04Unit 5 Review
Consolidate your understanding of quantum physics, atomic and nuclear physics, and elementary particle physics with mixed conceptual questions, calculation problems, and a student self-check.
Modern physics — quantum mechanics, nuclear physics, and particle physics — underpins every technology from semiconductors to MRI machines to nuclear energy. Mastering these concepts connects classical physics to the frontier of scientific knowledge.
How did the discovery that energy and matter are quantized — and that particles behave like waves — transform our understanding of atoms, nuclei, and the fundamental building blocks of the universe?
Unit Summary
Unit 5 explores the revolutionary ideas of modern physics. Chapter 1 introduces quantum physics — the photoelectric effect, photon energy, and wave-particle duality. Chapter 2 covers atomic and nuclear physics — the Bohr model, energy levels, radioactive decay, and nuclear reactions. Chapter 3 surveys elementary particle physics — the Standard Model, quarks, leptons, force carriers, and conservation laws.
Quantum Physics
Photoelectric effect · E = hf · de Broglie wavelength · wave-particle duality
Atomic & Nuclear Physics
Bohr model · energy levels · radioactive decay · half-life · fission & fusion
Elementary Particle Physics
Standard Model · quarks · leptons · bosons · conservation laws · antimatter
Key Equations
Photon Energy
E = hf
Photon (wavelength)
E = hc/λ
Photoelectric Effect
KE_max = hf − φ
de Broglie
λ = h/p = h/mv
Bohr Energy Level
Eₙ = −13.6/n² eV
Photon Emission
ΔE = hf
Half-Life Decay
N = N₀(½)^(t/t½)
Mass-Energy
E = mc²
h = 6.626 × 10⁻³⁴ J·s = 4.136 × 10⁻¹⁵ eV·s | c = 3.00 × 10⁸ m/s | 1 eV = 1.6 × 10⁻¹⁹ J
Worked Examples
Calculate the energy of a photon with frequency 6.0 × 10¹⁴ Hz.
Use E = hf.
E = (6.626 × 10⁻³⁴ J·s)(6.0 × 10¹⁴ Hz)
E = 3.98 × 10⁻¹⁹ J
Convert: 3.98 × 10⁻¹⁹ J ÷ 1.6 × 10⁻¹⁹ J/eV ≈ 2.49 eV
Light of frequency 8.0 × 10¹⁴ Hz strikes a metal with work function φ = 2.0 eV. Find the maximum kinetic energy of the ejected electrons.
KE_max = hf − φ
hf = (4.136 × 10⁻¹⁵ eV·s)(8.0 × 10¹⁴ Hz) = 3.31 eV
KE_max = 3.31 eV − 2.0 eV = 1.31 eV
An electron in a hydrogen atom transitions from n = 4 to n = 2. What is the energy of the emitted photon?
E₄ = −13.6/4² = −0.85 eV
E₂ = −13.6/2² = −3.40 eV
ΔE = E₄ − E₂ = −0.85 − (−3.40) = 2.55 eV (emitted)
A radioactive sample has a half-life of 5.0 years. What fraction remains after 20 years?
Number of half-lives: t/t½ = 20/5 = 4
N/N₀ = (½)⁴ = 1/16
Find the de Broglie wavelength of an electron (m = 9.11 × 10⁻³¹ kg) moving at 2.0 × 10⁶ m/s.
λ = h/mv
λ = (6.626 × 10⁻³⁴) / (9.11 × 10⁻³¹ × 2.0 × 10⁶)
λ = 6.626 × 10⁻³⁴ / 1.822 × 10⁻²⁴
λ ≈ 3.64 × 10⁻¹⁰ m = 0.364 nm
Guided Practice
A photon has wavelength 400 nm. Calculate its energy in eV.
Hint: Use E = hc/λ. Convert nm to m first, then divide by 1.6 × 10⁻¹⁹ to get eV.
The work function of sodium is 2.28 eV. What is the minimum frequency of light needed to eject electrons?
Hint: At threshold, KE_max = 0, so hf_min = φ. Solve for f_min = φ/h.
A hydrogen electron drops from n = 3 to n = 1. Is the photon emitted in the UV, visible, or IR range?
Hint: Calculate ΔE using Eₙ = −13.6/n² eV. Then find λ = hc/ΔE and compare to the visible range (400–700 nm).
Carbon-14 has a half-life of 5,730 years. A sample has 25% of its original ¹⁴C remaining. How old is the sample?
Hint: 25% = (½)² means 2 half-lives have passed. Age = 2 × 5,730 years.
A proton (m = 1.67 × 10⁻²⁷ kg) has a de Broglie wavelength of 1.0 × 10⁻¹⁰ m. Find its speed.
Hint: λ = h/mv → v = h/(mλ). Plug in values.
Key Vocabulary
Photon
A discrete packet (quantum) of electromagnetic energy with energy E = hf.
Example: Visible light photons have energies of about 1.8–3.1 eV.
Photoelectric Effect
The emission of electrons from a metal surface when light above a threshold frequency strikes it.
Example: Einstein's explanation earned him the 1921 Nobel Prize.
Wave-Particle Duality
The principle that all matter and light exhibit both wave-like and particle-like properties.
Example: Electrons produce interference patterns (wave) but land at discrete spots (particle).
Quantum Number (n)
An integer (1, 2, 3, …) that specifies the energy level of an electron in the Bohr model.
Example: n = 1 is the ground state; higher n means higher energy and larger orbit.
Radioactive Decay
The spontaneous emission of particles or energy from an unstable nucleus.
Example: Alpha (α), beta (β), and gamma (γ) decay are the three main types.
Half-Life
The time required for half of a radioactive sample to decay.
Example: Carbon-14 has a half-life of 5,730 years, used in radiocarbon dating.
Nuclear Fission
The splitting of a heavy nucleus into lighter nuclei, releasing large amounts of energy.
Example: Uranium-235 fission is used in nuclear power plants and atomic bombs.
Quark
A fundamental particle that combines to form hadrons (protons, neutrons). Quarks carry fractional electric charge.
Example: A proton is made of two up quarks and one down quark (uud).
Workbook Check
Interactive Practice — 5 Questions
Which observation BEST demonstrates the particle nature of light?
An electron in hydrogen is in the n = 3 state. How many different photon energies can it emit as it returns to the ground state?
A radioactive isotope has a half-life of 10 days. After 30 days, what fraction of the original nuclei remain?
Which particle is a lepton?
If the speed of an electron doubles, its de Broglie wavelength: