SPH4U · Exam review

Physics Exam Review

A practice exam with questions from all 5 units, then the key facts from every lesson, unit by unit. For a deeper look at one unit, open its test review.

Unit test reviews

Practice exam

35 questions, the same number from each unit. Each one shows the lesson it comes from.

Unit 1: Motion in Two Dimensions and Projectiles
1
At the same instant, one ball is dropped from a height and an identical ball is fired horizontally from the same height. Ignoring air resistance, which lands first?
Unit 1: Motion in Two Dimensions and Projectiles
2
Order the steps for solving a projectile launched at an angle from a cliff.
1. 1Combine final components if the impact velocity is needed
2. 2Use that time with the constant horizontal velocity to find the horizontal distance
3. 3Solve the vertical motion for the time of flight
4. 4Choose a positive direction and resolve the launch velocity into components
5. 5List the vertical knowns: initial vertical velocity, displacement and acceleration
Unit 1: Forces on Inclines and Friction
3
Which type of friction lets car tires grip the road without skidding when a car turns or brakes smoothly: static or kinetic?
Unit 1: Connected Objects and Frames of Reference
4
An elevator's cable snaps and it falls freely. What does a bathroom scale inside it read?
Unit 1: Uniform Circular Motion
5
What is the minimum speed a roller-coaster car must have at the top of a vertical loop of radius $8.0 m$ to stay on the track, in m/s? Give three significant figures.
m/s
Unit 1: Banked Curves, Rotating Frames and Artificial Gravity
6
A curve of radius $150 m$ is to be banked for a design speed of $90 km/h$ with no friction needed. What angle is required, in degrees? Give three significant figures.
°
Unit 1: Banked Curves, Rotating Frames and Artificial Gravity
7
Match each situation to the force that pulls or pushes the object toward the centre of its circle.
Car at the design speed on a banked curve
Car on a flat, dry curve
Astronaut on the rim of a spinning station
Rider on a rotor ride after the floor drops
Unit 2: Work, Energy and the Work-Energy Theorem
8
A child pulls a sled $8.0 m$ along level snow with a force of $60 N$ directed $4 0^{\circ}$ above the horizontal. How much work does the child do, in joules? Give three significant figures.
J
Unit 2: Work, Energy and the Work-Energy Theorem
9
A $10 N$ force acts on an object that moves $2 m$ . Order these angles between force and displacement from the most positive work to the most negative work.
1. 1 $18 0^{\circ}$
2. 2 $12 0^{\circ}$
3. 3 $9 0^{\circ}$
4. 4 $0^{\circ}$
5. 5 $6 0^{\circ}$
Unit 2: Springs and Simple Harmonic Motion
10
Where is a mass oscillating horizontally on a frictionless spring moving fastest?
Unit 2: Momentum and Impulse
11
What is the magnitude of the momentum of a $0.060 kg$ tennis ball moving at $50 m/s$ , in $kg \cdot m/s$ ?
kg·m/s
Unit 2: Momentum and Impulse
12
Two identical eggs fall from the same height, one onto a pillow and one onto a tile floor. Which quantity is the same for both eggs as they are stopped?
Unit 2: Collisions in One and Two Dimensions
13
Which quantity is conserved in every collision between two objects with no net external force?
Unit 2: Collisions in One and Two Dimensions
14
Match each event to the type of collision or interaction.
Two air-track gliders bounce off spring bumpers with no kinetic energy lost
A dart sticks in a hanging wooden block
A tennis ball bounces off a racket, losing some kinetic energy
Two skaters at rest push apart
Unit 3: Universal Gravitation and Orbits
15
The distance between the centres of two asteroids triples. What happens to the gravitational force between them?
Unit 3: Gravitational Potential Energy, Escape Speed and Kepler's Laws
16
What is the escape speed from the surface of the Moon ( $M = 7.35 \times 1 0^{22} kg$ , $R = 1.74 \times 1 0^{6} m$ ), in km/s? Give three significant figures.
km/s
Unit 3: Electric Forces and Fields
17
Two small spheres carry charges of $+ 1.5 μ C$ and $+ 2.5 μ C$ and are $5.0 cm$ apart. What is the size of the electric force between them, in newtons? Give three significant figures.
N
