AS Physics data and formulae
For use in exams from the June 2016 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo 𝑐 3.00 × 108 m s –1
permeability of free space 0 4π × 10–7 H m–1
permittivity of free space 0 8.85 × 10–12 F m–1
magnitude of the charge of electron 𝑒 1.60 × 10–19 C
the Planck constant ℎ 6.63 × 10–34 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 kg –2
the Avogadro constant 𝑁A 6.02 × 1023 mol–1
molar gas constant 𝑅 8.31 J K –1 mol–1
the Boltzmann constant 𝑘 1.38 × 10–23 J K –1
the Stefan constant 5.67 × 10–8 W m–2 K –4
the Wien constant 2.90 × 10–3 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit
u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length =r
− b ± b 2 − 4 ac
quadratic equation x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.6 1
,Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝜆 period 𝑓 =
𝑇
photon photon 0
first 1 𝑇
lepton neutrino ve 0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝐷 diffraction
electron e± 0.510999 𝑤 = 𝑑 sin 𝜃 = 𝑛𝜆
spacing 𝑠 grating
muon µ± 105.659 refractive index of a substance s, 𝑛 = 𝑐
𝑐
s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
π 0
134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
± 𝑛2
K meson K 493.821 critical angle sin 𝜃𝑐 = for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝑑
velocity and ∆𝑠 ∆𝑚
Properties of quarks 𝑚 = 𝑎 =
acceleration ∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑚
𝑚 = 𝑢 + 𝑎𝑡 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑡 2
𝑚 2 = 𝑢2 + 2𝑎𝑠 𝑠 = 𝑢𝑡 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑎
3 3
∆(𝑚𝑚)
1 1 force 𝐹 =
d − e + 0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
s −
1
e +
1
−1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑚2 Δ𝐸p = 𝑚𝑔Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝑚
Lepton number 𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝
− − 𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 =
Particles: e , νe ; µ , νµ +1 𝑒𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚 Hooke’s law 𝐹 = 𝑘 𝛥𝛥
Photons and energy levels density 𝜌 =
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝐴
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡
Young modulus
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛 ∆𝐿
photoelectricity ℎ𝑓 = + 𝐸k (max) tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2 1
energy stored 𝐸 = 2 𝐹Δ𝛥
ℎ ℎ
de Broglie Wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.6
, AQA AS PHYSICS DATA AND FORMULAE
Electricity
∆𝑄 𝑊 𝑉
current and pd 𝐼 = 𝑉 = 𝑅 =
∆𝑡 𝑄 𝐼
𝑅𝑅
resistivity 𝜌=
𝐿
resistors in series 𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + …
1 1 1 1
resistors in parallel = + + +⋯
𝑅T 𝑅1 𝑅2 𝑅3
𝑉2 2
power 𝑃 = 𝑉𝑉 = 𝐼 𝑅 =
𝑅
𝐸
emf 𝜀 = 𝜀 = 𝐼(𝑅 + 𝑟)
𝑄
Version 1.6 3
,4 Version 1.6
, Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
AS
PHYSICS
Paper 1
Wednesday 15 May 2024 Morning Time allowed: 1 hour 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
• a pencil and a ruler Question Mark
• a scientific calculator
1
• a Data and Formulae Booklet
• a protractor. 2
3
Instructions 4
• Use black ink or black ball-point pen.
5
• Fill in the boxes at the top of this page.
• Answer all questions. 6
• You must answer the questions in the spaces provided. Do not write TOTAL
outside the box around each page or on blank pages.
• If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
• Do all rough work in this book. Cross through any work you do not want
to be marked.
• Show all your working.
Information
• The marks for questions are shown in brackets.
• The maximum mark for this paper is 70.
• You are expected to use a scientific calculator where appropriate.
• A Data and Formulae Booklet is provided as a loose insert.
*JUN247407101*
IB/M/Jun24/G4001/E6 7407/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
0 1 An electron neutrino interacts with a chlorine-37 nucleus to produce an argon-37
nucleus and an electron.
