INTRODUCTION

    In early experiments that attempted to create radio waves, it was noticed that light shining on an electrode sometimes produced a visible spark. Later experimentation found that these sparks were created by the impact of light on an electrode, which caused the ejection of electrons. It was also found that these ejected electrons had kinetic energies that increased linearly with the frequency of the light used. These observational results were explained by Einstein assuming that light behaves as a particle.

THEORY

    The apparatus consists of a mercury source behind a slit, a diffraction grating and a lens which focuses an image of the slit in the wavelength of each mercury line on a photo tube. The electrons ejected from the surface in the photo tube run along a wire to charge a capacitor to roughly their highest energy (since they have to overcome the repulsive force of all the other electrons gathered on the capacitor to charge it), so the measured voltage gives us a measure of this energy (also called the stopping potential, V_stop).

The apparatus

Photo head detail

Electrons on the metal surface absorb photons of energy E = hf, where h is Planck's constant. When part of this photon energy (the work function, φ) is greater than the energy necessary to free the electron from the surface (the binding energy), the electron jumps off the surface with the remainder of the photon energy going into the electron’s kinetic energy:

K_max = hf - φ

These electrons strike one of the capacitor plates and charge it up. Eventually, the capacitor voltage becomes large enough to stop further charging. This happens when

K_max = eV_stop

Thus, using a little algebra, the stopping potential can be written as

Of the quantities in this equation,

• we can measure V_stop ,
• we can find f for each of the given mercury wavelengths (c = f λ ),
• we know e = 1.602 x 10^-19 Coulombs,
• we want to find φ, and
• we want to confirm the value of Planck’s constant, h.

The equation for V_stop looks suspiciously like our linear friend, y = mx + b. Thus, if we plot the measured V_stop versus f we should get a straight line. From the slope we can find Planck’s constant and from the intercept we can find the work function, φ, and hence the binding energy of the electrons.

EXPERIMENT

1. Calculate the frequency, f, for the mercury lines listed in the table below (spectroscopic tables tend to list the wavelengths). Note that the yellow line is actually a double line. You will only be able to resolve it as a single spectral line, so the wavelength given in the table is the average of the actual wavelengths (577.0 nm and 579.1 nm).

2. The diffraction grating is blazed, which means that the spectral lines on one side of the central image are brighter than the other. Using the 1^st and 2^nd order images on the brighter side, measure the stopping potential for each color. Be sure to use the green and yellow filters for the green and yellow lines. These filters limit higher frequencies of light from entering the phototube, which would interfere with the lower energy green and yellow light.

3. Take several measurements of the stopping potential for each line, then calculate the average, < V_stop >. As you collect your data, plot <V_stop> vs. f. You should get a straight line. If a point is not on the line, remeasure V_stop. If it still isn’t on the line, check to see if you have correctly identified the Mercury line (do any second-order lines overlap the first-order?).

   You'll note that the 2nd order image lines are fainter and broader than the 1st order. Since the kinetic energy of the ejected electrons depends upon the freqency (i.e. color), and not the intensity of the light used, your stopping potentials for the 1st and 2nd order images should be very close. Are they?

Line Color	Wavelength, λ (nm)	Frequency, f (Hz)	Vstop 1st order (volts)	Vstop 2nd order (volts)	<Vstop> 1st order (volts)	<Vstop> 2nd order (volts)
Violet #1	365.0
Violet #2	404.7
Blue	435.8
Green	546.1
Orange	578.1

4. When your hand graph is satisfactorily linear, use Excel to plot <V_stop> vs. f. Reject any really bad points, then find Planck’s constant and the electron binding energy from a linear fit.

CONCLUSION

• Report your value of Planck’s constant and the binding energy of the electrons in the phototube.
• Discuss whether or not your estimate of Planck’s constant is consistent with the accepted value (h = 6.626x10^–34 J•s), and compare your value of the binding energy with that of cold hydrogen, which is 13.6 eV (convert your measured value of φ to eV, recalling that 1 eV = 1.602x10^–19 J).

Return to Physics 104

©	St. Lawrence University	Department of Physics

Revised: 16 May 17

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