Photoelectric effect

Photoelectric effect

Theory

In 1902, Philipp Lenard, an assistant to Heinrich Hertz, used a high intensity carbon arc light to illuminate an emitter plate. Using a collector plate and a sensitive ammeter, he was able to measure the small current produced when the emitter plate was exposed to light. In order to measure the energy of the emitted electrons, Lenard charged the collector plate negatively so that the electrons from the emitter plate would be repelled. He found that there was a minimum “stopping” potential that kept all electrons from reaching the collector. He was surprised to discover that the “stopping” potential, $V$ (and therefore the energy of the emitted electrons) did not depend on the intensity of the light. He found that the maximum energy of the emitted electrons did depend on the color, or frequency, of the light.

Three years later, Einstein came up with an explanation for Lenard's observation. According to Planck's theory, the energy of particles is quantized. Thus, each of the photons arriving at the plate carries an energy $E=h\nu$, where $h$ is Planck constant and $\nu$ is the frequency of the light. On the other side, for an electron current to be measured we need to provide the electrons with:

1. enough energy to break their bond to the solid (let's call it $W_0$), and
2. some kinetic energy $K_E$ that allows them to move from their initial position to the ammeter.

The energy transfer takes place as an elastic collision: the energy of the photon is completely transferred to the electron (we could say that the photon was absorbed by the solid). Therefore we have \begin{equation} \label{eq:equation1} h\nu = W_0 + K_E\,, \quad \mathrm{or\,equivalently} \quad K_E = h\nu -W_0\,. \end{equation} Naturally, expression on the right of Eq. (\ref{eq:equation1}) is only valid when the energy of the impinging photon is larger than $W_0$. Finally, the connection between the kinectic energy of the electrons and the observed current (or voltage difference) is obtained by noting that the energy of electrons in motion is $K_E = e V$, with&bnsp;$e$ the charge of the electron and $V$ the voltage difference.

Procedures

Measuring Planck's constant

The setup is arranged following the instructions provided by Pasco.

Initial configuration

1. Cover the window of the Mercury Light Source Enclosure with the Mercury Lamp Cap. Cover the window of the Photodiode enclosure with the Photodiode Cap.
2. Adjust the distance between the Mercury Light Source enclosure and Photodiode enclosure so that the general spacing is between 30.0 cm to 40.0 cm. NOTE: The recommended distance is 35.0 cm.
3. On the Mercury Lamp Power Supply, press the button to turn on MERCURY LAMP. On the Tunable DC (Constant Voltage) Power Supply and DC Current Amplifier, push in the POWER button to the ON position.
4. Allow the light source and the apparatus to warm up for 10 minutes.
5. On the Tunable DC (Constant Voltage) Power Supply, set the Voltage Range switch to $-4.5\,\mathrm{V}$ – $0\,\mathrm{V}$. On the DC Current Amplifier, turn the CURRENT RANGES switch to $10^{-13}\,\mathrm{A}$.
6. On the DC Current Amplifier, push in the SIGNAL button to the “in” position for CALIBRATION.
7. Adjust the CURRENT RANGES knob until the ammeter shows that the current is zero.
8. Press the SIGNAL button so it moves to the “out” position for MEASURE.

Measurements

1. Gently pull the aperture dial away from the case of the Photodiode Enclosure and rotate the dial so that the 4 mm diameter aperture is aligned with the white line. Then rotate the filter wheel until the 365 nm filter is aligned with the white line. Finally, remove the cover cap.
2. Uncover the window of the Mercury Light Source. Spectral lines of 365 nm wavelength will shine on the cathode in the phototube.
3. Start previewing in Capstone and click the first row in the table display
4. Adjust the VOLTAGE ADJUST knob on the DC Power Supply until the digital meter on the DC Current Amplifier shows that the current is zero.
5. Press “Keep Sample” on the Sample Control bar to record the magnitude of the stopping potential for the 365 nm wavelength in the table display.
6. Rotate the filter wheel until the 405 nm filter is aligned with the white line. Spectral lines of 405 nm wavelength will shine on the cathode in the phototube.
7. Adjust the VOLTAGE ADJUST knob on the DC Power Supply until the digital meter on the DC Current Amplifier shows that the current.
8. Click the second row of the table display and press “Keep Sample” to record the magnitude of the stopping potential for the 405 nm wavelength in table display.
9. Repeat the measurement procedure for the other three filters. Record the magnitude of the stopping potential for each wavelength in the table, and then press “Stop” in the software.
10. Repeat all the measurements for the 2 mm and 8 mm apertures.
11. Turn off the MERCURY LAMP power switch and the POWER switch on the other pieces of equipment. Rotate the filter wheel until the 0 nm filter is aligned with the white line. Cover the windows of the Mercury Light Source Enclosure and Photodiode Enclosure.

