Physics SAT3 — Main Concepts & Equations

68 concept and application cards for topics 3.1–3.4, checked against all 46 supplied question topics and the class booklets. Includes relevant equations and the booklet’s SHE example. Basic definitions are in the separate Fundamentals set.

3.1 | How does a signal travel between antennas?

Transmitting electrons oscillate → an EM wave travels → its electric field drives receiving electrons. All have the same frequency. For a simple half-wave dipole, total length is about λ/2.

3.1 | Which antenna orientation receives the strongest signal?

Parallel to the incoming electric field, so electrons can move along the antenna. Perpendicular alignment ideally gives no signal.

3.1 | Why is light from a hot filament neither coherent nor monochromatic?

It contains many frequencies, emitted independently with changing phase relationships. There is no single frequency or stable phase relationship.

3.1 | When do waves make a bright fringe?

For sources starting in phase, path difference Δs = mλ, where m is a whole number. The waves arrive in phase and reinforce.

3.1 | When do waves make a dark fringe?

For sources starting in phase, Δs = (m + ½)λ. They arrive in opposite phase. Complete cancellation requires equal amplitudes.

3.1 | What happens to the amplitude when two identical waves reinforce?

It doubles: A + A = 2A. At that point, intensity is proportional to amplitude squared, I ∝ A², so two equal in-phase waves give four times one wave’s intensity.

3.1 | How do narrow slits produce a double-slit pattern?

Coherent light illuminates both slits. Each slit diffracts the light, so the two waves spread, overlap and interfere on the screen.

3.1 | What makes diffraction stronger?

A narrower opening compared with the wavelength produces more spreading. Slit width controls spreading; slit separation controls fringe spacing.

3.1 | Why is the middle double-slit fringe bright?

Both paths are equal, so Δs = 0. The waves arrive in phase and reinforce.

3.1 | What changes the spacing of double-slit fringes?

Δy ≈ λL/d for small angles. Longer λ or larger screen distance L spreads fringes out; larger slit separation d brings them closer. Measure across several gaps and divide by their number for a better estimate.

3.1 | Why does a diffraction grating give sharp, intense maxima?

Many narrow, equally spaced slits spread light. Waves reinforce at special angles, giving sharp maxima useful for separating close wavelengths in spectroscopy. More illuminated slits sharpen the peaks.

3.1 | What does the grating equation mean?

Neighbouring paths differ by Δs = d sin θ. A maximum needs Δs = mλ, giving d sin θ = mλ. d is spacing, θ is angle from straight ahead, and m is a whole-number order.

3.1 | Why does a grating give a white centre and coloured side bands?

At the centre, all wavelengths have Δs = 0 and combine as white. Elsewhere, d sin θ = mλ puts different wavelengths at different angles.

3.1 | Where do the colours and higher orders appear?

Red is farther out than violet because its wavelength is longer. Higher orders lie farther out and spread more; different orders can overlap. The pattern appears on both sides.

3.1 | How do you calculate wavelength with a grating and screen?

Measure screen distance L and distance y from centre to order m. θ = tan⁻¹(y/L), then λ = d sin θ/m. Use metres for lengths.

3.1 | How do you find grating spacing and the largest possible order?

For N lines per mm, d = 10⁻³/N metres. Orders must satisfy mλ/d ≤ 1, so the largest mathematical order is the whole-number part of d/λ.

3.1 | Why might a double-slit setup put a single slit before the two slits?

With a non-laser monochromatic source, a narrow first slit supplies light from one small region to both slits, helping make them coherent. A suitable laser already supplies coherent light.

3.2 | How does photon energy become electron energy?

One photon gives energy to one electron. hf = W + Kmax, so Kmax = hf − W. Escape uses energy W; the remainder is kinetic energy.

3.2 | Why does light below threshold fail even when very bright?

Each photon has hf < W, too little to free an electron. More photons cannot fix the energy shortfall of each individual photon.

3.2 | Why is photoelectric emission immediate above threshold?

A single photon supplies enough energy in one interaction. The electron does not gradually store energy from the light wave.

3.2 | How do frequency and intensity affect photoelectrons differently?

Higher frequency → larger Kmax = hf − W and stopping voltage. Higher intensity at fixed frequency above threshold → more electrons and current, but unchanged Kmax and stopping voltage.

3.2 | Why do emitted electrons have a range of energies?

Some need more than the minimum energy to escape, or lose energy before reaching the surface. Kmax describes the fastest electrons, not the average.

3.2 | How can stopping voltage test the photon model?

For several frequencies on the same metal, increase reverse voltage until current is zero. Calculate Kmax = eVₛ and plot against frequency. The fastest speed is vmax = √(2eVₛ/mₑ), at non-relativistic speeds.