The interaction is represented by the equation:
37 37
+
ve →
Cl + e
Ar
17 18
0 1 . 1 Explain, with reference to appropriate conservation laws, why the electron is emitted
in this interaction.
[2 marks]
0 1 . 2 Calculate the specific charge of the argon-37 nucleus.
[2 marks]
specific charge = C kg−1
*02*
IB/M/Jun24/7407/1
For use in exams from the June 2016 Series onwards
DATA - FUNDAMENTAL CONSTANTS AND VALUES
Quantity Symbol Value Units
speed of light in vacuo 𝑐 3.00 × 108 m s –1
permeability of free space 0 4π × 10–7 H m–1
permittivity of free space 0 8.85 × 10–12 F m–1
magnitude of the charge of electron 𝑒 1.60 × 10–19 C
the Planck constant ℎ 6.63 × 10–34 Js
gravitational constant 𝐺 6.67 × 10–11 N m2 kg –2
the Avogadro constant 𝑁A 6.02 × 1023 mol–1
molar gas constant 𝑅 8.31 J K –1 mol–1
the Boltzmann constant 𝑘 1.38 × 10–23 J K –1
the Stefan constant 5.67 × 10–8 W m–2 K –4
the Wien constant 2.90 × 10–3 mK
electron rest mass
𝑚e 9.11 × 10–31 kg
(equivalent to 5.5 × 10–4 u)
𝑒
magnitude of electron charge/mass ratio 1.76 × 1011 C kg –1
𝑚e
proton rest mass 𝑚p 1.67(3) × 10–27 kg
(equivalent to 1.00728 u)
𝑒
proton charge/mass ratio 9.58 × 107 C kg –1
𝑚p
neutron rest mass
𝑚n 1.67(5) × 10–27 kg
(equivalent to 1.00867 u)
gravitational field strength 𝑔 9.81 N kg –1
acceleration due to gravity 𝑔 9.81 m s –2
atomic mass unit
u 1.661 × 10–27 kg
(1u is equivalent to 931.5 MeV)
ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS
arc length =r
− b ± b 2 − 4 ac
quadratic equation x=
2a circumference of circle = 2πr
ASTRONOMICAL DATA area of circle = πr2
curved surface area of = 2πrh
Body Mass/kg Mean radius/m
cylinder
Sun 1.99 × 1030 6.96 × 108 surface area of sphere = 4πr2
4
Earth 5.97 × 1024 6.37 × 106 volume of sphere = πr3
3
Version 1.6 1
,Particle Physics Waves
Class Name Symbol Rest energy/MeV 1
wave speed 𝑐 = 𝑓𝜆 period 𝑓 =
𝑇
photon photon 0
first 1 𝑇
lepton neutrino ve 0 𝑓 = �
harmonic 2𝑙 𝜇
vµ 0
fringe 𝐷 diffraction
electron e± 0.510999 𝑤 = 𝑑 sin 𝜃 = 𝑛𝜆
spacing 𝑠 grating
muon µ± 105.659 refractive index of a substance s, 𝑛 = 𝑐
𝑐
s
mesons π meson π± 139.576
for two different substances of refractive indices n1 and n2,
π 0
134.972 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
± 𝑛2
K meson K 493.821 critical angle sin 𝜃𝑐 = for 𝑛1 > 𝑛2
𝑛1
0
K 497.762
baryons proton p 938.257 Mechanics
neutron n 939.551 moments moment = 𝐹𝑑
velocity and ∆𝑠 ∆𝑚
Properties of quarks 𝑚 = 𝑎 =
acceleration ∆𝑡 ∆𝑡
antiquarks have opposite signs
equations of 𝑢+𝑚
𝑚 = 𝑢 + 𝑎𝑡 𝑠 =� �𝑡
Baryon motion 2
Type Charge Strangeness
number 𝑎𝑡 2
𝑚 2 = 𝑢2 + 2𝑎𝑠 𝑠 = 𝑢𝑡 +
2
2 1
u + e + 0 force 𝐹 = 𝑚𝑎
3 3
∆(𝑚𝑚)
1 1 force 𝐹 =
d − e + 0 ∆𝑡
3 3
impulse 𝐹 Δ𝑡 = Δ(𝑚𝑚)
