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 𝜇0 4π × 10–7 H m–1
permittivity of free space 𝜀0 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 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 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 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length = r𝜃
quadratic equation − b ± b 2 − 4 ac
x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.7 1
, Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝑓 period 𝑓 =
𝑇
photon photon 𝛾 0
lepton neutrino ve first 1 𝑇
0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝜆𝜆 diffraction
electron e± 0.510999 spacing 𝑤 = grating
𝑑 sin 𝜃 = 𝑛𝑛
𝑠
muon µ± 105.659 refractive index of a substance s, 𝑛 =
𝑐
𝑐s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
0
π 134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
±
K meson K 493.821 critical angle sin 𝜃c =
𝑛2
for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝐹
velocity and ∆𝑠 ∆𝑣
Properties of quarks acceleration 𝑣 = 𝑎 =
∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑣
𝑣 = 𝑢 + 𝑎𝑎 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑎 2
𝑣 2 = 𝑢2 + 2𝑎𝑎 𝑠 = 𝑢𝑢 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑚
3 3
∆(𝑚𝑚)
1 1 force 𝐹 =
d − e + 0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
1 1
s − e + −1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑣2 Δ𝐸p = 𝑚𝑚Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝐹
Lepton number
𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝
Particles: e− , νe ; µ− , νµ +1 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =
𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚
Photons and energy levels density 𝜌 = Hooke’s law 𝐹 = 𝑘 Δ𝐿
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝜆 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝐴
Young modulus =
photoelectricity ℎ𝑓 = ϕ + 𝐸k (max) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐿
tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2
1
ℎ ℎ energy stored 𝐸 = 2 𝐹Δ𝐿
de Broglie wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.7
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 𝜇0 4π × 10–7 H m–1
permittivity of free space 𝜀0 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 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 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 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length = r𝜃
quadratic equation − b ± b 2 − 4 ac
x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.7 1
, Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝑓 period 𝑓 =
𝑇
photon photon 𝛾 0
lepton neutrino ve first 1 𝑇
0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝜆𝜆 diffraction
electron e± 0.510999 spacing 𝑤 = grating
𝑑 sin 𝜃 = 𝑛𝑛
𝑠
muon µ± 105.659 refractive index of a substance s, 𝑛 =
𝑐
𝑐s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
0
π 134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
±
K meson K 493.821 critical angle sin 𝜃c =
𝑛2
for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝐹
velocity and ∆𝑠 ∆𝑣
Properties of quarks acceleration 𝑣 = 𝑎 =
∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑣
𝑣 = 𝑢 + 𝑎𝑎 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑎 2
𝑣 2 = 𝑢2 + 2𝑎𝑎 𝑠 = 𝑢𝑢 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑚
3 3
∆(𝑚𝑚)
1 1 force 𝐹 =
d − e + 0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
1 1
s − e + −1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑣2 Δ𝐸p = 𝑚𝑚Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝐹
Lepton number
𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝
Particles: e− , νe ; µ− , νµ +1 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =
𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚
Photons and energy levels density 𝜌 = Hooke’s law 𝐹 = 𝑘 Δ𝐿
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝜆 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝐴
Young modulus =
photoelectricity ℎ𝑓 = ϕ + 𝐸k (max) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐿
tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2
1
ℎ ℎ energy stored 𝐸 = 2 𝐹Δ𝐿
de Broglie wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.7