Unit 3: Electric Potential Energy and Potential
18
Two parallel plates $4.0 mm$ apart are connected to a $120 V$ supply. What is the electric field strength between them, in V/m?
V/m
Unit 3: Electric Potential Energy and Potential
19
What was the most important conclusion of Millikan's oil-drop experiment?
Unit 3: Magnetic Fields and Forces
20
These particles all enter the same magnetic field at the same speed, perpendicular to the field. Order their circular paths from smallest radius to largest.
1. 1A proton
2. 2A singly charged ion with 20 times the mass of a proton
3. 3An alpha particle (two protons and two neutrons, charge $+ 2 e$ )
4. 4An electron
Unit 3: Charged Particles in Uniform Fields: Deflection and e/m
21
Match each technology to how it uses fields to control charged particles.
Oscilloscope
Continuous inkjet printer
Ion thruster
Mass spectrometer
Unit 4: Interference and Diffraction of Waves
22
Two in-phase sources produce waves with a wavelength of $1.2 cm$ . What is the path difference, in centimetres, for a point on the third nodal line?
cm
Unit 4: Interference and Diffraction of Waves
23
Order these steps for finding the wavelength from a photograph of a two-source ripple-tank pattern.
1. 1Solve for the wavelength and check it against v = f times wavelength
2. 2Set the path difference equal to (n - 1/2) times the wavelength
3. 3Subtract to find the path difference
4. 4Identify which nodal line the chosen point lies on, counting outward from the bisector
5. 5Measure the distances from the point to each source
Unit 4: Huygens' Principle and the Particle-vs-Wave Debate
24
Which principle says that every point on a wavefront acts as a source of new wavelets? Give its name.
Unit 4: Young's Double-Slit Experiment and Gratings
25
Laser light of wavelength $633 nm$ passes through a single slit onto a screen $1.5 m$ away. The first dark fringe is $8.0 mm$ from the centre. How wide is the slit, in millimetres? Give three significant figures.
mm
Unit 4: Thin Films and Polarization
26
A coating with $n = 1.25$ is applied to glass with $n = 1.52$ . What is the minimum coating thickness, in nanometres, that cancels reflected light of wavelength $500 nm$ ?
nm
Unit 4: Light as an Electromagnetic Wave
27
A Wi-Fi router transmits at $2.4 GHz$ . What is the wavelength of its signal, in centimetres?
cm
Unit 4: Light as an Electromagnetic Wave
28
Light enters glass with a refractive index of $1.50$ . What is its speed in the glass, in units of $1 0^{8} m/s$ ?
× 10⁸ m/s
Unit 5: Special Relativity
29
Which statement is one of Einstein's two postulates of special relativity?
Unit 5: Mass-Energy Equivalence and Relativistic Energy
30
Using $m_{e} = 9.11 \times 1 0^{- 31} kg$ , what is the rest energy of an electron, in MeV? Give three significant figures.
MeV
Unit 5: Blackbody Radiation and Planck's Quantum Hypothesis
31
What did classical physics predict for blackbody radiation at very short wavelengths?
Unit 5: Photons and the Photoelectric Effect
32
A very bright red light ejects no electrons from a metal, but a dim blue light does. What is the best explanation?
Unit 5: Matter Waves and Wave-Particle Duality
33
Why does a thrown baseball never show diffraction as it passes through a doorway?
Unit 5: The Uncertainty Principle and Probability Waves
34
Match each scientist to the idea or invention.
Max Born
Werner Heisenberg
Louis de Broglie
Gerd Binnig and Heinrich Rohrer
Unit 5: The Standard Model of Particle Physics
35
Match each force to the particle that carries it.
Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity

Key facts by unit

Unit 1: Dynamics

Motion in Two Dimensions and Projectiles

Components: $v_{x} = v cos θ$ and $v_{y} = v sin θ$ ; recombine with $v = v_{x}^{2} + v_{y}^{2}$ and $θ = tan^{- 1} (v_{y} / v_{x})$ .
Relative velocity adds as vectors: $v_{BG} = v_{B W} + v_{W G}$ .
For a projectile with no air resistance, $a_{x} = 0$ and $a_{y} = 9.81 m/s^{2}$ downward; time is the only link between the two directions.
At maximum height $v_{y} = 0$ , but $v_{x}$ is unchanged and the acceleration is still $9.81 m/s^{2}$ down.
Level ground only: $R = \frac{v ^{2} sin 2 θ}{g}$ , maximum at 45°, equal for complementary angles.

