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
3.00 10
m s–
permeability of free space
4
10–
H m–
permittivity of free space
8.85 10–
F m–
magnitude of the charge of electron
1.60 10–
C
the Planck constant
6.63 10–
Js
gravitational constant
6.67 10–
N m kg –
the Avogadro constant
6.02 10
mol–
8.31
molar gas constant
J K – mol–
the Boltzmann constant
1.38 10–
J K–
the Stefan constant
5.67 10–
W m– K –
the Wien constant
2.90 10–
mK
electron rest mass
(equivalent to 5.5 × 10–4 u)
9.11 10–
kg
electron charge/mass ratio
1.76 10
C kg –
proton rest mass
(equivalent to 1.00728 u)
1.67(3) 10–
kg
proton charge/mass ratio
9.58 10
C kg –
neutron rest mass
(equivalent to 1.00867 u)
1.67(5) 10–
kg
gravitational field strength
9.81
N kg –
acceleration due to gravity
9.81
m s–
atomic mass unit
(1u is equivalent to 931.5 MeV)
u
ALGEBRAIC EQUATION
quadratic equation
x
b
Mass/kg
kg
GEOMETRICAL EQUATIONS
b2
2a
4 ac
ASTRONOMICAL DATA
Body
1.661 10–
Mean radius/m
arc length
=r
circumference of circle
=2 r
area of circle
= r2
curved surface area of
cylinder
= 2 rh
Sun
1.99 × 10
6.96 × 10
area of sphere
= 4 r2
Earth
5.97 × 10
6.37 × 10
volume of sphere
=
Version 1.5
4
3
r3
1
Particle Physics
Waves
Class
Name
Symbol
photon
photon
lepton
neutrino
Rest energy/MeV
first
harmonic
0
e
0.510999
fringe
spacing
105.659
refractive index of a substance s,
139.576
K meson
K
0
law of refraction
493.821
critical angle sin
proton
p
938.257
Mechanics
neutron
n
939.551
moments
Properties of quarks
antiquarks have opposite signs
Baryon
number
+
d
s
+
1
3
1
e
3
+
1
3
1
e
3
+
e
=
134.972
497.762
Charge
=
=
=
for two different substances of refractive indices n1 and n2,
K
u
sin
v
0
2
3
diffraction
grating
1
2
0
meson
Type
=
ve
muon
baryons
1
period
0
electron
mesons
=
wave speed
sin
=
=
sin
for
>
moment =
velocity and
acceleration
=
equations of
motion
=
=
+
+
2
=
Strangeness
=
0
0
force
=
force
=
1
(
work, energy
and power
(
=
=
+
2
)
cos
=
Properties of Leptons
=
)
=
impulse
1
3
+ 2
1
2
,
=
=
Lepton number
Particles:
e ,
;
,
+1
Antiparticles:
e ,
,
,
1
=
Materials
density
Photons and energy levels
photon energy
=
=
photoelectricity
=
+
energy levels
=
–
de Broglie wavelength
=
=
2
Hooke’s law
=
=
tensile stress =
Young modulus =
(
)
tensile strain =
energy stored
=
Version 1.5
AQA A-LEVEL PHYSICS DATA AND FORMULAE
Electricity
Gravitational fields
=
current and pd
resistivity
=
=
=
resistors in series
=
resistors in parallel
=
+
+
+
+ …
+
+
force between two masses
=
gravitational field strength
=
magnitude of gravitational
field strength in a radial field
=
=
work done
gravitational potential
power
=
=
=
=
emf
=–
=–
= (
+ )
Electric fields and capacitors
Circular motion
magnitude of
angular speed
=
= 2
centripetal acceleration
=
centripetal force
=
=
Simple harmonic motion
=
displacement
=
speed
= ±
cos (
maximum speed
=
maximum acceleration
=
)
(
)
= 2
for a simple pendulum
=
field strength for a
uniform field
=
= 2
=
electric potential
=
field strength
=
capacitance
=
capacitor charging
decay of charge
energy to change
temperature
=
energy to change
state
=
gas law
=
=
kinetic theory model
=
1
2
4
=
field strength for a
radial field
capacitor energy
stored
Thermal physics
Version 1.5
force on a charge
1
1
4
1
4
=
for a mass-spring system
kinetic energy of gas
molecule
=
work done
=
acceleration
force between two
point charges
(
=
1
2
=
=
(1
=
e–
1
2
e–
=
1
2
)
time constant
1
3
(
) =
)
3
2
=
3
2
3
Magnetic fields
OPTIONS
force on a current
=
force on a moving charge
=
Astrophysics
magnetic flux
=
1 astronomical unit = 1.50 × 10
=
magnetic flux linkage
magnitude of induced emf
1 light year = 9.46 × 10
cos
cos
=
=
sin
Hubble constant,
t
=
2
=
transformer equations
m
= 3.26 ly
=
alternating current
m
1 parsec = 2.06 × 10 AU = 3.08 × 10
=
emf induced in a rotating coil
m
= 65 km s– Mpc–
=
2
telescope in normal
adjustment
=
Rayleigh criterion
efficiency =
s s
p p
–
= 5 log
Stefan’s law
=
=–
radioactive decay
,
=
activity
½
=
nuclear radius
=
energy-mass equation
=
=
e
10
= 2.9 × 10
Wien’s law
Nuclear physics
half-life
magnitude equation
mK
=
2GM
Schwarzschild radius
c2
=–
Doppler shift for v << c
=
ln 2
/
red shift
=
Hubble’s law
=
Medical physics
lens equations
=
1
=
=
threshold of hearing
+
= 1.0 × 10
= 10 log
intensity level
absorption
Wm
–
=
=
ultrasound imaging
=
=
half-lives
4
=
+
Version 1.5
AQA A-LEVEL PHYSICS DATA AND FORMULAE
Engineering physics
Turning points in physics
=
moment of inertia
electrons in fields
1
=
2
angular kinetic energy
equations of angular
motion
=
=
=
+
=
½
+ 2
Millikan’s experiment
=
+
(
=
=
2
=
=
= 6
+
2
)
Maxwell’s formula
1
=
=
torque
=
=
=
2
=
angular momentum
(
=
angular impulse
)
special relativity
=
1
=
work done
power
=
thermodynamics
=
+
=
=
= constant
adiabatic change
=
= constant
isothermal change
1
=
1
heat engines
=
efficiency =
Electronics
resonant frequency
maximum theoretical
efficiency =
Q-factor
work done per cycle = area of loop
input power = calorific value × fuel flow rate
indicated power = (
)
×(
×(
)
=
output or brake power
–
friction power =
heat pumps and refrigerators
refrigerator:
heat pump:
=
=
=
=
)
=
inverting amplifier
(
)
=
non-inverting amplifier
difference amplifier
2
=
operational amplifiers:
open loop
summing amplifier
1
=1+
=
+
=(
)
+
+
=
Bandwidth requirement:
for AM
for FM
Version 1.5
=2
= 2(
+
)
5
6
Version 1.5
AQA A-LEVEL PHYSICS DATA AND FORMULAE
Version 1.5
7
8
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