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A-level Physics data and formulae
For use in exams from the June 2017 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo 𝑐 3. 00 × 108 m s–^1
permeability of free space 𝜇 0 4 π × 10 –^7 H m–^1
permittivity of free space 𝜀 0 8. 85 × 10 –^12 F m–^1
magnitude of the charge of electron 𝑒 1. 60 × 10 –^19 C
the Planck constant ℎ 6. 63 × 10 –^34 J s
gravitational constant 𝐺 6. 67 × 10 –^11 N m^2 kg–^2
the Avogadro constant 𝑁A 6. 02 × 1023 mol–^1
molar gas constant 𝑅 8. 31 J K–^1 mol–^1
the Boltzmann constant 𝑘 1. 38 × 10 –^23 J K–^1
the Stefan constant σ 5. 67 × 10 –^8 W m–^2 K–^4
the Wien constant 𝛼 2. 90 × 10 –^3 m K
electron rest mass (equivalent to 5.5 × 10–^4 u)
𝑚e 9. 11 × 10 –^31 kg
electron charge/mass ratio
𝑚e
- 76 × 1011 C kg–^1
proton rest mass (equivalent to 1.00728 u)
𝑚p 1. 67 ( 3 ) × 10 –^27 kg
proton charge/mass ratio
𝑚p
- 58 × 107 C kg–^1
neutron rest mass (equivalent to 1.00867 u)
𝑚n 1. 67 ( 5 ) × 10 –^27 kg
gravitational field strength 𝑔 9. 81 N kg–^1
acceleration due to gravity 𝑔 9. 81 m s–^2
atomic mass unit ( 1 u is equivalent to 931.5 MeV)
u 1. 661 × 10 –^27 kg
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
quadratic equation a
x b b ac 2
2
arc length = r 𝜃
circumference of circle = 2π r
ASTRONOMICAL DATA area of circle^ =^ π r
2
Body Mass/kg Mean radius/m
curved surface area of cylinder
= 2π rh
Sun 1. 99 × 1030 6. 96 × 108 area of sphere = 4π r^2
Earth 5. 97 × 1024 6. 37 × 106 volume of sphere^ =^3
4
π r^3
Particle Physics
Class Name Symbol Rest energy/MeV
photon photon 𝛾 (^0)
lepton neutrino v e 0
v μ 0
electron e ±^ 0.
muon μ±^ 105.
mesons π meson π±^ 139.
π^0 134.
K meson K±^ 493.
K
0
baryons proton p 938.
neutron (^) n 939.
Properties of quarks
antiquarks have opposite signs
Type Charge
Baryon number
Strangeness
u +
3
2
e +^
3
1
d −^
3
1
e +
3
1
s −^
3
1
e +
3
1
Properties of Leptons
Lepton number
Particles: e
e ;^ μ
Antiparticles: e+, νe, μ+, ν μ − 1
Photons and energy levels
photon energy (^) 𝐸 = ℎ𝑓 =
photoelectricity ℎ𝑓^ =^ ϕ^ +^ 𝐸k (max)
energy levels (^) ℎ𝑓 = 𝐸 1 – 𝐸 2
de Broglie wavelength (^) 𝜆 =
Waves
wave speed (^) 𝑐 = 𝑓𝜆 period (^) 𝑓 =
first harmonic 𝑓^ =^
fringe spacing 𝑤^ =^
diffraction grating 𝑑 sin 𝜃 = 𝑛𝜆
refractive index of a substance s , 𝑛 = 𝑐 𝑐s for two different substances of refractive indices n 1 and n 2 , law of refraction 𝑛 1 sin 𝜃 1 = 𝑛 2 sin 𝜃 2
critical angle sin 𝜃c =
𝑛 2 𝑛 1
for 𝑛 1 > 𝑛 2
Mechanics
moments moment = 𝐹𝑑
velocity and acceleration 𝑚^ =^
equations of motion
𝑚^2 = 𝑢^2 + 2 𝑎𝑠 𝑠 = 𝑢𝑡 +
𝑎𝑡^2
force (^) 𝐹 = 𝑚𝑎
force (^) 𝐹 =
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚) work, energy and power
𝑊 = 𝐹 𝑠 cos 𝜃
𝐸k =
𝑚 𝑚^2 Δ𝐸p =^ 𝑚𝑔Δℎ
∆𝑊 ∆𝑡 ,^ 𝑃^ =^ 𝐹𝑚
𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 =
Materials
density 𝜌 =
𝑚 𝑉
Hooke’s law 𝐹 = 𝑘 Δ𝐿
Young modulus =
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛
tensile stress =
𝐹 𝐴
tensile strain =
∆𝐿 𝐿
energy stored 𝐸 =
