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AS Physics data and formulae
For use in exams from the June 2016 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Symbol Value Units
𝑐 3.^00 ×^108 m^ s–^1
0 4 π^ ×^10 –^7 H^ m–^1 0 8.^85 ×^10 –^12 F^ m–^1
𝑒 1.^60 ×^10 –^19 C
ℎ 6. 63 × 10 –^34 J^ s
𝐺 6. 67 × 10 –^11 N m^2 kg–^2
𝑁A 6. 02 × 1023 mol–^1
𝑅 8. 31 J K–^1 mol–^1
𝑘 1. 38 × 10 –^23 J K–^1
- 67 × 10 –^8 W m–^2 K–^4
- 90 × 10 –^3 m K
𝑚e 9. 11 × 10 –^31 kg
𝑚e^1.^76 ×^10
(^11) C kg– 1
𝑚p 1. 67 ( 3 ) × 10 –^27 kg
𝑚p 9.^58 ×^10
(^7) C kg– 1
𝑚n 1. 67 ( 5 ) × 10 –^27 kg
𝑔 9.^81 N kg–^1
𝑔 9. 81 m s–^2
Quantity
speed of light in vacuo permeability of free space permittivity of free space magnitude of the charge of electron the Planck constant gravitational constant the Avogadro constant molar gas constant the Boltzmann constant the Stefan constant the Wien constant electron rest mass (equivalent to 5.5 × 10–4^ u)
magnitude of electron charge/mass ratio
proton rest mass (equivalent to 1.00728 u)
proton charge/mass ratio
neutron rest mass (equivalent to 1.00867 u) gravitational field strength acceleration due to gravity atomic mass unit
( 1 u is equivalent to 931.5 MeV) u^1.^661 ×^10
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
quadratic equation a x b b ac 2
=− ±^2 −^4^ arc length^ =^ r
circumference of circle = 2π r
ASTRONOMICAL DATA area of circle^ = π r^2
Body Mass/kg Mean radius/m curved surface area ofcylinder = 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^ =^34 π r^3
Particle Physics
Class Name Symbol Rest energy/MeV photon photon (^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^0 497.
baryons proton p 938. neutron (^) n 939.
Properties of quarks
antiquarks have opposite signs
Type Charge (^) numberBaryon Strangeness
u + 32 e + 13 0
d − 13 e + 13 0
s −^13 e^ + 13 −^1
Properties of Leptons
Lepton number
Particles: e−, νe ; μ−, ν μ + 1
Antiparticles: e+, νe, μ+, ν μ − 1
Photons and energy levels
photon energy (^) 𝐸 = ℎ𝑓 = ℎ𝑐 photoelectricity ℎ𝑓^ =^ +^ 𝐸k (max) energy levels (^) ℎ𝑓 = 𝐸 1 – 𝐸 2 de Broglie Wavelength (^) 𝜆 = ℎ 𝑝 = (^) 𝑚𝑚ℎ
Waves
wave speed (^) 𝑐 = 𝑓𝜆 period (^) 𝑓 = (^1) 𝑇
first harmonic 𝑓^ =^
fringe spacing 𝑤^ =^
diffraction grating 𝑑^ sin^ 𝜃^ =^ 𝑛𝜆 refractive index of a substance s , 𝑛 = (^) 𝑐𝑐s 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 𝑛^21 for 𝑛 1 > 𝑛 2
Mechanics
moments moment = 𝐹𝑑 velocity and acceleration 𝑚^ =^
∆𝑡 𝑎^ =^
equations of motion 𝑚^ =^ 𝑢^ +^ 𝑎𝑡^ 𝑠^ =^ �
2 �^ 𝑡
𝑚^2 = 𝑢^2 + 2 𝑎𝑠 𝑠 = 𝑢𝑡 + 𝑎𝑡
2 2 force (^) 𝐹 = 𝑚𝑎 force (^) 𝐹 = ∆( ∆𝑚𝑚𝑡 ) impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚) work, energy and power
𝑊 = 𝐹 𝑠 cos 𝜃 𝐸k = 12 𝑚 𝑚^2 Δ𝐸p =^ 𝑚𝑔Δℎ 𝑃 = ∆ ∆𝑊𝑡 , 𝑃 = 𝐹𝑚 𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 = 𝑢𝑠𝑒𝑓𝑢𝑙 𝑒𝑛𝑝𝑢𝑡^ 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝^ 𝑝𝑜𝑤𝑒𝑝
Materials
density 𝜌 = 𝑚 𝑉^ Hooke’s law^ 𝐹^ =^ 𝑘^ 𝛥𝛥
Young modulus 𝑡𝑡𝑛𝑡𝑡𝑡𝑡𝑡𝑡𝑛𝑡𝑡𝑡𝑡^ 𝑡𝑡𝑠𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑛
tensile stress = 𝐹 𝐴 tensile strain = ∆ 𝐿𝐿
energy stored 𝐸 = 12 𝐹Δ𝛥