3.2 | What can you read from a Kmax-versus-frequency graph?

Kmax = hf − W is a straight line: slope h if energy is in J, frequency intercept f₀, and extended vertical intercept −W. With energy in eV, slope = h/e.

3.2 | What do the filament and tube voltage do in an X-ray tube?

Heating releases electrons from the filament (thermionic emission). The voltage accelerates them towards the positive target. Electrical work is qΔV, giving each electron K ≈ eV; the target converts this into X-rays and heat.

3.2 | Why does an X-ray tube need a vacuum and target cooling?

Vacuum prevents electrons losing energy in gas collisions. Cooling removes heat because most electron energy becomes heat at the target; only some becomes X-rays.

3.2 | What produces the continuous X-ray spectrum?

Electrons slow or change direction near target nuclei. Different energy losses produce photons with different energies, E = hf. This is braking radiation, or bremsstrahlung.

3.2 | What sets the X-ray frequency and wavelength limits?

The most energetic photon receives all an electron’s kinetic energy: hfmax = eV. So fmax = eV/h and λmin = hc/(eV).

3.2 | How are characteristic X-ray peaks made?

An incident electron ejects an inner-shell electron. A higher-level electron fills the vacancy and emits a photon: hf = ΔE. Fixed gaps give peaks specific to the target element.

3.2 | What does raising X-ray tube voltage change?

It gives electrons more energy (K ≈ eV), raising fmax and lowering λmin. The beam becomes harder. Characteristic peak frequencies stay fixed for the same target.

3.2 | What does raising filament current change?

More electrons leave the filament each second → more X-ray photons → greater intensity. At fixed tube voltage, maximum photon energy does not change.

3.2 | Why do some tissues look whiter in an X-ray image?

Thicker, denser and higher-atomic-number material generally attenuates more. Bone lets fewer photons reach the detector, so it appears whiter in the usual display.

3.2 | How do X-ray energy and intensity affect imaging?

Higher photon energy (E = hf) generally gives more penetration. At fixed hardness, intensity × exposure time is roughly constant for the same detector exposure: double intensity, half the time.

3.2 | How does accelerating an electron change its wavelength?

More speed means more momentum and shorter λ = h/p. Non-relativistically, ½mv² = eV, so λ = h/√(2meV) for acceleration from rest.

3.2 | What does electron double-slit interference show?

Even single electron arrivals build alternating high- and low-detection regions. Their wave behaviour produces interference; each detection is a separate particle-like hit.

3.2 | How did Davisson–Germer support matter waves?

A nickel crystal scattered electrons strongly at particular angles. Its regular atomic spacing caused diffraction, and the measured wavelength agreed with λ = h/p.

3.2 | Do electrons need the wavelength of visible light to diffract?

No. Their wavelength must suit the structure used, such as crystal atomic spacing. The same wavelength and slit geometry would give the same fringe positions, regardless of the kind of wave.

3.2 | How do photoelectric graphs for different metals compare?

Kmax = hf − W gives parallel lines: slope h is universal, but W and f₀ vary by metal. A larger work function shifts the threshold right and gives less electron energy at the same frequency.

3.2 | What do development and collaboration mean in the photon-research example?

Development: better methods for measuring single-photon shapes can enable new technology, such as secure communication. Collaboration: researchers from different institutions or countries combine expertise to make progress.

3.3 | What changes when an incandescent object gets hotter?

It emits more intensely, and its peak moves to shorter wavelengths. The spectrum remains continuous; the colour can change from red towards white or blue-white.

3.3 | How can spectral lines identify an element?

Each element has unique energy levels and therefore characteristic line wavelengths. Match a set of observed lines with reference spectra; a mixture can contain several elements’ lines.

3.3 | How do atoms become excited and then emit light?

They gain energy from light, heat or particle collisions. An electron moves up an allowed level, then a downward transition can emit a photon.

3.3 | How does an energy-level gap set the photon’s colour?

ΔE = Ehigh − Elow = hf = hc/λ. A bigger downward gap gives higher frequency and shorter wavelength. Example: −2 eV to −5 eV releases 3 eV.

3.3 | Why are spectral lines evidence for discrete energy levels?

Only certain photon frequencies occur. Since E = hf, only certain energy losses occur, showing that the atom has fixed allowed energy gaps.

3.3 | What do energy-level arrows and negative energies mean?

Up means energy gained; down means energy lost. Bound levels are negative; E = 0 is a free electron. Hydrogen levels are unevenly spaced and crowd together towards zero. Arrows show energy changes, not physical paths.

3.3 | How do you calculate ionisation energy?

From level En, required energy = 0 − En. Hydrogen’s ground state is −13.6 eV, so freeing its electron needs +13.6 eV.

3.3 | What defines the three main hydrogen series?

