A-level Physics Specimen data booklet Physics

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

𝐹 =

1 𝑄1 𝑄2 4𝜋𝜀0 𝑟 2

𝐹 = 𝐸𝐸 𝐸 =

𝑉 𝑑

𝐸 =

1 𝑄 4𝜋𝜀0 𝑟 2

Δ𝑊 = 𝑄Δ𝑉

𝑉 =

1 𝑄 4𝜋𝜀0 𝑟

𝐸 =

1 1 1 𝑄2 𝑄𝑄 = 𝐶𝑉 2 = 2 2 2 𝐶

Δ𝑉 Δ𝑟 𝑄 𝐶 = 𝑉 𝐴𝜀0 𝜀r 𝐶 = 𝑑

𝐸 =

𝑡

𝑄 = 𝑄0 (1 − e– 𝑅𝑅 ) 𝑡

𝑄 = 𝑄0 e– 𝑅𝑅 𝑅𝑅

𝑝𝑝 = 𝑛𝑛𝑛 𝑝𝑝 = 𝑁𝑁𝑁

1 𝑁𝑁 (𝑐rms )2 3 1 3 3𝑅𝑅 𝑚 (𝑐rms )2 = 𝑘𝑘 = 2 2 2𝑁A 𝑝𝑝 =

3

Magnetic fields force on a current

OPTIONS

𝐹 = 𝐵𝐵𝐵

force on a moving charge

Astrophysics

𝐹 = 𝐵𝐵𝐵

magnetic flux magnetic flux linkage

Ф = 𝐵𝐵

1 astronomical unit = 1.50 × 1011 m

𝜀 = 𝑁

= 3.26 ly

magnitude of induced emf

𝑁Ф = 𝐵𝐵𝐵 cos 𝜃

emf induced in a rotating coil

𝑁Ф = 𝐵𝐵𝐵 cos 𝜃

alternating current transformer equations

𝜀 = 𝐵𝐵𝐵𝐵 sin 𝜔 t

𝐼rms =

𝑁s

𝐼0

√2

𝑁p

=

inverse square law for γ radiation

activity half-life nuclear radius energy-mass equation

𝑉s

𝑉rms =

𝑉p

efficiency =

Nuclear physics

radioactive decay

ΔФ Δ𝑡

Δ𝑁 Δ𝑡

𝐼 =

𝑇½ =

ln 2 𝜆

𝑅 = 𝑅0 𝐴1/3 𝐸 = 𝑚𝑚

2

√2

𝐼s 𝑉s 𝐼p 𝑉p

𝑘 𝑥2

1 parsec = 2.06 × 105 AU = 3.08 × 1016 m

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

𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑖𝑖𝑖𝑖𝑖 𝑎𝑎 𝑒𝑒𝑒 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎 𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑒𝑒𝑒

telescope in normal adjustment Rayleigh criterion

magnitude equation Wien’s law Stefan’s law

= – 𝜆 𝑁, 𝑁 = 𝑁o e

𝐴 = 𝜆𝜆

𝑉0

1 light year = 9.46 × 1015 m

−𝜆𝜆

Schwarzschild radius Doppler shift for v << c red shift Hubble’s law

Medical physics lens equations

threshold of hearing intensity level absorption

ultrasound imaging

𝑀 = 𝜃 ≈

4

𝜆 𝐷

𝑚 – 𝑀 = 5 log

𝑑 10

𝜆max 𝑇 = 2.9 × 10−3 m K 𝑃 = 𝜎𝜎𝑇 4 2GM

𝑅s ≈

c2

Δ𝑓 Δ𝜆 𝑣 =– = 𝑓 𝜆 𝑐 𝑣 𝑧= − 𝑐 𝑣 = 𝐻𝐻 1 𝑓 𝑣 𝑚 = 𝑢 𝑃 =

1

𝑓

=

1

+

𝑢

1 𝑣

𝐼0 = 1.0 × 10−12 W m−2 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙 = 10 log 𝐼 = 𝐼0 𝑒 –𝜇𝜇 𝜇 𝜇m = 𝜌 𝑍 = 𝑝𝑐 𝐼r

half-lives

𝑓0 𝑓e

𝐼i

1

𝑇E

=

�

=

𝐼 𝐼0

𝑍2 − 𝑍1 2 𝑍2 + 𝑍1

1 𝑇B

+

�

1 𝑇P

Version 1.5

AQA A-LEVEL PHYSICS DATA AND FORMULAE Engineering physics moment of inertia angular kinetic energy equations of angular motion