1 2
Magnetic fields
force on a current 𝐹 = 𝐵𝐼𝑙 force on a moving charge 𝐹 = 𝐵𝑄𝑚
magnetic flux Ф = 𝐵𝑅 magnetic flux linkage 𝑁 Ф = 𝐵𝑅𝑁 cos 𝜃
magnitude of induced emf (^) 𝜀 = 𝑁
Δ Ф
𝑁 Ф = 𝐵𝑅𝑁 cos 𝜃 emf induced in a rotating coil 𝜀 = 𝐵𝑅𝑁𝜔 sin 𝜔 t
alternating current 𝐼rms =
𝑉rms =
transformer equations
𝑁s 𝑁p
𝑉s 𝑉p
efficiency =
𝐼s𝑉s
𝐼p𝑉p
Nuclear physics
inverse square law for γ radiation (^) 𝐼 =
𝑥^2
radioactive decay Δ𝑁 Δ𝑡
= – 𝜆 𝑁 , 𝑁 = 𝑁oe−𝜆𝑡
activity 𝑅 = 𝜆𝑁
half-life (^) 𝑇½ =
ln 2 𝜆 nuclear radius (^) 𝑅 = 𝑅 0 𝑅^1 /^3
energy-mass equation 𝐸 = 𝑚𝑐^2
OPTIONS
Astrophysics
1 astronomical unit = 1. 50 × 1011 m
1 light year = 9. 46 × 1015 m 1 parsec = 2. 06 × 105 AU = 3. 08 × 1016 m = 3. 26 ly
Hubble constant, 𝐻 = 65 km s–^1 Mpc–^1
telescope in normal adjustment
𝑓e
Rayleigh criterion (^) 𝜃 ≈
magnitude equation (^) 𝑚 – 𝐺 = 5 log
Wien’s law 𝜆max 𝑇 = 2. 9 × 10 −^3 m K
Stefan’s law (^) 𝑃 = 𝜎𝑅𝑇^4
Schwarzschild radius 𝑅s ≈ (^2)
2 c
GM
Doppler shift for v << c
red shift (^) 𝑧 = −
Hubble’s law (^) 𝑚 = 𝐻𝑑
Medical physics
lens equations 𝑃^ =^
1 𝑓
1 𝑢
1 𝑣 threshold of hearing (^) 𝐼 0 = 1. 0 × 10 −^12 W m−^2
intensity level 𝑒𝑛𝑡𝑒𝑛𝑠𝑒𝑡𝑒 𝑙𝑒𝑚𝑒𝑙 = 10 log
absorption (^) 𝐼 = 𝐼 0 𝑒–𝜇𝜇
𝜇m =
ultrasound imaging (^) 𝑍 = 𝑝 𝑐
𝐼r 𝐼i
𝑍 2 − 𝑍 1 𝑍 2 + 𝑍 1
2
half-lives
1 𝑇E
𝑇B
𝑇P
AQA A-LEVEL PHYSICS DATA AND FORMULAE
Engineering physics
moment of inertia 𝐼 = Σ𝑚𝑝^2
angular kinetic energy (^) 𝐸𝑘 =
𝐼𝜔^2
equations of angular motion 𝜔 2 = 𝜔 1 + 𝛼 𝑡
𝜔 22 = 𝜔 12 + 2 𝛼𝜃
𝛼𝑡^2
torque 𝑇 = 𝐼 𝛼 𝑇 = 𝐹 𝑝 angular momentum (^) 𝑎𝑛𝑔𝑢𝑙𝑎𝑝 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝐼𝜔
angular impulse 𝑇Δ𝑡 = Δ(𝐼𝜔) work done 𝑊 = 𝑇𝜃 power (^) 𝑃 = 𝑇𝜔
thermodynamics 𝑄 = Δ𝑈 + 𝑊 𝑊 = 𝑝Δ𝑉 adiabatic change (^) 𝑝𝑉𝛾^ = constant
isothermal change 𝑝𝑉 = constant heat engines
efficiency =
𝑄H
𝑄H − 𝑄C
𝑄H
maximum theoretical efficiency =
𝑇H − 𝑇C
𝑇H
work done per cycle = area of loop
input power = calorific value × fuel flow rate indicated power = (𝑎𝑝𝑒𝑎 𝑜𝑓 𝑝 − 𝑉 𝑙𝑜𝑜𝑝) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑐𝑙𝑒𝑠 𝑝𝑒𝑝 𝑠𝑒𝑐𝑜𝑛𝑑) × (𝑛𝑢𝑚𝑠𝑒𝑝 𝑜𝑓 𝑐𝑒𝑙𝑒𝑛𝑑𝑒𝑝𝑠)
output or brake power 𝑃 = 𝑇𝜔
friction power = 𝑒𝑛𝑑𝑒𝑐𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑝 – 𝑠𝑝𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑝 heat pumps and refrigerators
refrigerator: 𝐶𝐶𝑃ref =
𝑄C 𝑊
𝑄C 𝑄H− 𝑄C
heat pum p : 𝐶𝐶𝑃hp =
𝑄H 𝑊
𝑄H 𝑄H− 𝑄C
Turning points in physics
electrons in fields (^) 𝐹 =
½ 𝑚𝑚^2 = 𝑒𝑉
Millikan’s experiment
Maxwell’s formula 𝑐^ =^
√^2 𝑚𝑒𝑉
special relativity 𝑡^ =^
2 𝑐 2
𝑚^2
𝑐^2
𝐸 = 𝑚 𝑐^2 =
𝑚 0 𝑐^2
2 𝑐 2
Electronics
resonant frequency 𝑓 0 =
Q-factor 𝑄 =
𝑓B
operational amplifiers: open loop 𝑉out =^ 𝑅OL(𝑉+ −^ 𝑉−) inverting amplifier 𝑉out 𝑉in
𝑅f 𝑅in non-inverting amplifier 𝑉out 𝑉in
𝑅f 𝑅l summing amplifier 𝑉out = −𝑅f �
difference amplifier 𝑉out = (𝑉+ − 𝑉−)
𝑅f 𝑅l
Bandwidth requirement: for AM 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2 𝑓M for FM (^) 𝑠𝑎𝑛𝑑𝑤𝑒𝑑𝑡ℎ = 2 (∆𝑓 + 𝑓M)
AQA A-LEVEL PHYSICS DATA AND FORMULAE
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