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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 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
Symbol
Value
Units
𝑐
3.00 × 108
m s –1
𝜇0
H m–1
1.60 × 10–19
C
𝜀0
8.85 × 10–12
𝐺
𝑒
F m–1
ℎ
6.63 × 10–34 6.67 × 10–11
N m2 kg –2
𝑅
8.31
J K –1 mol–1
𝑁A
molar gas constant
4π × 10–7
6.02 × 1023
Js
mol–1
𝑘
1.38 × 10–23 5.67 × 10–8
W m–2 K –4
electron rest mass (equivalent to 5.5 × 10–4 u)
𝑚e
9.11 × 10–31
kg
proton rest mass (equivalent to 1.00728 u)
𝑚p
1.67(3) × 10–27
neutron rest mass (equivalent to 1.00867 u)
𝑚n
1.67(5) × 10–27
𝑔
9.81
the Boltzmann constant the Stefan constant
σ
the Wien constant
𝛼
𝑒 𝑚e
electron charge/mass ratio
𝑒 𝑚p
proton charge/mass ratio
gravitational field strength acceleration due to gravity
atomic mass unit (1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION
quadratic equation
− b ± b 2 − 4 ac x= 2a
ASTRONOMICAL DATA Body
Mass/kg
Mean radius/m
Sun
1.99 × 1030
6.96 × 108
Earth
Version 1.5
5.97 × 1024
6.37 × 106
𝑔 u
2.90 × 10–3
J K –1 mK
1.76 × 1011
C kg –1
9.58 × 107
C kg –1
9.81
N kg –1
1.661 × 10–27
kg
kg
kg
m s –2
GEOMETRICAL EQUATIONS circumference of circle
= r𝜃
area of circle
= πr2
curved surface area of cylinder
= 2πrh
area of sphere
= 4πr2
volume of sphere
=
arc length
= 2πr
4 3
πr3
1
Particle Physics
Waves
Class
Name
Symbol
Rest energy/MeV
wave speed
photon
photon
lepton
neutrino
𝛾
0
vµ
0
first harmonic
mesons
ve
electron
e±
muon
µ±
π meson
π±
0 0.510999
π
±
K meson
K
baryons
proton neutron
Properties of quarks Charge
939.551
1 3
1 e 3
+
1 3
0
1 e 3
+
1 3
−1
+
2 3
d
−
s
−
Strangeness
e
0
moments velocity and acceleration
𝑣 =
equations of motion
Photons and energy levels photon energy photoelectricity energy levels de Broglie wavelength
2
ℎ𝑐 𝜆 ℎ𝑓 = ϕ + 𝐸k (max) 𝐸 = ℎ𝑓 =
ℎ𝑓 = 𝐸1 – 𝐸2 𝜆 =
ℎ ℎ = 𝑝 𝑚𝑚
𝐹 = 𝑚𝑚
force
𝐹 =
∆𝑣 ∆𝑡
𝑠 =�
𝑢+𝑣 �𝑡 2
𝑠 = 𝑢𝑢 +
∆(𝑚𝑚) ∆𝑡
𝑎𝑎 2 2
𝐹 Δ𝑡 = Δ(𝑚𝑚)
work, energy and power
𝑊 = 𝐹 𝑠 cos 𝜃
𝑃 =
∆𝑊 ∆𝑡
1 𝑚 𝑣2 2
, 𝑃 = 𝐹𝐹
𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 =
Materials 𝑚
Δ𝐸p = 𝑚𝑚Δℎ
𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝 𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝
Hooke’s law 𝐹 = 𝑘 Δ𝐿
𝑉
Young modulus =
energy stored
𝑎 =
𝑣 2 = 𝑢2 + 2𝑎𝑎
force
density 𝜌 =
for 𝑛1 > 𝑛2
𝑣 = 𝑢 + 𝑎𝑎
+1 −1
𝑛1
∆𝑠 ∆𝑡
𝐸k =
e+ , ν e , µ + , ν µ
𝑛2
moment = 𝐹𝐹
Lepton number
Antiparticles:
s
critical angle sin 𝜃c =
Properties of Leptons Particles:
𝑐
for two different substances of refractive indices n1 and n2,
impulse
e− , νe ; µ− , νµ
1 𝑇
𝑑 sin 𝜃 = 𝑛𝑛
Mechanics
938.257
+
u
diffraction grating
497.762
p
Baryon number
𝜆𝜆 𝑠
law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
antiquarks have opposite signs
Type
𝑤 =
134.972
K
n
1 𝑇 � 2𝑙 𝜇
refractive index of a substance s, 𝑛 = 𝑐
493.821
0
𝑓 =
𝑓 =
105.659 139.576
0
fringe spacing
period
𝑐 = 𝑓𝑓
𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠
1
𝐸 = 2 𝐹Δ𝐿
tensile stress =
tensile strain =
𝐹
𝐴 ∆𝐿 𝐿
Version 1.5
AQA A-LEVEL PHYSICS DATA AND FORMULAE Electricity
Gravitational fields
current and pd resistivity resistors in series resistors in parallel
power emf
Circular motion
𝐼 =
𝜌=
∆𝑄 ∆𝑡
𝑉 =
𝑅𝑅 𝐿
𝑊 𝑄
𝑅 =
𝑉 𝐼
𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + … 1
𝑅T
1
=
𝑅1
+
1
𝑅2
+
1
𝑅3
𝑃 = 𝑉𝑉 = 𝐼 2 𝑅 = 𝜀 =
magnitude of angular speed
𝐸 𝑄
𝜔 =
+⋯ 𝑉 𝑅
2
𝜀 = 𝐼(𝑅 + 𝑟)
𝑣 𝑟
centripetal force
Simple harmonic motion acceleration displacement
𝑥 = 𝐴 cos (𝜔𝜔)
speed
𝑣 = ±𝜔
maximum speed
𝑣max = 𝜔𝜔
maximum acceleration for a mass-spring system for a simple pendulum
Thermal physics energy to change temperature energy to change state gas law
kinetic theory model kinetic energy of gas molecule Version 1.5
�(𝐴2 2
−
𝑥 2)
𝑎max = 𝜔 𝐴 𝑚 𝑘
𝑇 = 2𝜋 �
𝑙 𝑇 = 2𝜋 � 𝑔 𝑄 = 𝑚𝑚Δ𝜃 𝑄 = 𝑚𝑚
𝐺𝑚1 𝑚2 𝑟2
𝐹 𝑚
𝐺𝐺 𝑟2
Δ𝑊 = 𝑚Δ𝑉 𝐺𝐺 𝑟 Δ𝑉 𝑔 =– Δ𝑟
gravitational potential
𝑉 =–
Electric fields and capacitors
work done field strength for a radial field electric potential
𝑎 = − 𝜔2 𝑥
𝑔 =
work done
field strength for a uniform field
𝑚𝑚 2 𝐹 = = 𝑚𝑚2 𝑟 𝑟
𝑔 =
magnitude of gravitational field strength in a radial field
force on a charge
𝑣2 𝑎 = = 𝜔2 𝑟 𝑟
𝐹 =
gravitational field strength
force between two point charges
𝜔 = 2𝜋𝜋
centripetal acceleration
force between two masses
field strength capacitance
capacitor energy stored capacitor charging decay of charge time constant