Forces on Inclines and Friction

On an incline: $F_{g ∥} = m g sin θ$ along the slope and $F_{g ⊥} = m g cos θ$ into it.
With no other perpendicular forces, $F_{N} = m g cos θ$ .
Static friction: $F_{s} \leq μ_{s} F_{N}$ . Kinetic friction: $F_{k} = μ_{k} F_{N}$ , and usually $μ_{k} < μ_{s}$ .
Sliding down with friction: $a = g (sin θ - μ_{k} cos θ)$ .
A resting block starts to slide when $tan θ = μ_{s}$ .

Connected Objects and Frames of Reference

Treat objects moving together as a system: $a = \frac{F _{n e t, e x t er na l}}{m _{t o t a l}};$ tension is internal and cancels.
Find tension from one object's free-body diagram, for example $F_{T} = m_{2} (g - a)$ for a hanging mass accelerating down.
Atwood machine: $a = \frac{( m _{2} - m _{1} ) g}{m _{1} + m _{2}}$ .
An inertial frame is not accelerating; Newton's laws hold there using only real forces.
In an accelerating elevator the scale reads $F_{N} = m (g + a)$ with up as positive; in free fall it reads zero.

Uniform Circular Motion

Uniform circular motion has constant speed but changing velocity, so there is an acceleration toward the centre.
$a_{c} = \frac{v ^{2}}{r} = \frac{4 π ^{2} r}{T ^{2}} = 4 π^{2} r f^{2},$ with $v = \frac{2 π r}{T}$ and $f = \frac{1}{T}$ .
$F_{c} = \frac{m v ^{2}}{r}$ is supplied by real forces such as friction, tension, gravity or the normal force; it is never an extra force.
Flat curve: $v_{ma x} = μ_{s} g r$ .
Vertical circle: the minimum speed at the top is $v = g r$ ; tension is greatest at the bottom.

Banked Curves, Rotating Frames and Artificial Gravity

On a banked curve the horizontal component of the normal force, $F_{N} sin θ$ , supplies centripetal force.
Frictionless banking: $tan θ = \frac{v ^{2}}{r g}$ , independent of mass; at the design speed no friction is needed.
With friction, speeds between $v_{min}$ and $v_{ma x}$ are safe; friction points down the slope above the design speed and up the slope below it.
Use horizontal and vertical axes on a banked curve, because the acceleration is horizontal; $F_{N} = m g / cos θ$ at the design speed.
In a rotating frame, centrifugal ( $m ω^{2} r$ outward) and Coriolis (sideways on moving objects) effects are apparent, not real, forces. On Earth, Coriolis deflection is to the right in the Northern Hemisphere.
Artificial gravity: the floor of a spinning station supplies $ω^{2} r = \frac{4 π ^{2} r}{T ^{2}}$ ; for $g$ , $T = 2 π r / g$ .

Unit 2: Energy and Momentum

Work, Energy and the Work-Energy Theorem

Work by a constant force: $W = F Δ d cos θ$ . It is a scalar in joules and is negative when the force opposes the motion.
A force perpendicular to the displacement ( $θ = 9 0^{\circ}$ ) does zero work.
Work-energy theorem: $W_{n e t} = Δ E_{k} = \frac{1}{2} m v_{2}^{2} - \frac{1}{2} m v_{1}^{2} .$
With friction: $E_{k 1} + E_{g 1} = E_{k 2} + E_{g 2} + E_{t h}$ , where $E_{t h} = F_{f} Δ d$ and $F_{f} = μ_{k} F_{N}$ .
Power: $P = W /Δ t$ , and for a constant force along the motion $P = F v$ . $1 W = 1 J/s$ .

