AQA-7408-SDB - Syllibus AQA PDF

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Syllibus AQA...

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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

Symbol

speed of light in vacuo

Units

3.00 × 108

m s–1

𝜀0

4π × 10–7

H m–1

8.85 × 10–12

F m–1

ℎ

1.60 × 10–19

C

6.63 × 10–34

Js

𝜇0

permeability of free space permittivity of free space magnitude of the charge of electron the Planck constant

𝑒

𝐺

gravitational constant

𝑁A

the Avogadro constant

𝑅

molar gas constant the Boltzmann constant

the Wien constant

1.38 × 10–23

J K–1

𝛼

5.67 × 10–8

W m–2 K–4

2.90 × 10–3

mK

9.11 × 10–31

kg

1.76 × 1011

C kg–1

1.67(3) × 10–27

kg

9.58 × 107

C kg–1

1.67(5) × 10–27

kg

9.81

N kg–1

9.81

m s–2

1.661 × 10–27

kg

𝑚p

proton rest mass (equivalent to 1.00728 u)

𝑒 𝑚p

proton charge/mass ratio

𝑚n

neutron rest mass (equivalent to 1.00867 u)

𝑔

gravitational field strength acceleration due to gravity atomic mass unit (1u is equivalent to 931.5 MeV)

ALGEBRAIC EQUATION − b ± b 2 − 4 ac x= 2a

ASTRONOMICAL DATA

mol–1

𝑘

𝑒 𝑚e

electron charge/mass ratio

6.02 × 1023

J K–1 mol–1

𝑚e

electron rest mass (equivalent to 5.5 × 10–4 u)

N m2 kg–2

6.67 × 10–11

8.31

σ

the Stefan constant

quadratic equation

𝑐

Value

𝑔 u

GEOMETRICAL EQUATIONS arc length circumference of circle

= r𝜃

= 2πr

area of circle

= πr2

curved surface area of cylinder

= 2πrh

Body

Mass/kg

Mean radius/m

Sun

1.99 × 1030

6.96 × 108

area of sphere

= 4πr2

Earth

5.97 × 1024

6.37 × 106

volume of sphere

=

Version 1.5

4 3

πr3

1

Particle Physics

Waves

Class

Name

photon

photon

lepton

neutrino

mesons

Symbol

Rest energy/MeV

𝛾

0 first harmonic

𝑓 =

0

vµ

0

electron

e±

0.510999

muon

µ±

105.659

π meson

π±

139.576

0

134.972

K

±

493.821

K

0

497.762

critical angle sin 𝜃c =

K meson

fringe spacing

Mechanics

neutron

n

939.551

moments

Charge

u d s

+

2 3

−

1 3

−

1 3

e e e

Strangeness

+

1 3

+

1 3

0

1 3

−1

+

0

Antiparticles:

e−, ν e ; µ−, νµ

photon energy photoelectricity energy levels de Broglie wavelength

2

𝐸 = ℎ𝑓 =

ℎ𝑐 𝜆

ℎ𝑓 = ϕ + 𝐸k (max) ℎ𝑓 = 𝐸1 – 𝐸2 𝜆 =

ℎ ℎ = 𝑚𝑚 𝑝

for 𝑛1 > 𝑛2

𝑎 =

𝐹 = 𝑚𝑎

force

𝐹 =

force

𝑢+𝑚 �𝑡 2

𝑠 = 𝑢𝑡 +

𝑎𝑡 2 2

∆𝑡

𝐸k =

𝑃 =

∆𝑊 ∆𝑡

1 𝑚 𝑚2 2

, 𝑃 = 𝐹𝑚

𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 = density 𝜌 =

𝑠 =�

∆(𝑚𝑚)

𝑊 = 𝐹 𝑠 cos 𝜃

work, energy and power

Materials

∆𝑚 ∆𝑡

𝐹 Δ𝑡 = Δ(𝑚𝑚)

+1

Photons and energy levels

𝑛2

𝑛1

𝑚 2 = 𝑢2 + 2𝑎𝑠

Lepton number

−1

𝑐 𝑐s

𝑚 = 𝑢 + 𝑎𝑡

equations of motion

impulse

e+, ν e , µ+, νµ

𝑑 sin 𝜃 = 𝑛𝜆

∆𝑠 𝑚 = ∆𝑡

Properties of Leptons

Particles:

diffraction grating

moment = 𝐹𝑑

velocity and acceleration

Baryon number

𝜆𝜆 𝑠

law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2

938.257

Type

𝑤 =

1 𝑇

for two different substances of refractive indices n1 and n2,

p

antiquarks have opposite signs

𝑓 =

refractive index of a substance s, 𝑛 =

proton

Properties of quarks

period

1 𝑇 � 2𝑙 𝜇

ve

π

baryons

𝑐 = 𝑓𝜆

wave speed

𝑚 𝑉

Young modulus =

𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝 𝑒𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝

