Flashcards · H556 · Topic 4

Electrons, waves and photons flashcards

48 cards on Topic 4, subtopics 4.1 to 4.5. Pick a subtopic or study them all.

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4.1 Charge and current

Electric current, and the coulomb: Current: rate of flow of charge, I = ΔQ/Δt. 1 C is the charge delivered by a steady current of 1 A in 1 s.
What does it mean that charge is quantised?: The net charge on any object or particle is ne, where n is a whole number and e = 1.6 × 10⁻¹⁹ C.
Conventional current vs electron flow: Conventional current leaves the source at its positive terminal. Electrons drift the opposite way, from negative towards positive.
Kirchhoff's first law: The total current into a junction equals the total current out. It follows from conservation of charge.
Drift velocity equation, and why drift velocity in a metal is tiny: I = Anev, where n is the number density of charge carriers. In a metal n is very large, so v is small, of the order of a fraction of a millimetre per second.
Charge carriers in a metal and in an electrolyte: Metal: electrons. Electrolyte: positive and negative ions, moving in opposite directions, both adding to the current.
Conductors, semiconductors and insulators in terms of n: Conductor: very large number density of charge carriers. Semiconductor: much smaller (not zero), rising with temperature. Insulator: almost zero.

4.2 Energy, power and resistance

Potential difference vs e.m.f.: P.d.: energy transferred per unit charge from electrical to other forms between two points (W = VQ). E.m.f.: energy given to each unit of charge by a source, converting other forms to electrical (W = EQ).
Speed of a charged particle accelerated from rest through a p.d. V: qV = ½mv², so v = √(2qV/m). Use q = e for an electron or proton, 2e for an alpha particle.
Resistance, and Ohm's law: R = V/I at a given p.d. (1 Ω = 1 V A⁻¹). Ohm's law: current is directly proportional to p.d. at constant temperature (and other physical conditions).
I–V characteristics of a filament lamp and a diode: Lamp: curve that flattens, symmetrical about the origin; the filament heats, ions vibrate more, R rises. Diode: negligible current in reverse and below about 0.6–0.7 V forward, then a steep rise.
Resistivity, and the effect of doubling L and halving d: R = ρL/A (ρ in Ω m), with A = πd²/4. Doubling L doubles R; halving d quarters A, so R × 4. Overall R × 8.
Effect of temperature on the resistivity of a metal and of a semiconductor: Metal: increases (ions vibrate more, more collisions; carrier number barely changes). Semiconductor (e.g. NTC thermistor): decreases, because many more charge carriers are released.
The three equations for electrical power: P = VI = I²R = V²/R. Energy W = VIt = Pt.
A 3.0 kW heater runs for 2.0 h at 20p per kW h. Find the energy in kW h and J, and the cost.: Energy = 3.0 × 2.0 = 6.0 kW h = 6.0 × 3.6 × 10⁶ = 2.16 × 10⁷ J. Cost = 6.0 × 20p = £1.20.
Why use small currents when measuring the resistivity of a wire?: So the wire does not heat up: a temperature rise would change its resistivity.

4.3 Electrical circuits

Kirchhoff's second law: Around any closed loop, the sum of the e.m.f.s equals the sum of the p.d.s (ΣIR). It follows from conservation of energy.
Total resistance in series and in parallel: Series: R = R₁ + R₂ + … (larger than any one). Parallel: 1/R = 1/R₁ + 1/R₂ + … (smaller than the smallest). Take the reciprocal at the end.
Internal resistance, terminal p.d. and lost volts: E = I(R + r) = V + Ir. Terminal p.d. V = E − Ir. Lost volts = Ir, which grows with current. With no current, V = E. Short-circuit current = E/r.
Graph of terminal p.d. V against current I for a cell: Vertical intercept = E. Gradient = −r. Horizontal intercept = E/r (the short-circuit current).
Potential divider output: V_out = R₂/(R₁ + R₂) × V_in, where R₂ is the component the output is across. Also V₁/V₂ = R₁/R₂.
Thermistor potential divider: where should V_out be taken to rise with temperature?: Across the fixed resistor. The NTC thermistor's resistance falls as it warms, so the fixed resistor takes a larger share of the p.d.
Effect of connecting a load across the output of a potential divider: The load is in parallel with R₂, so the effective resistance of that part falls and V_out falls.
Potentiometer as a potential divider: A uniform resistive track across a supply with a sliding contact. V_out is proportional to the length from the end: V_out = (l/L) × V_in.