Springs and Simple Harmonic Motion

Hooke's law: the spring force is $F_{x} = - k x$ , a restoring force proportional to the displacement from equilibrium.
Elastic potential energy: $E_{e} = \frac{1}{2} k x^{2}$ , the area under the force-extension graph.
In a frictionless mass-spring system, $\frac{1}{2} k A^{2} = \frac{1}{2} m v^{2} + \frac{1}{2} k x^{2}$ and $v_{ma x} = A k / m$ .
Period of a mass on a spring: $T = 2 π m / k$ , independent of amplitude and of $g$ .
SHM is the projection of uniform circular motion onto a straight line.
Damping converts the oscillation's mechanical energy into thermal energy, so the amplitude decreases.

Momentum and Impulse

Momentum: $p = m v$ , a vector in $kg \cdot m/s$ that points along the velocity.
Impulse-momentum theorem: $F_{n e t} Δ t = Δ p = m v_{2} - m v_{1}$ .
Impulse is the area under a force-time graph; $1 N \cdot s = 1 kg \cdot m/s$ .
Average force: $F_{a vg} = Δ p /Δ t$ . For the same $Δ p$ , a longer time means a smaller force.
A rebound reverses the velocity, so its change in momentum is larger than for stopping alone.

Collisions in One and Two Dimensions

Conservation of momentum for an isolated system: $m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{1}^{'} + m_{2} v_{2}^{'} .$
Momentum is conserved in every collision and explosion; kinetic energy is conserved only in elastic collisions.
Perfectly inelastic (objects stick): $m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v^{'} .$
Elastic, head-on, target at rest: $v_{1}^{'} = \frac{m _{1} - m _{2}}{m _{1} + m _{2}} v_{1}$ and $v_{2}^{'} = \frac{2 m _{1}}{m _{1} + m _{2}} v_{1}$ .
In two dimensions, conserve the $x$ and $y$ components of momentum separately.

Unit 3: Gravitational, Electric, and Magnetic Fields

Universal Gravitation and Orbits

Universal gravitation: $F_{g} = \frac{G m _{1} m _{2}}{r ^{2}}$ , with $r$ measured centre to centre and $G = 6.67 \times 1 0^{- 11} N \cdot m^{2} / kg^{2}$ .
Gravitational field strength: $g = \frac{F _{g}}{m} = \frac{GM}{r ^{2}}$ , in $N/kg$ .
For a circular orbit gravity is the centripetal force, so $v = \frac{GM}{r}$ and $T = \frac{2 π r}{v}$ .
Orbital radius is Earth's radius plus altitude: $r = R_{E} + h$ . The satellite's own mass does not affect its speed or period.
A geostationary satellite orbits above the equator with a period of one day, at $r \approx 4.22 \times 1 0^{7} m$ .
Apparent weightlessness happens when an object and its surroundings share the same free-fall acceleration, so no support force acts.

Gravitational Potential Energy, Escape Speed and Kepler's Laws

Gravitational potential energy with zero at infinity: $E_{p} = - \frac{GM m}{r}$ ; it is negative because the object is bound.
Change in potential energy between two radii: $Δ E_{p} = GM m (\frac{1}{r _{1}} - \frac{1}{r _{2}})$ , which reduces to $m g h$ near the surface.
In a circular orbit, $E_{k} = \frac{GM m}{2 r}$ and $E_{t o t a l} = - \frac{GM m}{2 r}$ ; the binding energy is $\frac{GM m}{2 r}$ .
Escape speed: $v_{esc} = \frac{2 GM}{r} = 2 v_{or bi t}$ , independent of the object's mass and launch direction.
Kepler's laws: elliptical orbits with the Sun at one focus; equal areas in equal times; $T^{2} \propto r^{3}$ , so $\frac{T _{1}^{2}}{r _{1}^{3}} = \frac{T _{2}^{2}}{r _{2}^{3}}$ for the same central body.