Turning points in physics 𝐼 = Σ𝑚𝑚 2 𝐸𝑘 =

electrons in fields

1 2 𝐼𝐼 2

2

𝛼𝛼 2 (𝜔1 + 𝜔2 ) 𝑡 𝜃 = 2 𝜃 = 𝜔1 𝑡 +

torque

½ 𝑚𝑚 2 = 𝑒𝑒 𝑄𝑄 = 𝑚𝑚 𝑑

Millikan’s experiment

𝐹 = 6𝜋𝜋𝜋𝜋 𝑐 =

Maxwell’s formula

𝑇 = 𝐼𝛼

𝑇 = 𝐹𝑟

angular momentum

𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐼𝐼

angular impulse

𝑇Δ𝑡 = Δ(𝐼𝐼)

work done

𝜆 = 𝑡 =

special relativity

𝑊 = 𝑇𝑇

power

𝑃 = 𝑇𝑇

thermodynamics

𝑄 = Δ𝑈 + 𝑊

𝑝𝑝 𝛾 = constant

isothermal change

efficiency = maximum theoretical efficiency =

𝑊 𝑄H − 𝑄C = 𝑄H 𝑄H

𝑇H − 𝑇C 𝑇H

input power = calorific value × fuel flow rate indicated power = (𝑎𝑎𝑎𝑎 𝑜𝑜 𝑝 − 𝑉 𝑙𝑙𝑙𝑙)

× (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠) × (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐)

resonant frequency

heat pumps and refrigerators

summing amplifier

heat pump: 𝐶𝐶𝐶hp =

𝑄C 𝑊

𝑄H 𝑊

=

=

𝑄C

𝑄H − 𝑄C 𝑄H

𝑄H − 𝑄C

𝑣2 𝑐2

difference amplifier

2

�1 − 𝑣 2 𝑐

1

𝑉out = 𝐴OL (𝑉+ − 𝑉− ) 𝑉out 𝑅f =− 𝑉in 𝑅in

𝑉out 𝑅f =1+ 𝑉in 𝑅l

𝑉out = −𝑅f �

𝑉1 𝑉2 𝑉3 + + + ⋯� 𝑅1 𝑅2 𝑅3

𝑉out = (𝑉+ − 𝑉− )

Bandwidth requirement: for AM for FM

𝑚0 𝑐 2

2𝜋 √𝐿𝐿 𝑓0 𝑄= 𝑓B

inverting amplifier non-inverting amplifier

refrigerator: 𝐶𝐶𝐶ref =

2

�1 − 𝑣 2 𝑐

𝑓0 =

operational amplifiers: open loop

output or brake power 𝑃 = 𝑇𝜔

friction power = 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝 – 𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑝𝑝𝑝

ℎ ℎ = 𝑝 √2𝑚𝑚𝑚 𝑡0

Electronics

Q-factor

work done per cycle = area of loop

�𝜇0 𝜀0

𝐸 = 𝑚 𝑐2 =

𝑝𝑝 = constant

heat engines

1

𝑙 = 𝑙0 �1 −

𝑊 = 𝑝Δ𝑉

adiabatic change

𝑒𝑒 𝑑

𝐹 = 𝐵𝐵𝐵 𝑚𝑚 𝑟 = 𝐵𝐵

𝜔2 = 𝜔1 + 𝛼 𝑡

𝜔2 2 = 𝜔1 2 + 2𝛼𝛼

Version 1.5

𝐹 =

𝑅f 𝑅l

𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2𝑓M

𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2(∆𝑓 + 𝑓M )

5

6

Version 1.5

AQA A-LEVEL PHYSICS DATA AND FORMULAE

Version 1.5

7

8

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