A-level Physics data and formulae - AQA

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 molar gas constant the Boltzmann constant the Stefan constant the Wien constant electron rest mass (equivalent to 5.5 ? 10?4 u)

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 (1u is equivalent to 931.5 MeV)

Symbol

0 0 A

e e

p p

n

u

Value 3.00 ? 108 4 ? 10?7 8.85 ? 10?12 1.60 ? 10?19 6.63 ? 10?34 6.67 ? 10?11 6.02 ? 1023

8.31 1.38 ? 10?23 5.67 ? 10?8 2.90 ? 10?3 9.11 ? 10?31

1.76 ? 1011

1.67(3) ? 10?27

9.58 ? 107

1.67(5) ? 10?27

9.81 9.81 1.661 ? 10?27

Units m s?1 H m?1 F m?1

C J s N m2 kg?2 mol?1 J K?1 mol?1 J K?1 W m?2 K?4 m K

kg

C kg?1

kg

C kg?1

kg N kg?1 m s?2

kg

ALGEBRAIC EQUATION

quadratic equation

x = - b ? b2 - 4ac

2a

ASTRONOMICAL DATA

Body

Mass/kg

Mean radius/m

Sun

1.99 ? 1030

6.96 ? 108

Earth 5.97 ? 1024

6.37 ? 106

GEOMETRICAL EQUATIONS

arc length circumference of circle area of circle curved surface area of cylinder area of sphere

volume of sphere

= r = 2r = r2 = 2rh

= 4r2 = 4 r3

3

Version 1.5

1

Particle Physics

Class

photon lepton

mesons

baryons

Name

photon neutrino

electron muon

meson

K meson

proton neutron

Symbol

v e v ? e ? ? ? ? 0 K ? K0 p n

Rest energy/MeV 0 0 0

0.510999 105.659 139.576 134.972 493.821 497.762 938.257 939.551

Properties of quarks

antiquarks have opposite signs

Type Charge

Baryon number

u

+ 2e

+ 1

3

3

d

- 1e

3

+ 1

3

s

- 1e

3

+ 1

3

Strangeness 0 0 - 1

Properties of Leptons

Particles: Antiparticles:

e-, e ; ?-, ? e+, e, ?+, ?

Lepton number + 1 - 1

Photons and energy levels

photon energy photoelectricity energy levels de Broglie wavelength

= = = + k (max)

= 1 ? 2

= =

Waves

wave speed = period

1

=

first harmonic

=

1 2

fringe spacing

=

diffraction grating

refractive index of a substance s,

=

s

sin =

for two different substances of refractive indices n1 and n2,

law of refraction 1 sin 1 = 2 sin 2

critical angle

sin c

=

2 1

for

1

>

2

Mechanics

moments velocity and acceleration equations of motion

force

force

impulse work, energy and power

moment =

=

= +

2 = 2 + 2

=

+ = 2

2 = + 2

=

() = = ()

= cos

k

=

1 2

2

p =

=

,

=

=

Materials

density

=

Hooke's law =

Young

modulus

=

tensile stress =

tensile strain =

energy stored

=

1 2

2

Version 1.5

AQA A-LEVEL PHYSICS DATA AND FORMULAE

Electricity

current and pd resistivity resistors in series

= = =

=

T = 1 + 2 + 3 + ...

resistors in parallel

1 T

=

1+

1

1+

2

1 3

+

power emf

Circular motion

= = 2 =

2

=

= ( + )

magnitude of angular speed

=

= 2

centripetal acceleration centripetal force

2 = =

2

=

2 =

2

Simple harmonic motion

acceleration displacement speed maximum speed maximum acceleration

for a mass-spring system

= - 2 = cos ()

= ? (2 - 2) max = max = 2 = 2

for a simple pendulum

Thermal physics

= 2

energy to change temperature energy to change state gas law

kinetic theory model

kinetic energy of gas molecule

=

=

=

=

=

1 3

(rms)2

1 2

(rms)2

=

3 2

=

3 2A

Version 1.5

Gravitational fields

force between two masses

gravitational field strength magnitude of gravitational field strength in a radial field work done gravitational potential

=

12 2

=

= 2

=

= ?

= ?

Electric fields and capacitors

force between two point charges

force on a charge

field strength for a uniform field

work done

=

1 12 40 2

=

=

=

field strength for a radial field electric potential

field strength

capacitance

capacitor energy stored capacitor charging decay of charge time constant

1 = 40 2

1

= 40

=

=

= 0r

1 = 2

=

1 2

2

1 2 =

2

=

0(1

-

e?

)

=

0e?

3

Magnetic fields

force on a current

=

force on a moving charge

=

magnetic flux

=

magnetic flux linkage

= cos

magnitude of induced emf

= = cos

emf induced in a rotating coil = sin t

alternating current transformer equations

rms

= 0 2

rms

= 0 2

s = s

p p

efficiency

=

ss pp

Nuclear physics

inverse square law for radiation

= 2

radioactive decay

= ?

,

=

oe-

activity

=

half-life

nuclear radius energy-mass equation

ln 2 ? = = 0 1/3 = 2

4

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, = 65 km s?1 Mpc?1

=

telescope in normal adjustment Rayleigh criterion

magnitude equation

Wien's law Stefan's law

= 0 e

? = 5 log 10

max = 2.9 ? 10-3 m K

= 4

Schwarzschild radius

Doppler shift for v ................
................

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