Electric Forces and Fields

Coulomb's law: $F_{e} = \frac{k q _{1} q _{2}}{r ^{2}}$ with $k = 8.99 \times 1 0^{9} N \cdot m^{2} / C^{2}$ . Like charges repel; unlike charges attract.
Superposition: the net force (or field) from several charges is the vector sum of the individual forces (or fields).
Electric field strength: $E = F_{e} / q$ in N/C, directed as the force on a positive test charge.
Field of a point charge: $E = \frac{k q}{r ^{2}}$ , pointing away from positive and toward negative charges.
Between large parallel plates the field is uniform; around a point charge it is radial and inverse square.

Electric Potential Energy and Potential

Electric potential energy of two charges: $E_{e} = \frac{k q _{1} q _{2}}{r}$ , zero at infinite separation, used with signs.
Electric potential: $V = E_{e} / q$ and, for a point charge, $V = \frac{k q}{r}$ . Potentials add as scalars.
Work to move a charge between two points: $W = q Δ V$ .
Uniform field between parallel plates: $E = \frac{Δ V}{d}$ , in V/m, which equals N/C.
A charge accelerated from rest through $Δ V$ gains $E_{k} = ∣ q ∣Δ V$ ; $1 eV = 1.60 \times 1 0^{- 19} J$ .
Millikan's balanced drop: $qE = m g$ , so $q = \frac{m g d}{Δ V}$ ; every charge is a whole-number multiple of $e$ .

Magnetic Fields and Forces

Force on a moving charge: $F = q v B sin θ$ , maximum when $v$ is perpendicular to $B$ and zero when parallel.
Right-hand rule 3 (positive charge or conventional current): fingers along $B$ , thumb along $v$ or $I$ , palm gives the force. Reverse the direction for a negative charge.
In a uniform field a charge moving perpendicular to $B$ circles with radius $r = \frac{m v}{qB}$ . The magnetic force does no work.
Force on a current-carrying wire: $F = B I L sin θ$ .
Right-hand rules 1 and 2: thumb along the current in a straight wire gives the circular field; fingers along the current in a coil give the north end at the thumb.
Velocity selector: only charges with $v = E / B$ pass straight through crossed electric and magnetic fields.

Charged Particles in Uniform Fields: Deflection and e/m

Electron gun: $q Δ V = \frac{1}{2} m v^{2}$ , so $v = 2 q Δ V / m$ for a charge starting from rest.
Between parallel plates a charge has constant velocity along the plates and constant acceleration $a = qE / m = q Δ V / (m d)$ across them, so its path is a parabola.
Treat deflection like a horizontal projectile: $t = L / v_{x}$ , $y = \frac{1}{2} a t^{2}$ , and $tan θ = v_{y} / v_{x}$ on exit.
Velocity selector: crossed fields pass undeflected only the particles with $v = E / B$ .
Thomson's method: $\frac{e}{m} = \frac{v}{B r} = \frac{E}{B ^{2} r}$ ; the accepted value is $1.76 \times 1 0^{11} C/kg$ .
Electric and gravitational fields do work and bend paths into parabolas; a magnetic field does no work and bends paths into circles.

Unit 4: The Wave Nature of Light

Interference and Diffraction of Waves

Superposition: where waves overlap, the resulting displacement is the sum of the individual displacements.
For two in-phase sources, a point is on an antinodal line if $∣ P S_{1} - P S_{2} ∣ = mλ$ and on a nodal line if $∣ P S_{1} - P S_{2} ∣ = (n - \frac{1}{2}) λ$ .
For distant points: $sin θ_{n} = (n - \frac{1}{2}) \frac{λ}{d} \approx \frac{x _{n}}{L}$ .
Shorter wavelength or larger source separation gives more nodal lines, closer together.
Diffraction is significant when $λ / w$ is roughly 1 or larger, and negligible when the opening is many wavelengths wide.
The wave equation still links the quantities: $v = f λ$ .

