Ch 1 · 22 Quantum Physics · A Level Physics 9702
Topic 1 of 2 in Quantum and Nuclear Physics — A Level Physics 9702 — 38 lessons.
Introduction
Light behaves as a wave when it diffracts, but as a stream of particles when it knocks electrons out of a metal. Electrons, normally thought of as particles, diffract like waves. Quantum physics accepts both pictures, and explains why each element gives out its own fingerprint of colours. (Syllabus topic 22: sections 22.1–22.4.)
Key ideas — 22.1 Photons
Electromagnetic radiation has a particulate nature: it is emitted and absorbed in discrete packets called photons. A photon is a quantum of electromagnetic energy:
🧑🏫 Teacher's explanation
Imagine you are playing a game of pool. In classical wave theory, you might think of light like a continuous stream of water hitting a target—the more water you spray, the more force you apply. However, quantum physics tells us light is actually like a stream of individual billiard balls (photons). Each ball carries a specific amount of energy determined solely by its color (frequency). If a ball doesn't have enough 'oomph' to knock a target loose, it doesn't matter how many balls you throw; nothing happens. You need a ball with enough individual energy to overcome the target's grip.
📖 Definitions
🔍 Worked example — Exam-style
An electron is traveling at 2.00 × 10^6 m/s. Calculate the de Broglie wavelength associated with the electron. Use h = 6.63 × 10^-34 J s and mass of electron m = 9.11 × 10^-31 kg.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — 22.2 The photoelectric effect
When electromagnetic radiation of high enough frequency shines on a metal surface, electrons (photoelectrons) are emitted.
🧑🏫 Teacher's explanation
Imagine you are playing a game of arcade basketball where you have to throw a ball into a hoop. The 'work function' is like the height of the hoop. If you throw a ball very softly (low frequency), it doesn't matter if you throw a thousand balls per minute (high intensity); none will ever go in because they lack the energy to reach the height. However, if you throw the ball with enough force (high frequency), it goes in immediately.
📖 Definitions
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — 22.3 Wave–particle duality
Electron diffraction. A beam of electrons passed through a thin layer of graphite produces rings on a fluorescent screen, just like a diffraction pattern for waves. This is evidence that particles have a wave nature. Increasing the accelerating p.d. (faster electrons, more momentum) makes the rings smaller: shorter wavelength, less diffraction. The spacing between atoms in graphite (about 10^-10 m) is similar to the electrons' wavelength, which is why the diffraction is noticeable.
🧑🏫 Teacher's explanation
Imagine you are playing a game of billiards. If you hit a ball with a cue stick, the ball moves as a single, solid object—this is like the 'particle' nature of light. However, if you throw a handful of sand at a wall, the grains spread out and create a pattern—this is like the 'wave' nature. In the quantum world, everything is a bit of both. Light behaves like a particle (a photon) when it hits a metal surface and knocks electrons off, but it behaves like a wave when it bends around corners (diffraction) or overlaps with other waves (interference).
📖 Definitions
🔍 Worked example — Easy
Calculate the de Broglie wavelength of an electron moving at a velocity of 3.0 imes 10^6 m s^-1. (Use h = 6.63 × 10^-34 J s and mass of electron m = 9.11 × 10^-31 kg)
🔍 Worked example — Standard
A photon has an energy of 4.0 × 10^-19 J. Calculate its momentum p. (Use c = 3.0 × 10^8 m s^-1)
🔍 Worked example — Exam-style
An electron is accelerated through a potential difference of 500 V. Calculate its de Broglie wavelength. (Mass of electron m = 9.11 × 10^-31 kg, charge e = 1.60 × 10^-19 C, h = 6.63 × 10^-34 J s)
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — 22.4 Energy levels and line spectra
Electrons in an isolated atom (e.g. atomic hydrogen) can only have certain discrete energy levels. An electron moves between levels by absorbing or emitting one photon whose energy equals the difference between the levels:
🧑🏫 Teacher's explanation
Imagine a ladder where the rungs are spaced at very specific, fixed heights. You can stand on the first rung or the second rung, but you cannot hover in the empty space between them. Electrons in an atom behave exactly like this; they are restricted to specific 'rungs' called energy levels. They cannot exist 'between' levels.
📖 Definitions
🔍 Worked example — Exam-style
An emission spectrum shows a bright line at a wavelength of 486 nm. This corresponds to an electron falling from E_2 to E_1. Calculate the energy difference between these levels in Joules. (h = 6.63 × 10^-34 J s, c = 3.00 × 10^8 m/s)
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Worked example
Example 1. Find the energy of a photon of wavelength 500 nm, in J and eV. E = hc/λ = (6.63 × 10^-34 × 3.00 × 10^8)/(500 × 10^-9) = 3.98 × 10^-19 J = 2.49 eV.
Common mistakes
Practice
Answers: (1) A quantum (discrete packet) of electromagnetic energy, E = hf. (2) One photon gives its energy to one electron; if hf is less than the work function, no electron can escape, whatever the intensity. (3) p = h/λ = 1.1 × 10^-27 kg m s⁻¹. (4) Electrons passing through thin graphite form diffraction rings, like waves; the rings shrink as the electrons' speed increases. (5) λ = 6.63 × 10^-34/1.5 = 4.4 × 10^-34 m; far smaller than any gap or obstacle, so diffraction is undetectable. (6) White light passes through a cool gas; electrons absorb photons with energies equal to differences between energy levels, so those wavelengths are removed (re-emitted in all directions), leaving dark lines.