The Photoelectric Effect: A Sharp Energy Threshold

1 · Predict

Light of different wavelengths hits a metal with work function 2.3 eV. As long as both wavelengths are short enough to eject electrons at all (their photon energy is above the threshold energy), does a bluer (shorter-wavelength) photon eject an electron with more kinetic energy?

• No — kinetic energy depends only on light intensity, not wavelength.
• It depends on the metal's color, not the light's wavelength.
• Yes — above threshold, shorter wavelength means higher photon energy, so ejected electrons have more kinetic energy.

2 · Set Up

1. Open the photoelectric-threshold preset and press Reset. The photocell's work function is fixed at 2.3 eV.
2. Enable the photon-energy and maximum-kinetic-energy readouts.
3. Set the light's wavelength for each trial and record the maximum kinetic energy of ejected electrons.

3 · Collect Data

Plot K_max (y-axis) against 1/λ (x-axis) for your three trials. Is the line straight?

4 · Analyze

1. For one trial, compute E_γ = hc/λ using h = 6.626×10⁻³⁴ J·s, c = 2.998×10⁸ m/s, then K_max = E_γ − φ using φ = 2.3 eV. Compare both to the table.
2. Explain why K_max increases linearly with photon energy (and therefore with 1/λ) once you're above threshold, with a slope of hc (≈1240 eV·nm when λ is in nm) and a y-intercept of −φ.

5 · Extend

1. Classical wave theory predicted that even dim, low-frequency light should eventually eject electrons if you wait long enough or turn up the intensity. Explain why the photoelectric effect's sharp energy threshold (independent of intensity) was so surprising before Einstein's photon explanation.
2. If you doubled the light's intensity at the same wavelength, would K_max change? What would change instead?

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