Huygens' Principle and the Particle-vs-Wave Debate

Huygens' principle: every point on a wavefront is a source of wavelets moving at the wave speed; the new wavefront is the line tangent to all the wavelets.
Snell's law in wave form: $\frac{sin θ _{1}}{sin θ _{2}} = \frac{v _{1}}{v _{2}} = \frac{λ _{1}}{λ _{2}} = \frac{n _{2}}{n _{1}} .$
Crossing a boundary changes a wave's speed and wavelength but not its frequency; in a medium of index $n$ , $v = c / n$ and $λ = λ_{v a c uu m} / n$ .
Newton's particle model predicted light is faster in water; the wave model predicted slower. Foucault (1850) found it slower.
Key evidence for waves: Young's interference (1801 to 1803), the Poisson–Arago spot (1818 to 1819), Foucault's speed in water (1850), Maxwell's electromagnetic waves (1860s).

Young's Double-Slit Experiment and Gratings

Double slit or grating, bright fringes: $d sin θ_{m} = mλ$ ; dark fringes: $d sin θ_{n} = (n - \frac{1}{2}) λ$ .
Small-angle fringe spacing: $Δ y = \frac{λ L}{d}$ , so $λ = \frac{d Δ y}{L}$ .
Grating spacing: $d = \frac{1}{lines per unit length}$ ; the highest visible order is the largest whole number $m$ with $m \leq d / λ$ .
Single slit, dark fringes: $w sin θ_{n} = nλ$ ; the central maximum is about $2 λ L / w$ wide.
Young's interference fringes showed that light is a wave and gave a way to measure its wavelength directly.

Thin Films and Polarization

Wavelength inside a film: $λ_{f i l m} = λ / n_{f i l m}$ ; the frequency does not change.
Reflection off a higher-index medium flips the wave by half a wavelength; reflection off a lower-index medium does not.
One phase change: bright when $2 t = (m + \frac{1}{2}) λ_{f i l m}$ . Zero or two: bright when $2 t = m λ_{f i l m}$ . The dark conditions swap.
The thinnest non-reflecting coating (two phase changes) has $t = \frac{λ}{4 n}$ .
Unpolarized light through one filter keeps half its intensity; crossed filters block it; Malus's law $I = I_{1} cos^{2} θ$ gives the in-between cases.
Only transverse waves can be polarized, so polarization shows light is transverse.

Light as an Electromagnetic Wave

Electromagnetic waves are produced by accelerating charges, such as an oscillating electric dipole in an antenna.
In a vacuum all electromagnetic waves travel at $c = 3.00 \times 1 0^{8} m/s$ and obey $c = f λ$ .
Longest to shortest wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.
Dispersion: the refractive index depends on wavelength, so violet bends more than red in glass.
Resolution limit: $θ_{min} \approx 1.22 λ / D$ in radians. Bigger openings and shorter wavelengths see finer detail.

Unit 5: Revolutions in Modern Physics

Special Relativity

Postulates: the laws of physics are the same in all inertial frames, and light in a vacuum travels at $c$ for every inertial observer.
Lorentz factor: $γ = \frac{1}{1 - v ^{2} / c ^{2}} \geq 1$ .
Time dilation: $Δ t = γ Δ t_{0}$ , where the proper time $Δ t_{0}$ is measured by a clock present at both events.
Length contraction: $L = L_{0} / γ$ , only along the direction of motion; $L_{0}$ is the proper length.
Relativistic momentum $p = γm v$ ; rest energy $E = m c^{2}$ ; kinetic energy $(γ - 1) m c^{2}$ .
Events simultaneous in one frame need not be simultaneous in another.

Mass-Energy Equivalence and Relativistic Energy

Rest energy: $E_{0} = m c^{2}$ ; one gram of mass is equivalent to $9.0 \times 1 0^{13} J$ .
Total energy $E = γm c^{2}$ and kinetic energy $E_{k} = (γ - 1) m c^{2}$ ; at low speeds $E_{k} \approx \frac{1}{2} m v^{2}$ .
No object with mass can reach $c$ , because $γ$ and the kinetic energy grow without limit as $v \to c$ .
Mass defect: a nucleus is lighter than its separate nucleons; the binding energy is $Δ m c^{2}$ . Fission and fusion release energy because the products are more tightly bound.
Pair production needs a photon of at least $2 m_{e} c^{2} = 1.02 MeV$ ; electron-positron annihilation at rest gives two $0.511 MeV$ photons.
Conversions: $1 MeV = 1.60 \times 1 0^{- 13} J$ and $1 u = 1.66 \times 1 0^{- 27} kg$ .

