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Physics Unit 10: Modern and nuclear physics

Energy comes in quanta, matter and light behave as both waves and particles, and nuclear reactions convert mass into energy.

Covers: Photons and the photoelectric effect, wave-particle duality, energy levels and spectra, the Standard Model, mass-energy equivalence, nuclear forces, fission and fusion

Study guide

At the atomic scale, energy is quantized. Light consists of photons, each with energy E = hf = hc/λ, where h = 6.63 × 10⁻³⁴ J·s is Planck's constant. In the photoelectric effect, light ejects electrons from a metal only if its frequency is above a threshold; brighter light ejects more electrons but doesn't give them more energy, which showed light acts as particles. In the Compton effect, an X-ray photon collides with an electron and loses energy, so its wavelength increases, showing photons carry momentum. Matter also acts like a wave: a moving particle has a de Broglie wavelength λ = h/p, confirmed by electron diffraction. This wave-particle duality applies to both light and matter.

In the Bohr model, electrons occupy specific energy levels. An electron that absorbs a photon with exactly the right energy jumps to a higher level, and one that drops to a lower level emits a photon with energy equal to the difference: E_photon = E_initial − E_final. That's why each element has a unique bright-line spectrum. Energies are often given in electronvolts (1 eV = 1.60 × 10⁻¹⁹ J). Ionization occurs when an electron gains enough energy to leave the atom.

The Standard Model organizes matter into fundamental particles. Hadrons, such as protons and neutrons, are made of quarks: a proton is two up quarks and one down quark (uud), and a neutron is one up and two down (udd). Up quarks have a charge of +2/3 e and down quarks −1/3 e. Leptons, such as electrons and neutrinos, are fundamental. Every particle has an antiparticle with the opposite charge. There are four fundamental forces: the strong force (strongest, very short range, holds nuclei together), the electromagnetic force, the weak force (involved in beta decay) and gravity (weakest). Mass and energy are equivalent: E = mc². A nucleus has slightly less mass than its separate protons and neutrons; this mass defect is the binding energy that holds it together. One atomic mass unit is equivalent to 931 MeV. In fission and fusion, a small amount of mass is converted into a large amount of energy.

Key ideas

• Photon energy is E = hf.
• The photoelectric and Compton effects show light acts as particles.
• Electron transitions emit or absorb photons equal to the energy difference.
• Protons (uud) and neutrons (udd) are made of quarks.
• E = mc² explains binding energy and nuclear energy.

Formulas and rules

Common mistakes

• Thinking brighter light gives ejected electrons more energy; only higher frequency does.
• Forgetting to convert eV to joules before using E = hf.

Words to know

Quantum

The smallest discrete amount of energy.

Photon

A particle of light with energy E = hf.

Planck's constant

h = 6.63 × 10⁻³⁴ J·s.

Photoelectric effect

Light ejecting electrons from a metal surface.

Compton effect

A photon losing energy and increasing wavelength after hitting an electron.

De Broglie wavelength

The wavelength of a moving particle: λ = h/p.

Wave-particle duality

Light and matter behave as both waves and particles.

Energy level

An allowed energy for an electron in an atom.

Bright-line spectrum

The specific wavelengths emitted by an element.

Electronvolt

Energy unit equal to 1.60 × 10⁻¹⁹ J.

Quark

A fundamental particle that makes up protons and neutrons.

Hadron

A particle made of quarks, like a proton or neutron.

Lepton

A fundamental particle like the electron or neutrino.

Antiparticle

A particle with the same mass but opposite charge.

Strong force

The strongest force, holding the nucleus together.

Mass-energy equivalence

E = mc².

Mass defect

The mass lost when a nucleus forms, released as binding energy.

Sample practice questions

15 more questions like these, from level 1 to 5, are in the practice set.