The Photoelectric Effect
Turn the lamp up and nothing comes off faster. This is the experiment that made light countable, and the graph that hands you Planck's constant.
Introduction
Shine light on a clean metal and electrons come off: light carries energy, and energy shakes them free. The trouble starts when you turn the lamp up.
A caesium surface is emitting electrons under 450 nm light. You double the number of photons per second arriving. What happens to the maximum kinetic energy of the escaping electrons?
Brightness does not buy speed
A brighter beam delivers more energy per second, and the beam-power readout climbs. But only energy per photon can be handed to a single electron, which is why the intensity control counts photons per second.
The threshold is a cliff
Caesium has the lowest work function in the metal list, φ = 2.14 eV, and even so there is a wavelength beyond which nothing happens.
Caesium's threshold wavelength is 579 nm. You point a 650 nm beam at it and turn the intensity all the way up. What does the ammeter read?
Holding the electrons back
Put a battery in the loop the other way round, so the collector is negative. Now an electron has to climb a hill of height to reach it. The voltage that turns back even the fastest one is the stopping voltage: , measured in volts.
Light of nm falls on caesium, φ = 2.14 eV. What is the stopping voltage?
Measuring Planck's constant
The automatic scan steps the light through twelve frequencies, evenly spaced from to Hz. At each one it raises the retarding voltage until the ammeter reads nothing, and plots that stopping voltage as a point.
You run the same scan again with a platinum cathode (φ = 5.65 eV) instead of caesium (φ = 2.14 eV). What happens to the straight line?
The delay that never happens
A classical wave spreads its energy evenly over the surface, and each atom has to soak up its share until it adds up to the work function. The "Classical wave would need" readout does that arithmetic: minutes. What is observed is no delay at all.
In the scan you watched a family of current–voltage curves build up. You double the beam intensity and run the whole scan again. What is different?
What comes next
Einstein published this in 1905, and his 1921 Nobel Prize cited it by name. Millikan measured from the slope of this line in 1916 to better than one percent, while remaining openly unconvinced by the light-quantum picture behind it. Light now diffracts as a wave and lands as a quantum. Next, the question in reverse: does something everyone called a particle travel as a wave?
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “A brighter beam gives the electrons more energy”
- “Dim light below threshold just takes longer to shake an electron loose”
- “A metal that holds its electrons tighter gives a steeper graph”
- “A photon is a tiny bright dot riding along the wave”
Finished with this lesson?
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Research behind this lesson
- Ambrose et al. 1999: University students who had studied physical optics at introductory level and beyond often could not account for the pattern light makes on a screen after a single or double slit; many did not know whether to apply geometrical or physical optics to a given situation and inappropriately combined elements of both, and some difficulties were serious enough to preclude even a qualitative wave model for light.
- McKagan et al. 2009: Faculty commonly assume the photoelectric effect is straightforward for students. A curriculum of interactive simulation, peer instruction and conceptual homework aimed at documented student difficulties left about 85% of students able to predict how the results of the experiment change, but far fewer able to connect those observations to the photon model of light.
- Steinberg et al. 1996: Many students in a sophomore-level modern physics course could not interpret the photoelectric experiment in terms of a photon model of light, even after instruction. The conceptual and reasoning difficulties identified guided an interactive computer-based tutorial whose central instructional strategy was drawing and interpreting graphs of current against voltage for the circuit.
- Van Heuvelen 1991: Experts move fluently between words, pictures, diagrams, graphs and equations; novices tend to jump straight to equations. Explicit practice moving between representations is what closes the gap.
- White & Gunstone 1992: The Predict–Observe–Explain cycle: committing to a prediction before observing makes a conflicting result impossible to ignore, which is what forces a belief to be revised rather than merely supplemented.