The final level: Lyman ends at n = 1 (UV); Balmer at n = 2 (visible lines extending into UV); Paschen at n = 3 (IR).

3.3 | What is a series limit?

The largest energy drop ending at a chosen lower level, starting at the free-electron limit. It gives that series’ highest frequency and shortest wavelength.

3.3 | Why do atoms absorb only selected wavelengths?

A photon must match an allowed gap from the atom’s starting level: hf = ΔE. Those wavelengths can also appear in emission; absorption depends on which lower levels are occupied.

3.3 | Why does room-temperature hydrogen not absorb visible light?

Nearly all atoms start at n = 1. The smallest upward gap is 10.2 eV, requiring UV. Visible photons do not have enough energy.

3.3 | Why are there dark lines in the Sun’s spectrum?

Cooler gas above hotter emitting layers absorbs photons matching atomic gaps. Re-emission in many directions leaves less light at those wavelengths along our sightline: Fraunhofer lines.

3.3 | How does fluorescence turn UV into lower-energy light?

In the booklet’s model, one high-energy photon excites an atom. Several smaller downward steps emit lower-energy, longer-wavelength photons. If no energy becomes heat, their energies add to the absorbed energy.

3.3 | Why does stimulated emission make coherent light?

A photon with hf = ΔE triggers an excited atom to drop. The added photon matches its frequency, phase, direction and polarisation. Repeated matching emissions amplify coherent light.

3.3 | What lets a laser amplify light instead of mainly absorbing it?

Pumping adds energy. A metastable upper level allows population inversion. Photons matching the energy gap then cause more stimulated emission than absorption.

3.3 | What are the mirrors for in a laser?

They send light repeatedly through the excited material for amplification. One mirror transmits some light as the output beam.

3.3 | What makes laser light useful, and how is it handled safely?

It is coherent, nearly monochromatic and spreads little, so it focuses intensely. Never aim at eyes or reflective surfaces; use wavelength-rated eyewear. The eye focuses the beam onto the retina, which can be damaged.

3.3 | How do you find all possible emission lines from an excited level?

Include every possible downward jump through the reachable levels, not just the jump straight to ground. Calculate each gap with ΔE = hf. For levels 1–4, there are six possible downward pairs across many atoms.

3.3 | Does “warm white” mean a higher colour temperature?

No. “Warm” describes a reddish or yellowish appearance, which has a lower Kelvin colour temperature. “Cool white” looks bluer and has a higher colour temperature. An LED’s colour temperature is not its physical temperature.

3.4 | How do quarks make a proton or neutron?

Proton uud: ⅔ + ⅔ − ⅓ = +1e. Neutron udd: ⅔ − ⅓ − ⅓ = 0. Both are three-quark baryons.

3.4 | How do you find the charge of a meson or antiparticle?

Add constituent charges, reversing each quark’s sign for its antiquark. π⁺ = u + anti-d = ⅔ + ⅓ = +1e. Antibaryons contain three antiquarks.

3.4 | Which particles feel the electromagnetic force, and what carries it?

Charged particles, including charged leptons and all quarks. The carrier is the photon. Like charges repel; opposites attract. It has infinite range, with force between point charges decreasing as 1/r².

3.4 | How does the strong force bind matter?

Gluons bind quarks into hadrons and also interact with gluons. The residual strong force binds nucleons over roughly nuclear distances (~10⁻¹⁵ m), often described using meson exchange. Leptons are unaffected.

3.4 | Which particles feel the weak force, and what can it do?

Quarks and all leptons, including neutrinos. W and Z bosons carry it over an extremely short range (~10⁻¹⁸ m). It can change quark type and cause beta decay.

3.4 | Where do gravity and the Higgs fit?

Gravity attracts masses and has infinite range, weakening as 1/r² for point masses. It is outside the Standard Model; the graviton is hypothetical. The Higgs is in the model but is not a gauge boson.

3.4 | How do you check a particle reaction?

Add charge, baryon number and each relevant lepton-family number separately before and after. Every total must match. Energy and momentum must also conserve.

3.4 | Why does beta minus decay produce an antineutrino?

n → p + e⁻ + electron antineutrino. A down quark becomes up. Charge balances: 0 = +1 − 1 + 0. Lepton number balances: 0 = +1 − 1. Baryon number stays 1.

3.4 | What happens in electron–positron annihilation?

e⁻ + e⁺ → two gamma photons. For a pair initially at rest, photons have equal energies and opposite momenta, preserving total energy and zero total momentum.

3.4 | How much energy does annihilation release?

Use ΔE = Δmc², adding any initial kinetic energy. An electron–positron pair at rest gives 2mₑc² = 1.022 MeV total, or 0.511 MeV per photon in two-photon annihilation.