Optics & Waves · AP Physics 2 (Modern Physics)
Photoelectric Effect & Stopping Voltage Simulator
Key exam takeaway: Emission depends solely on frequency exceeding threshold ν0 (intensity does not help). Max kinetic energy Ek = hν - W0 depends strictly on frequency.
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Live Derivations & Metrics
Photon Energy E
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Work Function W0
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Max Kinetic Energy Ek
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Stopping Voltage Uc
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Sodium work function is 2.29eV. Does 400nm light trigger emission? Find Ek,max and stopping potential Uc.
Step-by-Step Derivation:
- E = hc/λ = 3.11eV > 2.29eV (yes). Max kinetic energy Ek = 3.11 - 2.29 = 0.82eV. Stopping voltage Uc = 0.82V.
Worked Problem
Problem: What 3 paradoxes doomed classical wave theory in explaining the photoelectric effect?
Step-by-Step Derivation:
- 1) Classical waves predicted intensity determines energy (failing threshold rule); 2) energy accumulation delays (emission was instant); 3) electron energy matched frequency not intensity.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: If light intensity doubles at constant frequency, what happens to Ek,max and saturation current?
Answer Key: Max kinetic energy Ek remains unchanged. Saturation photocurrent doubles because photon arrival rate doubles.
Q2. Variant 2: In a plot of stopping voltage Uc vs frequency ν, what do the slope and intercepts represent?
Answer Key: Slope equals h/e (Planck constant over electron charge). Vertical intercept is -W0/e; horizontal intercept is threshold frequency ν0.
Q3. Variant 3: What modern devices utilize phototubes? What is the operating mechanism?
Answer Key: Solar panels, optical sensors, night vision, barcode scanners. Light ejects electrons, creating current that converts light into electrical signals.
Frequently Asked Questions & Misconceptions
Why did Einstein win the Nobel Prize for the photoelectric effect rather than relativity?
Relativity was contentious in 1921; the photoelectric quantum hypothesis was conclusively verified by Millikan's precision experiments.
If photon energy exactly equals the work function (hν = W0), does emission occur?
Yes, the electron just escapes to the surface with zero excess kinetic energy (Ek = 0) and zero launch velocity.
Why does photocurrent drop smoothly rather than abruptly as reverse voltage rises?
Emitted electrons have a velocity spread from 0 to Ek,max. Higher voltage filters out slower electrons progressively.
Is light fundamentally a wave or a stream of particles?
Light possesses wave-particle duality. Propagation exhibits wave phenomena (interference, diffraction); emission and absorption exhibit particle behavior.