Quantum physics and atomic structure

Physics · Modern physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Light behaves as particles called photons, each of energy hf. This explains the photoelectric effect: one photon frees one electron, so below the threshold frequency no electrons leave, however bright the light. The Compton effect confirms that photons carry momentum. Matter in turn has wave properties, with the de Broglie wavelength h/p, shown by electron diffraction. Position and momentum cannot both be known exactly.

Bohr explained the hydrogen spectrum with allowed orbits of quantised angular momentum; a photon is emitted when the electron drops between levels. The Schrödinger equation replaces orbits with a wave function ψ, where |ψ|2 gives the probability density of finding the particle. Solving it for a bound particle gives quantised energies.

Rules to remember

Common mistake

Thinking brighter light gives faster photoelectrons. The maximum kinetic energy and the stopping potential depend only on the frequency; intensity changes only the current.

Worked example

Light of wavelength 310 nm falls on a metal of work function 2.5 eV. Taking hc = 1240 eV nm, find the maximum kinetic energy of the photoelectrons, the stopping potential and the threshold wavelength.

  1. Photon energy = hc/λ = 1240 ÷ 310 = 4.0 eV.
  2. KEmax = 4.0 − 2.5 = 1.5 eV, so the stopping potential is 1.5 V.
  3. Threshold wavelength = hc/φ = 1240 ÷ 2.5 = 496 nm; longer wavelengths free no electrons.

Answer: 1.5 eV; 1.5 V; 496 nm.

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