Measuring the dependence on the intensity

Initial configuration

1. Cover the window of the Mercury Light Source enclosure with the Mercury Lamp Cap. Cover the window of the Photodiode enclosure with the Photodiode Cap.
2. Adjust the distance between the Mercury Light Source enclosure and Photodiode enclosure so that the general spacing is between 30.0 cm to 40.0 cm. NOTE: The recommended distance is 35.0 cm.
3. On the Mercury Lamp Power Supply, press the button to turn on MERCURY LAMP. On the Tunable DC (Constant Voltage) Power Supply and DC Current Amplifier, push in the POWER button to the ON position.
4. Allow the light source and the apparatus to warm up for 10 minutes.
5. On the DC (Constant Voltage) Power Supply, set the Voltage Range switch to $-4.5\,\mathrm{V}$ – $30\,\mathrm{V}$. On the DC Current Amplifier, turn the CURRENT RANGES switch to $10^{-11}\,\mathrm{A}$. (If $10^{-11}\,\mathrm{A}$ is not large enough, please turn the CURRENT RANGES Switch to $10^{-10}\,\mathrm{A}$.)
6. Push in the SIGNAL button to the “in” position for CALIBRATION.
7. Adjust the CURRENT RANGES knob until the ammeter shows that the current is zero.
8. Press the SIGNAL button so it moves to the “out” position for MEASURE.

Measurements

1. Gently pull the aperture dial away from the Photodiode Enclosure and rotate the dial so that the 2 mm aperture is aligned with the white line. Then rotate the filter wheel until the 436 nm filter is aligned with the white line. Finally remove the cover cap.
2. Uncover the window of the Mercury Light Source. Spectral lines of 436 nm wavelength will shine on the cathode in the phototube.
3. Adjust the $-4.5\,\mathrm{V}$– $30\,\mathrm{V}$ VOLTAGE ADJUST knob until the current on the ammeter is zero. Record the voltage and current.
4. Increase the voltage by a small amount. Record the new voltage and current.
5. Continue to increase the voltage by the same small increment. Record the new voltage and current each time. Stop when you reach the end of the VOLTAGE range.
6. Repeat the measurements with the 4mm and 8mm apertures.

Measuring the dependence on the frequency

Initial configuration

1. Cover the window of the Mercury Light Source enclosure with the Mercury Lamp Cap. Cover the window of the Photodiode enclosure with the Photodiode Cap.
2. Adjust the distance between the Mercury Light Source enclosure and Photodiode enclosure so that the general spacing is between 30.0 cm to 40.0 cm. NOTE: The recommended distance is 35.0 cm.
3. On the Mercury Lamp Power Supply, press the button to turn on MERCURY LAMP. On the Tunable DC (Constant Voltage) Power Supply and DC Current Amplifier, push in the POWER button to the ON position.
4. Allow the light source and the apparatus to warm up for 10 minutes.
5. On the DC (Constant Voltage) Power Supply, set the Voltage Range switch to $-4.5\,\mathrm{V}$ – $30\,\mathrm{V}$. On the DC Current Amplifier, turn the CURRENT RANGES switch to $10^{-11}\,\mathrm{A}$. (If $10^{-11}\,\mathrm{A}$ is not large enough, please turn the CURRENT RANGES Switch to $10^{-10}\,\mathrm{A}$.)
6. Push in the SIGNAL button to the “in” position for CALIBRATION.
7. Adjust the CURRENT RANGES knob until the ammeter shows that the current is zero.
8. Press the SIGNAL button so it moves to the “out” position for MEASURE.

Measurements

1. Gently pull the aperture dial and rotate it so that the 4 mm aperture is aligned with the white line. Then rotate the filter wheel until the 365 nm filter is aligned with the white line. Finally remove the cover cap.
2. Uncover the window of the Mercury Light Source Enclosure. Spectral lines of 365 nm will shine on the cathode in the Photodiode Enclosure.
3. Adjust the $-4.5\,\mathrm{V}$–$30\,\mathrm{V}$ VOLTAGE ADJUST knob so that the current display is zero. Record the voltage and current.
4. Increase the voltage by a small amount. Record the new voltage and current.
5. Continue to increase the voltage by the same small increment. Record the new voltage and current each time. Stop when you reach the end of the VOLTAGE range.
6. Repeat the measurements for the filter of 405 nm, 436nm and 546 nm.