SIGNAL button in to CALIBRATION. 7. Adjust the CURRENT CALIBRATION knob until the current is zero. 8. Press the PHOTOTUBE SIGNAL button to MEASURE. 9. Reconnect the A, K, and down arrow (GROUND) cables to the back of the apparatus. Measurement 1. Uncover the window of the Photodiode enclosure. Place the 4 mm diameter aperture and the 365 nm filter onto the window of the enclosure. (Note: Always have a filter on the window of the Photodiode enclosure, and put the cap on the Mercury Light source when- ever you change the filter or aperture. Never let the light from the Mercury Light source shine directly into the Photo- diode enclosure. ) 2. Uncover the window of the Mercury Light Source. Spectral lines of 365 nm wavelength will shine on the cathode in the phototube. 3. Adjust the VOLTAGE ADJUST knob until the current on the ammeter is zero. 4. Record the magnitude of the stopping potential for the 365 nm wavelength 5. Cover the window of the Mercury Light Source. 6. Replace the 365 nm filter with the 405 nm filter. 7. Uncover the window of the Mercury Light Source. Spectral lines of 405 nm wavelength will shine on the cathode in the phototube. 8. Adjust the VOLTAGE ADJUST knob until the current on the ammeter is zero. 9. Record the magnitude of the stopping potential for the 405 nm wavelength. 10. Cover the window of the Mercury Light Source. 11. Repeat the measurement procedure for the other filters. Record the magnitude of the stopping potential for each wavelength.

5 Experiment 2: Measuring Current-Voltage Characteristics of Spectral Lines - Constant Frequency, Different Intensity Preparation for Measurement 1. Cover the window of the Mercury Light Source enclosure with the Mercury Lamp Cap from the Optical Filters box. Cover the window of the Photodiode enclosure with the Photodiode Cap from the Optical Filters box. 2. on the h/e Power Supply, turn on POWER and MERCURY LAMP. On the Photoelectric Effect Apparatus, push in the POWER button to the ON position. 3. Allow the light source and the apparatus to warm up for 20 minutes. 4. On the apparatus, set the VOLTAGE Range Switch to V. Turn the CURRENT RANGES Switch to To set the current amplifier to zero, first disconnect the A, K, and down arrow (GROUND) cables from the back panel of the apparatus. 6. Press the PHOTOTUBE SIGNAL button in to CALIBRATION. 7. Adjust the CURRENT CALIBRATION knob until the current is zero. 8. Press the PHOTOTUBE SIGNAL button to MEASURE. 9. Reconnect the A, K, and down arrow (GROUND) cables to the back of the apparatus. Measurement - Constant Frequency, Different Intensities 2 mm Aperture 1. Uncover the window of the Photodiode enclosure. Place the 2 mm diameter aperture and the 436 nm filter in the window of the enclosure. 2. Uncover the window of the Mercury Light Source enclosure. A spectral line of 436 nm will shine on the cathode in the Photodiode enclosure. 3. Adjust the V VOLTAGE ADJUST knob so that the current display is zero. Record the voltage and current in the Table. 4. Increase the voltage by a small amount (for example, 1 V). Record the new voltage and current in the Table. 5. Continue to increase the voltage by the same small increment. Record the new voltage and current each time in the Table. Stop when you reach the end of the VOLTAGE range. 6. Repeat steps from 1 to 5 with a two deferent apertures. 7. Turn off the POWER on the apparatus. Turn off the MERCURY LAMP power switch and the POWER switch on the power supply. Return the apertures, filters, and caps to the OPTICAL FILTERS box.

6 Experiment 3: Measuring Current-Voltage Characteristics of Spectral Lines - Different Frequencies, Constant Intensity Preparation for Measurement Repeat steps from 1-9 in the previous experiment. Measurement - Different Frequencies, Constant Intensity 436 nm Wavelength 1. Uncover the window of the Photodiode enclosure. Place the 4 mm diameter aperture and the 436 nm filter in the window of the enclosure. 2. Uncover the window of the Mercury Light Source enclosure. A spectral line of 436 nm will shine on the cathode in the Photodiode enclosure. 3. Adjust the V VOLTAGE ADJUST knob so that the current display is zero. Record the voltage and current in the Table. 4. Increase the voltage by a small amount (for example, 1 V). Record the new voltage and current in Table Continue to increase the voltage by the same small increment. Record the new voltage and current each time in the Table. Stop when you reach the end of the VOLTAGE range. Repeat steps from 1-5 with two deferent wavelengths.