s −
1
e +
1
−1 work, energy 𝑊 = 𝐹 𝑠 cos 𝜃
3 3 and power
1
𝐸k = 𝑚 𝑚2 Δ𝐸p = 𝑚𝑔Δℎ
2
Properties of Leptons ∆𝑊
𝑃 = ∆𝑡
, 𝑃 = 𝐹𝑚
Lepton number 𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝
− − 𝑒𝑓𝑓𝑒𝑐𝑒𝑒𝑛𝑐𝑒 =
Particles: e , νe ; µ , νµ +1 𝑒𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑝
Antiparticles: e+ , ν e , µ + , ν µ −1
Materials
𝑚 Hooke’s law 𝐹 = 𝑘 𝛥𝛥
Photons and energy levels density 𝜌 =
𝑉
ℎ𝑐 𝐹
photon energy 𝐸 = ℎ𝑓 = tensile stress =
𝐴
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑡𝑡𝑡
Young modulus
𝑡𝑡𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑠𝑠𝑡𝑛 ∆𝐿
photoelectricity ℎ𝑓 = + 𝐸k (max) tensile strain =
𝐿
energy levels ℎ𝑓 = 𝐸1 – 𝐸2 1
energy stored 𝐸 = 2 𝐹Δ𝛥
ℎ ℎ
de Broglie Wavelength 𝜆 = =
𝑝 𝑚𝑚
2 Version 1.6
, AQA AS PHYSICS DATA AND FORMULAE
Electricity
∆𝑄 𝑊 𝑉
current and pd 𝐼 = 𝑉 = 𝑅 =
∆𝑡 𝑄 𝐼
𝑅𝑅
resistivity 𝜌=
𝐿
resistors in series 𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + …
1 1 1 1
resistors in parallel = + + +⋯
𝑅T 𝑅1 𝑅2 𝑅3
𝑉2 2
power 𝑃 = 𝑉𝑉 = 𝐼 𝑅 =
𝑅
𝐸
emf 𝜀 = 𝜀 = 𝐼(𝑅 + 𝑟)
𝑄
Version 1.6 3
,4 Version 1.6
, Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
AS
PHYSICS
Paper 1
Wednesday 15 May 2024 Morning Time allowed: 1 hour 30 minutes
Materials
For Examiner’s Use
For this paper you must have:
• a pencil and a ruler Question Mark
• a scientific calculator
1
• a Data and Formulae Booklet
• a protractor. 2
3
Instructions 4
• Use black ink or black ball-point pen.
5
• Fill in the boxes at the top of this page.
• Answer all questions. 6
• You must answer the questions in the spaces provided. Do not write TOTAL
outside the box around each page or on blank pages.
• If you need extra space for your answer(s), use the lined pages at the end of
this book. Write the question number against your answer(s).
• Do all rough work in this book. Cross through any work you do not want
to be marked.
• Show all your working.
Information
• The marks for questions are shown in brackets.
• The maximum mark for this paper is 70.
• You are expected to use a scientific calculator where appropriate.
• A Data and Formulae Booklet is provided as a loose insert.
*JUN247407101*
IB/M/Jun24/G4001/E6 7407/1
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
0 1 An electron neutrino interacts with a chlorine-37 nucleus to produce an argon-37
nucleus and an electron.
The interaction is represented by the equation:
37 37
+
ve →
Cl + e
Ar
17 18
0 1 . 1 Explain, with reference to appropriate conservation laws, why the electron is emitted
in this interaction.
[2 marks]
0 1 . 2 Calculate the specific charge of the argon-37 nucleus.
[2 marks]
specific charge = C kg−1
*02*
IB/M/Jun24/7407/1
