22. Quantum physics

Electromagnetic radiation shows wave behaviour such as interference and diffraction and particle behaviour such as quantised photon interactions.

Use the model that explains the observation; neither classical wave nor classical particle language alone covers every experiment.

A diffraction pattern supports wave behaviour, while the photoelectric effect requires discrete energy transfers.

Wave–particle duality is not a claim that light alternates between two physical substances during travel.

A photon is a discrete packet of electromagnetic energy with energy proportional to frequency and zero rest mass.

Photons travel at c in vacuum and are absorbed or emitted as whole quanta in interactions.

A higher-frequency ultraviolet photon carries more energy than a visible red photon.

A photon is not a tiny classical wave crest, and increasing intensity increases photon number at fixed frequency rather than each photon’s energy.

The energy of one photon is E=hf=hc/λ, where h is Planck’s constant, f frequency and λ wavelength.

Use frequency in hertz or wavelength in metres and check that higher frequency means higher photon energy.

Halving wavelength doubles photon energy in vacuum.

E=hf is energy per photon, not total beam energy; total energy also depends on how many photons arrive.

One electronvolt is 1 eV=1.60×10⁻¹⁹ J, the energy transfer when a charge of magnitude e moves through 1 V.

Use eV for particle-scale energies and convert to joules when applying SI equations or comparing macroscopic work.

A 5.0 eV electron has energy about 8.0×10⁻¹⁹ J.

An electronvolt is an energy unit, not a voltage or an electron’s mass.

For a photon, momentum magnitude p=E/c=h/λ. Photons carry momentum despite having zero rest mass.

Use photon energy from frequency or wavelength, then divide by c; momentum direction follows propagation direction.

Shorter-wavelength photons have greater momentum because p=h/λ.

Zero rest mass does not mean zero momentum or zero pressure when photons are absorbed or reflected.

The photoelectric effect is emission of electrons from a metal when incident photons have enough energy to overcome the surface work function.

Increasing intensity above threshold increases the number of emitted electrons, while frequency controls each photon’s energy and maximum electron speed.

Dim ultraviolet light can eject electrons while bright red light may not if red photon energy is below threshold.

Photoemission is not caused by accumulating energy over time from sub-threshold photons in the simple model.

Threshold frequency f₀ is the minimum photon frequency that ejects electrons; threshold wavelength λ₀ is the maximum wavelength, related by c=f₀λ₀.

Below f₀ or above λ₀ no electrons are emitted regardless of intensity in the ideal model.

A metal with threshold frequency 6.0×10¹⁴ Hz has threshold wavelength about 500 nm.

Threshold frequency is not the frequency of emitted electrons, and higher intensity cannot compensate for lower photon frequency.

A photon ejects an electron if hf≥Φ, where Φ is the work function; any excess becomes the electron’s kinetic energy.

Use Φ as the minimum energy needed to escape the surface and connect it to threshold frequency via Φ=hf₀.

Increasing frequency above threshold increases maximum photoelectron kinetic energy by the excess photon energy.

Work function is not the same as binding energy of every electron in the bulk and does not depend on beam intensity in this model.

Einstein’s photoelectric equation balances one photon’s energy: hf=Φ+½mv_max².

Use the maximum kinetic energy, not an average, and rearrange to find threshold, speed or stopping potential.

A plot of maximum kinetic energy against frequency has gradient h and intercept −Φ.

Increasing intensity raises photocurrent but not maximum kinetic energy when frequency is fixed.

For photoelectrons, the maximum kinetic energy is set by the energy of one incident photon: K_max=hf−Φ.

At a fixed frequency above threshold, raising intensity sends more photons per second, so the photocurrent can rise, but each photon still supplies the same energy and K_max is unchanged.

Doubling the intensity of ultraviolet light doubles the possible emission rate in an ideal experiment, not the stopping potential.

Intensity is not a substitute for frequency: sub-threshold photons do not eject electrons simply because the beam is brighter.

Photoemission is evidence that light transfers energy in discrete photons, each with energy E=hf.

The threshold frequency, near-instant emission and intensity–frequency separation are difficult to explain with a purely continuous-wave energy supply.

A low-intensity beam above threshold can eject electrons immediately, whereas a bright beam below threshold cannot in the ideal model.

This evidence supports quantised energy transfer; it does not mean every classical wave description is useless in every context.

When electrons pass through a thin crystal or narrow spacing, they can form diffraction patterns rather than only particle-like spots.

The pattern is explained by a wavelength associated with the moving electrons; changing electron momentum changes the spacing of maxima and minima.

A ring pattern from a polycrystalline film is evidence of constructive interference from many crystal orientations.

Diffraction does not say an electron is a classical water wave; it reveals wave-like interference in the probability description.

A particle with momentum p has de Broglie wavelength λ=h/p, so greater momentum means a shorter wavelength.

For a non-relativistic electron p=mv; use the momentum actually delivered by the apparatus, not simply the particle’s rest mass.

Accelerating an electron through a larger potential difference increases its speed and reduces λ, changing the diffraction scale.

The wavelength is not a path the particle visibly traces; it predicts the scale of interference and diffraction effects.

Use λ=h/p with h=6.63×10⁻³⁴ J s and momentum p in kg m s⁻¹.

If speed is known and v is far below c, calculate p=mv first; keep units consistent before comparing λ with a slit or lattice spacing.

For a 9.11×10⁻³¹ kg electron moving at 2.0×10⁶ m s⁻¹, λ is about 0.36 nm, comparable with atomic spacings.

Do not substitute kinetic energy directly for p unless you first use the appropriate relation; rounding p too early can distort λ.

An isolated atom allows electrons only in particular energy states, not every energy between them.

An electron changes level by absorbing or emitting a photon whose energy equals the gap: ΔE=hf. Larger gaps correspond to higher-frequency, shorter-wavelength lines.

A hydrogen emission spectrum contains separate lines because only certain transitions are allowed between its levels.

The electron does not radiate continuously while remaining in a stationary level; emission occurs during a transition between allowed states.

understand the appearance and formation of emission and absorption line spectra.

Use —the appearance and formation of emission and absorption line spectra to connect the rule to the data and decision in the question.

This matters because —the appearance and formation of emission and absorption line spectra determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply —the appearance and formation of emission and absorption line spectra to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: —The appearance and formation of emission and absorption line spectra is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

recall and use hf = E1 – E2.

Use —hf = e1 – e2 to connect the rule to the data and decision in the question.

This matters because —hf = e1 – e2 determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply —hf = e1 – e2 to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: —Hf = E1 – E2 is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.