Physics data booklet
For use during the course and in the examinations
First assessment 2025
Version 1.1
Diploma Programme
Physics data booklet
Published February 2023
Updated May 2023
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Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
A. Space, time and motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
B. The particulate nature of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
C. Wave behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
D. Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
E. Nuclear and quantum physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Physics data booklet
This page is intentionally blank.
Physics data booklet
Introduction
This Diploma Programme (DP) Physics data booklet accompanies the DP Physics guide and DP
Physics teacher support material. It contains electrical symbols, mathematics equations, constants,
and physics equations relevant to the course.
Students must have access to a copy of this booklet for the duration of the course so that they
can become familiar with its contents. Direct reference is made to relevant equations in the
“Understandings” sections of the guide. This helps to maintain the emphasis on interpretation and
application rather than memorization of symbols, constants and equations.
The Physics data booklet is split into two sections. The first includes information which is used
throughout the teaching of DP physics and the second contains equations relevant to specific themes
and topics. Note that all equations relate to the magnitude of the quantities only. Vector notation has
not been used.
Each student must have access to a clean copy of the Physics data booklet during examinations.
It is the responsibility of the school to download a copy of this booklet from IBIS or the Programme
Resource Centre and to ensure that there are sufficient copies available for all students.
Physics data booklet
1
Mathematical equations
1
(bh ) where b is the base, h is the height
2
Area of a triangle
A=
Area of a circle
A = πr 2 where r is the radius
Circumference of a circle
C = 2πr
Volume of a cuboid
V = lwh where l is the length, w is the width, h is the
height
Volume of a cylinder
V
Volume of a prism
V = Ah where A is the area of cross-section
Volume of a sphere
V=
4 3
πr
3
Area of the curved surface
of a cylinder
A
2 rh
Vectors
r 2h
A
AV
θ
Trigonometric relationships
AH
A cos
AV
A sin
tan θ =
AH
sin θ
cos θ
sin2 θ + cos2 θ = 1
2
Physics data booklet
Uncertainties
If: y = a ± b
then: ∆y = ∆a + ∆b
ab
c
then:
∆y ∆a ∆b ∆c
=
+
+
y
a
b
c
If: y = a n
then:
∆y
∆a
= n
y
a
If: y =
Fundamental constants
Quantity
Symbol
Approximate value
Acceleration of free fall
g
9.8 m s−2 (Earth’s surface)
Gravitational constant
G
6.67 × 10−11 Nm2 kg−2
Avogadro constant
NA
6.02 × 1023 mol−1
Gas constant
R
8.31JK −1 mol−1
Boltzmann constant
kB
1.38 × 10−23 JK −1
Stefan–Boltzmann constant
σ
5.67 × 10−8 W m−2 K −4
Coulomb constant
k
8.99 × 109 Nm2 C−2
Permittivity of free space
ε0
8.85 × 10−12 C2 N−1 m−2
Permeability of free space
4π × 10−7 T mA −1
Speed of light in vacuum
c
3.00 × 108 m s−1
Planck constant
h
6.63 × 10−34 Js
Elementary charge
e
1.60 × 10−19 C
Electron rest mass
me
9.110 × 10−31 kg = 0.000549 u = 0.511MeV c −2
Proton rest mass
mp
1.673 × 10−27 kg = 1.007276 u = 938 MeV c −2
Neutron rest mass
mn
1.675 × 10−27 kg = 1.008665 u = 940 MeV c −2
(Unified) atomic mass unit
u
1.661× 10−27 kg = 931.5 MeV c −2
Solar constant
S
1.36 × 103 W m−2
Fermi radius
R0
1.20 × 10−15 m
Physics data booklet
3
Metric (SI) multipliers
Prefix
Abbreviation
Value
peta
P
1015
tera
T
1012
giga
G
109
mega
M
106
kilo
k
103
hecto
h
102
deca
da
101
deci
d
10−1
centi
c
10−2
milli
m
10−3
micro
μ
10−6
nano
n
10−9
pico
p
10−12
femto
f
10−15
Unit conversions
1 radian (rad) ≡
180°
π
Temperature (K ) = temperature ( °C ) + 273
1 light year ( ly ) = 9.46 × 1015 m
1 parsec (pc ) = 3.26 ly
1 astronomical unit ( AU) = 1.50 × 1011 m
1 kilowatt-hour ( kWh ) = 3.60 × 106 J
h c = 1.99 × 10−25 Jm = 1.24 × 10 −6 eV m
4
Physics data booklet
Electrical circuit symbols
Cell
Battery
Switch
Voltmeter
Ammeter
Resistor
Variable resistor
Light-dependent resistor
(LDR)
Thermistor
Potentiometer
Lamp
Light emitting diode (LED)
Heating element
Motor
Earth (ground)
Electromagnetic spectrum
energy
10 −16
10 −14
 rays
10 −12
10 −10
X-rays
10 −8
UV
10 −6
IR
10 −4
10 −2
microwaves
100
102
10 4
106
108 wavelength / m
radio waves
V I B G Y O R
400
700
wavelength / nm
Physics data booklet
5
A. Space, time and motion
Standard level and higher level
A.1 Kinematics
s=
u +v
t
2
v = u + at
s = ut +
1 2
at
2
v 2 = u 2 + 2as
A.2 Forces and momentum
Ff ≤ µsFN
Ff = µdFN
FH = −k x
Fd = 6πη rv
Fb = ρVg
Fg = mg
p = mv
J = F ∆t
F = ma =
A.3 Work, energy and power
∆p
∆t
a=
v2
4π 2 r
= ω 2r = 2
r
T
v=
2π r
= ωr
T
W = Fs cos θ
1
p2
mv 2 2
2m
Ek ∆Ep = mg ∆h
EH =
6
1
k ∆x 2
2
P=
∆W
= Fv
∆t
η=
useful work out useful power out
=
total work in
total power in
Physics data booklet
Additional higher level
A.4 Rigid body mechanics
τ = Fr sin θ
∆θ =
ωf + ωi
t
2
ωf = ωi + α t
1
∆θ = ωit + α t 2
2
ωf2 = ωi2 + 2α∆θ
I = Σmr 2
τ = Iα
L = Iω
∆L = τ∆t
∆L = ∆( I ω )
Ek =
A.5 Galilean and special relativity
1 2 L2
Iω =
2
2I
x ' = x − vt
t'=t
u' = u −v
x ' = γ ( x − vt ) where γ =
1
1−
v2
c2
 vx 
t ' = γ t − 2 
c 

