In the Laboratory
W
Investigating the Photoelectric Effect Using LEDs and a Modular Spectroscope Lucia Diaz and Charles A. Smith* Department of Chemistry, Our Lady of the Lake University, San Antonio, TX 78207; *
[email protected] Elementary spectroscopic investigations often utilize a commercial spectroscope (1–4). To maintain calibration, these devices have fixed positions for the slits and dispersive element. Due to the rigidity and non-modular nature of these spectroscopes, they may seem like a “black box” to students since the students cannot investigate the role of each component or the effect of position and orientation of each component on calibration or resolution of the instrument. However, use of a modular spectroscope allows students to understand the operation of the components. A lab-built modular spectroscope is used in this experiment. Once the students fully understand the operation of the components, they calibrate the spectroscope using a light source with a known spectrum. A circuit board containing colored light-emitting diodes (i.e., LEDs) is then used to measure a value for Planck’s constant through a photoelectric-effect-type equation. This experiment uses common items found in chemistry laboratories and local electronics stores. The experiment is suitable for both college and high school courses. Background When a p-type semiconductor is manufactured with an n-type semiconductor, the result is a p–n junction. A lightemitting diode is a p–n junction. When a forward bias is applied to the LED (i.e., positive terminal is attached to the p side and the negative terminal is attached to the n side) holes are “injected” into the n side and electrons are “injected” into the p side. The emission of light occurs when the holes recombine with the electrons (5). Regardless of whether the semiconductor is of the n or p type, the unit charge that is moved across the gap is the charge of an electron, (qe = 1.602 × 10᎑19 C.) Since voltage is electrical potential energy per unit charge, the quantity of work, W, necessary to move a charge
in a region of voltage, V, is W = q eV
(1)
When the voltage applied across the gap is sufficient, the gap may be crossed and emission will occur; in this way emission from an LED is similar to the photoelectric effect. In the photoelectric effect, energy is conserved since the energy of the incoming photon is equal to the sum of the work function of the metal, Φ, and the kinetic energy of the removed electron. A typical photoelectric equation is represented by hν = Φ +
1 me v e2 2
(2)
where h is Planck’s constant, ν is the frequency of radiation, m is the mass of the electron, and v is the velocity of the electron. The situation is somewhat different for emission of light from an LED. No longer is the energy of the photon equal to the total energy. The work necessary to move a charge across the band gap in a semiconductor is equal to the sum of the energy of the released photon and the energy lost to inefficiencies in the LED (e.g., heat). Hence, for LED emission the following equation holds where M represents any energy loss during the emission process. W = q eV = h ν + M
(3)
In this exercise it is assumed that all the LEDs have the same value of M. This should be a good approximation since M is small as LEDs are efficient consumers of energy converting very little energy to heat. Preparation The setup for calibration of the modular spectroscope is illustrated in Figure 1. A mercury discharge lamp serves as
zero band slit on box
slit
mercury lamp
open box
path of light
grating
projection on wall
Figure 1. Schematic of the modular spectroscope. Each component is freely adjustable. The setup shows a mercury lamp as the calibration light source.
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In the Laboratory
a calibration light source since its emission spectrum is known and spans a wide range of visible wavelengths. In Figure 1, the slit after the light source consists of narrowly spaced razor blades taped onto a cardboard flat. A second razor blade slit is on the side of a cardboard box, with the opposite side open, that has been prepared by the instructor. The box serves to prevent extraneous light from reaching the dispersed projection on the wall. A holographic grating1 suspended by a clamp and lab stand is placed after the box. The LED light source and power supply are illustrated in Figure 2. The diodes and circuit board were purchased from Radio Shack. The diodes have clear rather than colored plastic and each emits a different wavelength. A regulated power supply that outputs 4 V is sufficient. Slightly lower or higher voltages may be necessary if a different resistor or variable transformer2 is incorporated into the setup shown in Figure 2. Variable transformers are commonly found in chemistry laboratories since they are used for controlling the power supplied to heating mantles. The transformer is used to make fine adjustments to the voltage applied across the LED. A voltmeter with 0.01 mV resolution is connected across the LED to monitor the voltage. LEDs are easy to short circuit. The manufacturer’s specifications stated on the packaging of a diode specify its current and voltage maxima. To safeguard each LED, the output of the power supply is kept constant and the voltage applied across the LED is controlled with the transformer. The instructor provides either the maximum transformer setting or the maximum voltage allowed for each diode. The 1.1 kΩ resistor in Figure 2 limits the current. Procedure If a mercury lamp is used in a properly aligned system, students will observe a projection on the wall similar to that shown in Figure 3. Students move the light source, slits, and grating making special note of the effect on resolution of the colored bands, their width, and the position of the zero band.
