Quantum and Atomic Physics

Atoms do not behave like tiny solar systems. Their electrons occupy quantized states described by probabilities, and light is exchanged in discrete packets called photons.

This lesson supports Chapter 24 of High School Physics.

Energy comes in allowed amounts

Bound electrons in an atom occupy discrete energy levels. Once an electron is ionized, its unbound states form a continuum of energies. An electron absorbs a photon to move to a higher allowed level and emits a photon when it drops to a lower one. The positive photon energy equals the magnitude of the level difference, \(E_\gamma=|E_f-E_i|=hf\). The atom gains this energy in absorption and loses it in emission. This produces characteristic atomic spectra.

Light and matter show wave-particle behavior

Photons carry energy \(E=hf\) and momentum \(p=\frac h\lambda\). Matter also has a de Broglie wavelength, \(\lambda=\frac hp\). Which behavior becomes visible depends on the experiment. The model does not say that a particle is secretly a classical wave or classical ball.

A wavefunction predicts probabilities

The wavefunction is a mathematical description. Its squared magnitude gives a probability density for measurement outcomes. The uncertainty principle sets a physical limit on simultaneous precision for pairs such as position and momentum. It is not merely a statement about poor instruments.

Worked example

An atom emits a photon when an electron drops by \(3.0\text{ eV}\). The photon carries \(3.0\text{ eV}\) of energy. Its frequency follows from \(f=\frac{E_\gamma}{h}\), and its wavelength follows from \(c=f\lambda\).

Watch the idea in action

Khan Academy gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. Are the allowed energies of bound atomic electrons continuous?
2. What happens when an electron drops to a lower level?
3. Write the photon energy formula.
4. Write the de Broglie relation.
5. What does the squared wavefunction represent?
6. Is quantum uncertainty caused only by faulty instruments?

Answers

1. No. Bound-state energies are discrete; ionized, unbound states form a continuum.
2. A photon is emitted.
3. \(E=hf\).
4. \(\lambda=\frac hp\).
5. Probability density.
6. No.

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

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