What is the Photoelectric Effect?
The photoelectric effect is the emission of electrons from a metal surface when light shines on it — a phenomenon that couldn't be explained by classical wave theory and led Einstein to propose that light is quantized into photons.
The photoelectric effect occurs when photons with enough energy strike a metal, ejecting electrons. The maximum kinetic energy of the ejected electrons follows KE_max = hf − φ, where h is Planck's constant, f is the light's frequency, and φ is the metal's work function.
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Step-by-step worked examples
Light of frequency 7×10¹⁴ Hz hits sodium, which has a work function of 2.3 eV. Find KE_max in eV.
Photon energy E = hf; in eV, E = 4.136×10⁻¹⁵ × 7×10¹⁴ = 2.895 eV KE_max = 2.895 − 2.3 = 0.595 eV
A metal has a work function of 4.5 eV. Find the threshold frequency below which no electrons are emitted.
φ = 4.5 eV = 4.5 × 1.602×10⁻¹⁹ J = 7.209×10⁻¹⁹ J f0 = φ/h = 7.209×10⁻¹⁹ / 6.626×10⁻³⁴ ≈ 1.088×10¹⁵ Hz
Light with wavelength 500 nm hits a metal with work function φ = 2.0 eV. Is emission possible, and what is KE_max?
f = c/λ = 3×10⁸ / 500×10⁻⁹ = 6×10¹⁴ Hz E = 4.136×10⁻¹⁵ × 6×10¹⁴ = 2.48 eV Since 2.48 eV > 2.0 eV, yes — KE_max = 2.48 − 2.0 = 0.48 eV
Flashcards
Quick quiz
Q1.What ejects an electron in the photoelectric effect?
Q2.Light of frequency 6×10¹⁴ Hz hits a metal with φ = 2.0 eV. Photon energy ≈ 2.48 eV. What is KE_max?
Q3.What happens if the light frequency is below the threshold frequency?
Q4.Which constant relates photon energy to frequency?
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Common mistakes
Assuming brighter light (more intensity) alone can eject electrons below the threshold frequency. — Correct: Only frequency (photon energy) determines whether emission occurs; intensity only affects the number of emitted electrons.
Thinking KE_max depends on light intensity. — Correct: KE_max depends only on frequency (KE_max = hf − φ); intensity affects the number of emitted electrons, not their maximum energy.
Treating light as purely a wave in this context. — Correct: The photoelectric effect requires light's particle (photon) nature — quantized energy packets E = hf.
Mixing eV and joule units inconsistently. — Correct: Keep units consistent — 1 eV = 1.602×10⁻¹⁹ J — when working with formulas that use the SI Planck's constant.
FAQ
What is the photoelectric effect?
The emission of electrons from a material's surface when light of sufficient frequency shines on it.
What is the formula for the photoelectric effect?
KE_max = hf − φ, where h is Planck's constant, f is light frequency, and φ is the work function.
What are examples of the photoelectric effect?
Solar cells, photomultiplier tubes, light meters, and the photoelectric sensors used in automatic doors.
How do you calculate the kinetic energy in the photoelectric effect?
Multiply Planck's constant by the light's frequency, then subtract the metal's work function: KE_max = hf − φ.