EFFECT
THEORY PHOTOELECTRIC When light of sufficiently high frequency falls on the surface of a metal, electrons (called photoelectrons) are emitted. It is observed that the maximum kinetic energy that may be attained by a photoelectron, KEmax, depends upon the frequency of the light and the characteristics of the metallic surface. One can determine KEmax by measuring the minimum voltage V0 (stopping potential) necessary to prevent all photoelectrons from escaping from the metal. The relationship between KEmax and V0 is given by Equation 1. The plot of this function is a straight line (See Fig. 1), with a slope of h/e, a y-intercept of V0 = (/e), and an x-intercept of fc. V0
Slope = h/e
0
KE max = eV0
where e = electron charge (1.602 x 10
19
1 C)
fc
f
It is also observed that a "cutoff frequency", fc, exists for each metal such that no photoelectrons will be emitted if the frequency of the incident light is less than fc, regardless of the light intensity. To explain the effect, Einstein assumed that light is quantized, i.e., it consists of a stream of "packets" of pure energy called photons with each photon having energy E=hf where h = Planck's constant and f = frequency. This assumption served as the basis for the derivation of Equation 2. KE max = hf - where = work function of the metal The work function is the minimum amount of energy that a photoelectron must gain in order to escape from the metal. One can use the relationship between KEmax and V0 to rewrite Equation 2 as V0 = h f e e 3 2
/e Figure 1 In this experiment, V0 will be measured for several frequencies of light and these data will be used to determine values for h, fc, and . PROCEDURE The experimental setup is shown in Fig. 2. Turn on the light source and allow it to warm up for about 5 minutes. A diffraction grating spreads the emitted light into a characteristic spectrum, separating light of different frequencies. One will observe the firstand second-order mercury spectral lines on the white reflective mask of the h/e apparatus as it is rotated to the right and left of the centerline from the mercury source. The frequencies of the observable spectral lines are given in Table I.
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1
the photodiode mask, slightly rotating the h/e Apparatus on its support base if necessary.
Figure 2. Experimental Setup. Table I MERCURY SPECTRAL LINES Color Violet #2 Violet #1 Blue Green Yellow Frequency (Hz) 8.20 x 1014 7.41 x 1014 6.88 x 1014 5.49 x 1014 5.19 x 1014 Figure 3. h/e Apparatus Note: The white reflective mask on the h/e Apparatus is made of a special fluorescent material in order that you can see the ultraviolet line (Violet #2) which will appear as a blue line. The violet line (Violet #1) will also appear more blue. You can see the actual colors of the light if you hold a piece of white non-fluorescent material in front of the mask. It is important that only one spectral line falls on the photodiode window. There must be no overlap from adjacent spectral lines. Be sure that the light shield is closed whenever taking data, to prevent stray light of other frequencies from entering the window. Press the ZERO button on the side panel of the h/e apparatus (near the ON/OFF switch) to discharge any accumulated potential in the unit's electronics. Read the output voltage on the voltmeter. digital (The voltmeter should be on the lowest setting for which it is not overloaded.) Wait until the voltmeter has stabilized at a constant value before recording the voltage. Repeat this procedure for each of the other four first-order spectral lines given in Table I. Important: Use the appropriate filters when making measurements with the Green and Yellow spectral lines. These filters have magnetic strips and can be attached to the white reflective mask. Be sure that the filter covers the slit in the reflective
Set the h/e Apparatus directly in front of the Mercury Vapor Light Source. By sliding the Lens/ Grating assembly back and forth on its support rods, focus the light onto the white reflective mask of the h/e Apparatus (Fig. 3). Roll the light shield of the Apparatus out of the way to reveal the white photodiode mask inside the Apparatus. Rotate the h/e Apparatus until the image of the aperture is centered on the window in the photodiode mask. Then tighten the thumbscrew on the base support to hold the Apparatus in place. Now further adjust the Lens/Grating assembly until you achieve the sharpest possible image of the aperture on the window in the photodiode mask. Tighten the thumbscrew on the Lens/Grating assembly and replace the light shield. Rotate the h/e Apparatus about the pin of the coupling bar to the right until the first first-order spectral line (Violet #2) falls on the slit in the white reflective mask. Open the Light Shield to be sure that this spectral line also falls on the window of 2
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mask. Repeat this procedure for the five second-order spectral lines of the same colors. Now move the h/e apparatus to the left side of the centerline and repeat the above procedure for each of the five spectral lines (first- and second-order) on that side of the diffraction grating. Aided by the data-analysis procedure described below, use Origin to plot average stopping potential versus the spectral line frequency. Determine t...