LED
The zero band consists of light from the source that passes through the grating without diffraction. Resolution is increased when the grating is moved farther from the projection since the bands become farther apart. Resolution is also increased when the slit width in the box is decreased since the bands do not change position but decrease in size, which increases the precision of determining the center of each band. These effects dramatically illustrate the advantages of using long monochromators in conjunction with narrow slit widths for maximum spectral resolution. Once the operation of the spectroscope is understood and resolution is optimized, students calibrate the apparatus by marking with a pencil the centers of each band on the projection. Calibration of the system involves measuring the center-to-center distance between every band and the zero band position. A plot of distance-from-the-zero-band versus wavelength may then be used to determine wavelengths of other sources shown through the spectroscope. When determining the distance from the zero band for a new light source, the zero band of the new light source and that of the marked the zero band position from the mercury lamp must overlap. In order to make this alignment and maintain calibration, the optimal spectroscope component to adjust is the light source. The wavelengths of emission of the diodes are determined using the plot described above. To determine Planck’s constant, a minimum voltage measurement for each diode is necessary. Minimum-voltage measurements are determined by slowly increasing from zero the voltage applied across each diode and stopping when the first faint glimmer of light is observed. This is a very fine measurement and the use of a voltage transformer greatly simplifies this measurement. Hazards Mercury lamps have strong peaks in the ultraviolet region. Do not look directly into a mercury lamp—eye damage may result.
variable transformer transformer output
voltmeter circuit board
1.1 kΩ resistor to regulated power supply
transformer input
Figure 2. Schematic of the LED light source and power supply. The power supply for the LED consists of a regulated power supply connected to the input (i.e., plug) of a variable transformer. The output of the transformer is connected across the LED and monitored with a voltmeter.
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Figure 3. The emission spectrum of a mercury lamp after passing through the spectroscope. The center band, which underwent no diffraction, is referred to as the zero band.
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In the Laboratory
Analysis From the data obtained using the mercury arc lamp, a calibration curve of distance-from-the-zero-band versus wavelength is prepared. From this plot, the emission wavelengths of the individual diodes are determined. The emission wavelengths of the diodes in conjunction with the minimum voltage measurements are then used to determine a value for Planck’s constant using the following equations. In eq 4 c is the speed of light and λ is the emission wavelength of the LED. ν =
c λ
(4)
Substituting eq 4 into eq 3 and rearranging we find that
made through the use of LEDs and a photoelectric-type equation. All components necessary for construction of the apparatus are inexpensive and consist of items commonly found in college-level chemistry courses and electronics stores. Typical student values of Planck’s constant have a relative percent error less than 7%. The error may be reduced by determining an average of two values for Planck constant when the bands on both sides of the zero band are used. College student evaluations reveal this laboratory exercise to be interesting and stimulating. Additional observations for students to perform include determining the emission wavelength of an “unknown” LED or comparing the emission spectrum of a white LED with that of an ordinary flashlight. An interesting twist would be for the unknown LED to be of the type that emits more than one color. W
V =
M hc 1 + qe qe λ
(5)
where V is the minimum voltage necessary to observe emission of wavelength λ. From eq 5 it can be seen that a plot of V versus
1 λ
(6)
will produce a slope of
hc qe
(7)
from which Planck’s constant may be determined. Conclusion This exercise involves manipulation of the components of a spectroscope to gain insight into its operation, calibration, and resolution. A determination of Planck’s constant is
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Supplemental Material
Instructions for the students and a sample of a student’s data are available in this issue of JCE Online. Notes 1. The grating, part 3054510, can be purchased from Edmund Scientific (1-800-728-6999). 2. The transformer, part 09-521-130, can be purchased from Fisher Scientific (1-800-766-7000).
Literature Cited 1. Wakabayashi, F.; Hamada, K.; Sone, K. J. Chem. Educ. 1998, 75, 1569. 2. Wickun, W. G. J. Chem. Educ. 1998, 75, 1477. 3. Cortel, A.; Fernandez, L. J. Chem. Educ. 1986, 63, 348. 4. Edwards, R. K.; Brandt, W. W.; Companion, A. L. J. Chem. Educ. 1962, 39, 147. 5. Fowles, G. F. In Introduction to Modern Optics; Dover: New York, 1989; p 288.
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