Light Work

Light frees electrons from a metal one photon at a time. The colour sets how much energy each electron can leave with; the brightness only sets how many leave. Push back on them with a voltage: the one that stops even the fastest is its kinetic energy in electronvolts.

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Collector +1.00 V
Guided investigation — ages 16–18 physics

The photoelectric effect, measured

Every task asks for a written prediction first. The idea that brighter light gives the electrons more energy is hard to shake, so the value is in recording what you believed before the meter told you otherwise.

1Stopping voltage

The voltage that stops them

Mode: Stop them  ·  15 min

Predict

Violet light (405 nm) falls on caesium and 0.8 nA flows with the collector at +2 V. Sketch how the current changes as you take the collector down to −2 V, and mark where you think it reaches zero.

  1. Record I at 0.2 V steps from +2.0 V to −1.2 V. Plot I against V and determine the stopping voltage.
  2. Calculate Emax in eV and in J, and the speed of the fastest electrons.
  3. Explain why the current falls gradually rather than all at once as the collector is made more negative.
  4. With the supply at 0 V there is still a current. Explain where the electrons get the energy to cross.
  5. Switch to 546 nm. Predict, then measure, the new stopping voltage.
2Intensity & frequency

Brightness or colour?

Modes: Brighter, Bluer  ·  20 min

Predict

You double the intensity of the light. State what happens to the saturation current and to the stopping voltage. Then do the same for changing green light to violet at the same intensity.

  1. In Brighter, trace the I–V curve at 100 nW and at 400 nW. Compare the saturation currents and the stopping voltages.
  2. Calculate the number of photons arriving per second at each power, and deduce the fraction of photons that free an electron.
  3. In Bluer, find the longest wavelength that frees electrons from sodium. Determine the work function from it.
  4. At the same power, compare the saturation currents at 436 nm and 254 nm. Explain the difference in terms of photons per second, and state the assumption this relies on.
3Planck constant

h from a straight line

Modes: Einstein’s line, No waiting  ·  25 min

Predict

You plot stopping voltage against frequency for caesium and then for zinc. Sketch both lines on one set of axes.

  1. Record Vs at five wavelengths for one metal. Plot Vs against f on paper.
  2. Determine the gradient and hence the Planck constant. Determine the threshold frequency and the work function.
  3. Repeat for a second metal. Comment on the two gradients.
  4. In a real tube every stopping voltage is shifted by the same small amount, set by the surfaces of the two electrodes. Explain why h can still be found accurately but Φ cannot.
  5. In No waiting, calculate how long a wave would take to give one electron its work function at the lowest intensity, and compare it with what you see.
The physicsEach photon carries E = hf, and each electron is freed by one photon, so Emax = hf − Φ and eVs = Emax, exact in every readout, taking the collector to have the same work function as the photo-surface. h = 6.626×10−34 J s, e = 1.602×10−19 C, hc = 1240 eV nm.
The modelElectrons leave with kinetic energies spread evenly from zero to Emax. One photon in a hundred frees an electron, at every wavelength; real surfaces vary strongly with wavelength. At 0 V half the electrons head for the collector, and a positive collector draws in the rest. Real tubes round off the foot of the curve.
The apparatusA lamp and a grating monochromator, 200–700 nm, with the mercury lines at 254, 365, 405, 436, 546 and 577 nm marked. Illuminated area 1.0 cm². Work functions: caesium 2.10, sodium 2.36, zinc 4.33, copper 4.65 eV — typical values; a real surface varies by a few tenths of an eV.
The drawingElectrons are slowed tens of millions of times. Each wave packet stands for 2×1010 photons and each dot for 2×108 electrons, except in No waiting, where each stands for one. The measured limit on the delay, under 3 ns, is from Lawrence and Beams (1928).
What it is built onDocumented student difficulties: that brighter light gives faster electrons, that the supply voltage is what pulls electrons out, and that the current–voltage graph is a straight line through the origin. Steinberg, Oberem & McDermott (1996), Am. J. Phys. 64, 1370; Steinberg & Oberem (2000), J. Comput. Math. Sci. Teach. 19, 115; McKagan, Handley, Perkins & Wieman (2009), Am. J. Phys. 77, 87.