u' =
u −v
uv
1− 2
c
( ∆s )2 = (c ∆t )2 − ∆x 2
∆t = γ∆t0
L=
L0
γ
tan θ =
Physics data booklet
v
c
7
B. The particulate nature of matter
Standard level and higher level
B.1 Thermal energy transfers
ρ=
m
V
Ek =
3
kBT
2
Q = mc ∆T
Q = mL
∆Q
∆T
= kA
∆t
∆x
L = σ AT 4
b=
L
4π d 2
λmaxT = 2.9 × 10−3 mK
B.2 Greenhouse effect
emissivity =
albedo =
B.3 Gas laws
P=
F
A
n=
N
NA
power radiated per unit area
σT 4
total scattered power
total incident power
PV
= constant
T
=
PV nRT
= NkBT
P=
=
U
8
1 2
ρv
3
3
3
=
nRT
NkBT
2
2
Physics data booklet
B.5 Current and circuits
I=
∆q
∆t
V=
W
q
R=
V
I
ρ=
RA
L
V2
=
P I=
V I R=
R
2
Series circuits
Parallel circuits
I= I=
I 2 = ...
1
I = I1 + I 2 + ...
V = V1 + V2 + ...
V= V=
V2 = ...
1
Rs = R1 + R2 + ...
1
1
1
=
+
+ ...
Rp R1 R2
ε = I(R + r )
Additional higher level
B.4 Thermodynamics
Q = ∆U + W
W = P ∆V
∆U =
∆S =
3
3
nR ∆T = NkB ∆T
2
2
∆Q
T
S = kB ln Ω
5
3
PV = constant
η=
useful work
input energy
ηCarnot = 1 −
Physics data booklet
Tc
Th
9
C. Wave behaviour
Standard level and higher level
C.1 Simple harmonic motion
a = −ω 2 x
T=
C.2 Wave model
C.3 Wave phenomena
1 2π
=
f
ω
T = 2π
m
k
T = 2π
l
g
v= fλ =
λ
T
n1 sin θ 2 v 2
=
=
n2 sin θ1 v1
Constructive interference:
path difference = nλ
Destructive interference:
1
path difference = (n + )λ
2
λD
d
∆f ∆λ v
=
≈
f
λ
c
s=
C.5 Doppler effect
Additional higher level
C.1 Simple harmonic motion
x = x0 sin(ωt + φ )
v = ω x0 cos(ωt + φ )
v = ±ω x0 2 − x 2
10
ET =
1
mω 2 x02
2
Ep =
1
mω 2 x 2
2
Physics data booklet
C.3 Wave phenomena
θ=
λ
b
nλ = d sin θ
C.5 Doppler effect

v 

 v ± us 
Moving source: f ′ = f 
 v ± uo 
Moving observer: f ′ = f 

 v 
Physics data booklet
11
D. Fields
Standard level and higher level
D.1 Gravitational fields
=
g
D.2 Electric and magnetic fields
D.3 Motion in electromagnetic fields
m1m2
r2
F =G
F
M
= G 2
m
r
F =k
E=
F
q
E=
V
d
q1q2
1
where k =
2
4πε 0
r
F = qvB sin θ
F = B I L sin θ
II
F
= µ0 1 2
2π r
L
Additional higher level
D.1 Gravitational fields
Ep = −G
m1m2
r
Vg = −G
M
r
g=−
∆Vg
∆r
W = m∆Vg
2GM
r
v esc =
v orbital =
D.2 Electric and magnetic fields
Ep = k
Ve =
GM
r
q1q2
r
kQ
r
E=−
∆Ve
∆r
W = q ∆Ve
12
Physics data booklet
D.4 Induction
Φ = BA cos θ
ε = −N
∆Φ
∆t
ε = BvL
E. Nuclear and quantum physics
Standard level and higher level
E.1 Structure of the atom
E =hf
E.3 Radioactive decay
E = mc 2
E.5 Fusion and stars
d(parsec) =
1
p(arc-second)
Additional higher level
E.1 Structure of the atom
1
R = R0 A 3
E=−
13.6
eV
n2
mvr =
E.2 Quantum physics
nh
2π
Emax = h f − Φ
λ=
h
p
λf − λi = ∆λ =
E.3 Radioactive decay
h
(1 − cos θ )
me c
N = N0 e − λ t
A = λ N = λ N0 e − λ t
T1 =
2
Physics data booklet
ln 2
λ
13