Blackbody Radiation and Planck's Quantum Hypothesis

A blackbody absorbs all incident radiation; its emitted spectrum depends only on its temperature.
Wien's displacement law: $λ_{ma x} T = 2.898 \times 1 0^{- 3} m \cdot K$ , with $T$ in kelvin.
Total power per unit area rises as $T^{4}$ (Stefan-Boltzmann): doubling $T$ multiplies it by 16.
Classical theory predicted unlimited intensity at short wavelengths, the ultraviolet catastrophe.
Planck's hypothesis: oscillator energy is quantized, $E = nh f$ , with $h = 6.63 \times 1 0^{- 34} J \cdot s$ .
The quantum story: Planck (1900), Einstein's photons (1905), Bohr's atom (1913), de Broglie's matter waves (1924).

Photons and the Photoelectric Effect

Photon energy: $E = h f = \frac{h c}{λ}$ , with $h = 6.63 \times 1 0^{- 34} J \cdot s$ .
$1 eV = 1.60 \times 1 0^{- 19} J$ ; divide joules by $1.60 \times 1 0^{- 19}$ to get electron-volts.
Photoelectric equation: $E_{k, ma x} = h f - W$ , and the threshold frequency satisfies $W = h f_{0}$ .
Stopping potential: $E_{k, ma x} = e V_{s}$ , so an energy of $x$ eV is stopped by $x$ volts.
Intensity changes the number of electrons emitted; only frequency changes their maximum kinetic energy.

Matter Waves and Wave-Particle Duality

Photon momentum: $p = \frac{h}{λ}$ . In the Compton effect, scattered X-rays have a longer wavelength because they gave momentum to electrons.
de Broglie wavelength of a particle: $λ = \frac{h}{m v}$ .
Electron diffraction by crystals (Davisson and Germer, G. P. Thomson) is the evidence that matter has wave properties.
An atomic transition emits or absorbs one photon with $h f = E_{ini t ia l} - E_{f ina l}$ ; hydrogen's levels are $E_{n} = - 13.6 eV / n^{2}$ .
Emission spectra are bright lines; absorption spectra are dark lines at the same wavelengths for the same element.

The Uncertainty Principle and Probability Waves

Sent one at a time, photons and electrons each land as a single dot, yet the dots build up an interference pattern; detecting which slit is used destroys the pattern.
The wave function $ψ$ describes a particle; $∣ ψ ∣^{2}$ gives the probability of finding it at each place (Born's interpretation).
Copenhagen interpretation: a measurement produces a definite result; wave and particle descriptions are complementary.
Heisenberg's uncertainty principle: $Δ x Δ p \geq \frac{h}{4 π}$ , so the minimum $Δ v = \frac{h}{4 πm Δ x}$ .
Quantum tunnelling lets particles cross barriers they classically could not; it underlies the scanning tunnelling microscope, flash memory and alpha decay.

The Standard Model of Particle Physics

Four fundamental forces, strongest to weakest: strong, electromagnetic, weak, gravity. Carriers: gluons, photons, W and Z bosons.
Six quarks (up, down, charm, strange, top, bottom) with charges $+ \frac{2}{3} e$ or $- \frac{1}{3} e$ ; six leptons (electron, muon, tau and their neutrinos).
Baryons are three quarks (proton uud, neutron udd); mesons are a quark and an antiquark.
An antiparticle has the same mass and opposite charge as its particle.
Pair creation needs at least $2 m_{e} c^{2} = 1.02 MeV$ ; electron-positron annihilation at rest gives two photons.
Reactions conserve charge, baryon number and lepton number, as well as energy and momentum.