Home / Courses / Physics 2 / Unit 7

Physics 2 Unit 7: Modern physics

Light and matter have both wave and particle properties, atoms have quantized energy levels, and nuclei release energy through decay, fission and fusion.

Covers: Photons and the photoelectric effect, wave–particle duality and de Broglie wavelength, atomic energy levels and spectra, nuclear structure, radioactive decay and half-life, mass–energy equivalence, fission and fusion

Study guide

Light comes in packets called 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 shining on a metal ejects electrons only if each photon has enough energy to overcome the metal's work function (φ). The maximum kinetic energy of ejected electrons is Kmax = hf − φ. Increasing light intensity increases the number of electrons but not their energy; only increasing frequency raises their energy. Below the threshold frequency, no electrons are emitted no matter how bright the light. This showed light behaves as particles, earning Einstein the Nobel Prize. Matter also has wave properties: the de Broglie wavelength is λ = h/p = h/(mv), confirmed by electron diffraction.

Electrons in atoms occupy quantized energy levels. When an electron drops from a higher level to a lower one, it emits a photon with energy equal to the difference: ΔE = hf. Absorbing a photon of exactly the right energy raises an electron to a higher level. Each element produces a unique line spectrum, which lets astronomers identify elements in stars. Energy-level diagrams show possible transitions; the number of possible emission lines grows with the number of levels.

The nucleus contains protons and neutrons (nucleons). The atomic number Z is the number of protons, and the mass number A is protons plus neutrons; isotopes differ in neutrons. The strong nuclear force holds nuclei together. In alpha decay, the nucleus emits a helium nucleus (A decreases by 4, Z by 2); in beta-minus decay, a neutron becomes a proton and emits an electron (Z increases by 1); in gamma decay, the nucleus emits a high-energy photon without changing A or Z. Nuclear equations must conserve both mass number and charge. Radioactive decay is random but follows a half-life: after each half-life, half of the remaining nuclei decay. Mass–energy equivalence, E = mc², explains binding energy and the mass defect. Fission splits heavy nuclei, like uranium-235, releasing energy in nuclear reactors; fusion combines light nuclei, like hydrogen, powering the sun.

In the Bohr model, the hydrogen atom's electron can occupy only certain energy levels, Eₙ = −13.6 eV/n². The ground state is n = 1, and the ionization energy is 13.6 eV. One electron-volt (eV) is 1.6 × 10⁻¹⁹ J. Every object emits thermal radiation over a range of wavelengths. A hotter object emits more total power, and its peak wavelength shifts shorter, from red toward blue (Wien's law: peak wavelength × T is constant).

Photons carry momentum p = h/λ. In Compton scattering, an X-ray photon bounces off an electron and transfers energy and momentum to it, so the scattered photon has a longer wavelength. This supports the particle model of light. In beta-plus decay, a proton becomes a neutron and emits a positron and a neutrino (Z decreases by 1). In electron capture, the nucleus absorbs an inner electron, which also lowers Z by 1. Beta-minus decay also emits an antineutrino, which carries off some of the energy.

Key ideas

• Photon energy is E = hf.
• The photoelectric effect depends on frequency, not intensity.
• Matter has a de Broglie wavelength λ = h/p.
• Electron transitions between energy levels emit or absorb specific photons.
• Nuclear decays conserve mass number and charge; E = mc² explains nuclear energy.

Formulas and rules

Common mistakes

• Thinking brighter light ejects faster electrons; only higher frequency does.
• Forgetting that after two half-lives, one-fourth (not zero) remains.

Words to know

Photon

A packet of light energy.

Planck's constant

h = 6.63 × 10⁻³⁴ J·s.

Photoelectric effect

Emission of electrons when light strikes a metal.

Work function

The minimum energy needed to eject an electron from a metal.

Threshold frequency

The minimum light frequency that ejects electrons.

Wave–particle duality

Light and matter show both wave and particle properties.

De Broglie wavelength

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

Energy level

A quantized energy an electron can have in an atom.

Emission spectrum

Specific wavelengths emitted by an element.

Absorption spectrum

Dark lines where an element absorbs specific wavelengths.

Isotope

Atoms of an element with different numbers of neutrons.

Strong nuclear force

The force holding protons and neutrons together.

Alpha decay

Emission of a helium nucleus.

Beta decay

A neutron changing into a proton and emitting an electron.

Gamma decay

Emission of a high-energy photon from a nucleus.

Half-life

Time for half of a radioactive sample to decay.

Mass defect

The mass lost when a nucleus forms, converted to binding energy.

Fission

Splitting a heavy nucleus into smaller ones.

Fusion

Combining light nuclei into a heavier one.

Sample practice questions

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