Hooke’s law 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡 𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛

energy stored 𝐸 =

1 𝐹Δ𝐿 2

Δ𝐸p = 𝑚𝑔Δℎ

𝐹 = 𝑘 Δ𝐿

tensile stress = tensile strain =

𝐹

𝐴

∆𝐿 𝐿

Version 1.5

AQA A-LEVEL PHYSICS DATA AND FORMULAE

Electricity 𝐼 =

current and pd resistivity resistors in series resistors in parallel

power

𝜌=

𝑅𝑅 𝐿

𝑉 =

1

𝑅T

magnitude of angular speed

1

𝑅1

=

1

𝑅2

+

𝐸 𝑄

for a mass-spring system

𝑔 =

𝑚𝑚 2 𝑝

= 𝑚𝜔 2 𝑝

�(𝑅2

−

𝑇 = 2𝜋 � 𝑇 = 2𝜋 �

Thermal physics

2

𝑚 𝑘 𝑙

𝑔

𝐺𝐺 𝑝2

𝐺𝐺 𝑝 Δ𝑉 𝑔 =– Δ𝑝

Electric fields and capacitors 𝐹 =

1 𝑄1𝑄2 4𝜋𝜀0 𝑝 2

𝐹 = 𝐸𝑄 𝐸 =

work done

𝑉 𝑑

Δ𝑊 = 𝑄Δ𝑉

field strength for a radial field

𝐸 =

1 𝑄 4𝜋𝜀0 𝑝 2

field strength capacitance

capacitor energy stored capacitor charging decay of charge

𝑄 = 𝑚𝑐Δ𝜃

𝐹 𝑚

𝑉 =–

gravitational potential

electric potential 𝑥 2)

𝐺𝑚1𝑚2 𝑝2

Δ𝑊 = 𝑚Δ𝑉

work done

field strength for a uniform field

𝑎max = 𝜔 𝑅

maximum acceleration

magnitude of gravitational field strength in a radial field

𝑚2 𝑎 = = 𝜔2𝑝 𝑝

𝑚max = 𝜔𝑅

maximum speed

𝑔 =

force on a charge

𝑚 = ±𝜔

speed

Version 1.5

𝑉 𝑅

2

gravitational field strength

force between two point charges

𝑥 = 𝑅 cos (𝜔𝑡)

displacement

kinetic energy of gas molecule

+⋯

𝑎 = − 𝜔2𝑥

acceleration

kinetic theory model

1

𝑅3

𝜀 = 𝐼(𝑅 + 𝑝)

Simple harmonic motion

gas law

+

𝐹 =

force between two masses

𝑚 𝜔 = 𝑝

𝐹 =

centripetal force

energy to change state

𝑉 𝐼

𝜔 = 2𝜋𝑓

centripetal acceleration

energy to change temperature

𝑅 =

𝑃 = 𝑉𝐼 = 𝐼2 𝑅 =

Circular motion

for a simple pendulum

𝑊 𝑄

𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + …

𝜀 =

emf

∆𝑄 ∆𝑡

Gravitational fields

time constant

𝑉 =

1 𝑄 4𝜋𝜀0 𝑝

𝐸 =

1 1 𝑄2 1 𝑄𝑉 = 𝐶𝑉 2 = 2 2 2 𝐶

Δ𝑉 Δ𝑝 𝑄 𝐶 = 𝑉 𝑅𝜀0𝜀r 𝐶 = 𝑑

𝐸 =

𝑡

𝑄 = 𝑄0(1 − e– 𝑅𝑅 ) 𝑡

𝑄 = 𝑄0e– 𝑅𝑅 𝑅𝐶

𝑄 = 𝑚𝑙

𝑝𝑉 = 𝑛𝑅𝑇 𝑝𝑉 = 𝑁𝑘𝑇 𝑝𝑉 =

1 𝑁𝑚 (𝑐rms)2 3 3 3𝑅𝑇 1 𝑚 (𝑐rms )2 = 𝑘𝑇 = 2 2 2𝑁A

3

Magnetic fields

𝐹 = 𝐵𝑄𝑚

force on a moving charge

Astrophysics

Ф = 𝐵𝑅

magnetic flux magnetic flux linkage

1 light year = 9.46 × 1015 m

𝑁Ф = 𝐵𝑅𝑁 cos 𝜃

= 3.26 ly

ΔФ Δ𝑡

𝜀 = 𝐵𝑅𝑁𝜔 sin 𝜔 t

emf induced in a rotating coil

𝐼rms =

𝐼0

√2

𝑁s

𝑁p

transformer equations

=

𝑉s

𝑉rms =

𝑉p

𝑉0

√2

𝐼s 𝑉s efficiency = 𝐼p 𝑉p

Nuclear physics 𝐼 =

inverse square law for γ radiation radioactive decay activity half-life nuclear radius energy-mass equation

Δ𝑁 Δ𝑡

𝑘 𝑥2

= – 𝜆 𝑁, 𝑁 = 𝑁o e−𝜆𝑡

𝑅 = 𝜆𝑁 𝑇½ =

1 astronomical unit = 1.50 × 1011 m

𝑁Ф = 𝐵𝑅𝑁 cos 𝜃 𝜀 = 𝑁

magnitude of induced emf

alternating current

OPTIONS

𝐹 = 𝐵𝐼𝑙

force on a current

𝐸 = 𝑚𝑐

2

Hubble constant, 𝐻 = 65 km s–1 Mpc –1 𝐺 =

𝑎𝑛𝑔𝑙𝑒 𝑠𝑢𝑠𝑡𝑒𝑛𝑑𝑒𝑑 𝑠𝑒 𝑒𝑚𝑎𝑔𝑒 𝑎𝑡 𝑒𝑒𝑒 𝑎𝑛𝑔𝑙𝑒 𝑠𝑢𝑠𝑡𝑒𝑛𝑑𝑒𝑑 𝑠𝑒 𝑜𝑠𝑜𝑒𝑐𝑡 𝑎𝑡 𝑢𝑛𝑎𝑒𝑑𝑒𝑑 𝑒𝑒𝑒

telescope in normal adjustment Rayleigh criterion

magnitude equation Wien’s law Stefan’s law Schwarzschild radius Doppler shift for v...