4.4 Waves

Transverse vs longitudinal waves: Transverse: oscillations perpendicular to the direction of energy transfer. Longitudinal: oscillations along it, with compressions and rarefactions.
Phase difference between two points a distance x apart on a wave: Phase difference = 2πx/λ radians (360x/λ degrees). In phase: 0 or whole cycles. Antiphase: half a cycle (π rad).
Intensity of a wave, and how it depends on distance and amplitude: Intensity = power per unit area, I = P/A. For an isotropic point source I = P/(4πr²), so doubling r gives ¼. I ∝ amplitude².
When is diffraction significant?: When the wavelength is comparable to the gap width. A gap much larger than λ gives little spreading.
What does polarisation show?: Only transverse waves can be polarised, so a wave that can be polarised is transverse. Sound cannot be polarised.
EM spectrum in order of increasing frequency, and properties shared by all EM waves: Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All are transverse, travel through a vacuum at 3.00 × 10⁸ m s⁻¹, and can be reflected, refracted, diffracted, polarised and interfere.
Refractive index and Snell's law: n = c/v. n₁ sin i₁ = n₂ sin i₂ (angles from the normal). Frequency is unchanged; speed and wavelength change.
Critical angle, and the conditions for total internal reflection: Critical angle: the angle of incidence in the denser medium for which the angle of refraction is 90°. sin C = 1/n (into air). TIR needs light going from higher to lower n, at an angle of incidence greater than C.
Principle of superposition: Where waves overlap, the resultant displacement is the sum of the displacements each wave would give alone.
Coherent sources, and the path difference for constructive and destructive interference: Coherent: a constant phase difference (so the same frequency). For sources in phase: constructive when path difference = nλ; destructive when (n + ½)λ.
Young's double-slit equation, and the effect of halving a and doubling D: λ = ax/D (a slit separation, x fringe spacing, D slit–screen distance; needs a ≪ D). x = λD/a, so halving a and doubling D multiplies x by 4.
Diffraction grating: 600 lines per mm, λ = 650 nm. Find the first-order angle.: d = 1/(6.00 × 10⁵) = 1.667 × 10⁻⁶ m. sin θ = λ/d = 650 × 10⁻⁹ ÷ 1.667 × 10⁻⁶ = 0.39, so θ = 23.0°.
Stationary wave: how it forms, and node spacing: Two progressive waves of the same frequency travelling in opposite directions superpose. Nodes (always antiphase) and antinodes (always in phase) alternate; adjacent nodes are λ/2 apart, node to antinode λ/4.
Harmonics of a tube closed at one end: Node at the closed end, antinode at the open end. L = λ/4 for the fundamental; only odd harmonics: f = (2n − 1)v/4L.
Resonance tube: why use λ = 2(L₂ − L₁)?: The antinode is slightly above the tube mouth. The same end correction appears in both resonance lengths, so it cancels in the difference.

4.5 Quantum physics

Photon: A quantum (packet) of electromagnetic energy, with energy E = hf = hc/λ.
Electronvolt: The energy an electron gains when accelerated across 1 V: 1 eV = 1.60 × 10⁻¹⁹ J.
Work function and threshold frequency: Work function φ: the minimum energy needed to remove an electron from the surface of the metal. Threshold frequency f₀: the minimum frequency causing emission; hf₀ = φ.
Einstein's photoelectric equation: hf = φ + KEmax. One photon gives all its energy to one electron.
Graph of KEmax against frequency: A straight line KEmax = hf − φ. Gradient = h; frequency-axis intercept = f₀; KEmax-axis intercept = −φ.
Photoelectric effect: what does increasing the intensity change?: Above f₀, the emission rate (photoelectric current) is proportional to intensity. KEmax does not change: it depends only on frequency. Below f₀ there is no emission at any intensity.
Estimating h with LEDs: Find the p.d. V at which each LED just lights; eV = hc/λ. Plot V against 1/λ: gradient = hc/e, so h = gradient × e/c.
Evidence for wave-particle duality: Photoelectric effect: the particle nature of EM radiation. Electron diffraction through polycrystalline graphite (rings): the wave nature of particles.
de Broglie wavelength, and the effect of a higher accelerating voltage on electron diffraction rings: λ = h/p = h/mv. Higher voltage → faster electrons → smaller λ → rings of smaller radius.