Physics data booklet
First assessment 2016
Diploma Programme
Physics data booklet
Published June 2014
Revised edition published November 2016
Published on behalf of the International Baccalaureate Organization, a not-for-profit
educational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva,
Switzerland by the
International Baccalaureate Organization (UK) Ltd
Peterson House, Malthouse Avenue, Cardiff Gate
Cardiff, Wales CF23 8GL
United Kingdom
Website: www.ibo.org
© International Baccalaureate Organization 2014
The International Baccalaureate Organization (known as the IB) offers four high-quality
and challenging educational programmes for a worldwide community of schools, aiming
to create a better, more peaceful world. This publication is one of a range of materials
produced to support these programmes.
The IB may use a variety of sources in its work and checks information to verify accuracy
and authenticity, particularly when using community-based knowledge sources such as
Wikipedia. The IB respects the principles of intellectual property and makes strenuous
efforts to identify and obtain permission before publication from rights holders of all
copyright material used. The IB is grateful for permissions received for material used
in this publication and will be pleased to correct any errors or omissions at the earliest
opportunity.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, without the prior written permission
of the IB, or as expressly permitted by law or by the IB’s own rules and policy. See
http://www.ibo.org/copyright.
IB merchandise and publications can be purchased through the IB store at
http://store.ibo.org.
Email: sales@ibo.org
International Baccalaureate, Baccalauréat International and Bachillerato Internacional
are registered trademarks of the International Baccalaureate Organization.
4082
Contents
Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Physics data booklet
Physics data booklet
Mathematical equations
Area of a circle
A = πr 2 , where r is the radius
Circumference of a circle
C = 2πr , where r is the radius
Surface area of a sphere
A = 4πr 2 , where r is the radius
Volume of a sphere
4
V = πr 3 , where r is the radius
3
Physics data booklet
1
Fundamental constants
Quantity
2
Symbol
Approximate value
Acceleration of free fall
(Earth’s surface)
g
9.81m s−2
Gravitational constant
G
6.67 × 10−11 Nm2 kg−2
Avogadro’s constant
NA
6.02 × 1023 mol−1
Gas constant
R
8.31JK −1 mol−1
Boltzmann’s 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
µ0
4π × 10−7 T m A −1
Speed of light in vacuum
c
3.00 × 108 m s−1
Planck’s 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
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
hc = 1.99 × 10−25 Jm = 1.24 × 10 −6 eV m
Physics data booklet
3
Electrical circuit symbols
cell
battery
ac supply
switch
voltmeter
4
V
ammeter
resistor
variable resistor
lamp
potentiometer
light-dependent
resistor (LDR)
thermistor
transformer
heating element
diode
capacitor
A
Physics data booklet
Equations—Core
Note: All equations relate to the magnitude of the quantities only. Vector notation has
not been used.
Sub-topic 1.2 – Uncertainties and errors
If: y = a ± b
then: ∆y = ∆a + ∆b
If: y =
then:
A
AV
ab
c
∆y
y
=
∆a ∆b ∆c
+
+
a
b
c
∆y
y
θ
= n
∆a
a
A V = A sin θ
Sub-topic 2.1 – Motion
1 2
at
2
v 2 = u 2 + 2as
s=
Sub-topic 2.2 – Forces
F = ma
v = u + at
s = ut +
AH
AH = A cos θ
If: y = a n
then:
Sub-topic 1.3 – Vectors and scalars
Ff ≤ µsR
Ff = µdR
(v + u ) t
2
Sub-topic 2.3 – Work, energy
and power
W = Fs cos θ
Sub-topic 2.4 – Momentum
and impulse
p = mv
EK =
1
mv 2
2
F=
Ep =
1
k ∆ x2
2
EK =
∆Ep = mg ∆h
power = Fv
efficiency =
=
∆p
∆t
p2
2m
impulse = F ∆t = ∆p
useful work out
total work in
useful power out
total power in
Physics data booklet
5
Sub-topic 3.1 – Thermal concepts
Q = mc ∆T
Sub-topic 3.2 – Modelling a gas
p=
F
A
n=
N
NA
Q = mL
pV = nRT
=
EK
Sub-topic 4.1 – Oscillations
T=
1
f
Sub-topic 4.2 – Travelling waves
c = fλ
Sub-topic 4.3 – Wave characteristics
I ∝ A2
I ∝ x −2
I = I 0 cos2 θ
6
3
3 R
=
kBT
T
2
2 NA
Sub-topic 4.4 – Wave behaviour
n1 sin θ 2 v 2
=
=
n2 sin θ1 v1
s=
λD
d
Constructive interference:
path difference = nλ
Destructive interference:


1
path difference =  n +  λ
2

Physics data booklet
Sub-topic 5.2 – Heating effect of
electric currents
Sub-topic 5.1 – Electric fields
I=
∆q
∆t
q1q2
r2
F =k
k=
1
4pε 0
Kirchhoff’s circuit laws:
ΣV = 0 (loop)
ΣI = 0 (junction)
R=
V
I
V=
W
q
=
P V=
I I 2R =
E=
F
q
Rtotal = R1 + R2 + ...
I = nAvq
1
Rtotal
ρ=
Sub-topic 5.3 – Electric cells
ε = I (R + r )
=
V2
R
1
1
+
+ ...
R1 R2
RA
L
Sub-topic 5.4 – Magnetic effects of
electric currents
F = qvB sin θ
F = B IL sin θ
Sub-topic 6.2 – Newton’s law of
gravitation
Sub-topic 6.1 – Circular motion
v = ωr
F =G
a=
v 2 4 π2 r
= 2
r
T
g=
F=
mv 2
= mω 2 r
r
g =G
Physics data booklet
Mm
r2
F
m
M
r2
7
Sub-topic 7.1 – Discrete energy and
radioactivity
E =hf
λ=
Sub-topic 7.2 – Nuclear reactions
∆E = ∆mc 2
hc
E
Sub-topic 7.3 – The structure of matter
Charge
2
e
3
1
− e
3
Baryon
number
Quarks
u
d
c
s
t
1
3
b
1
3
Charge
Leptons
–1
e
µ
τ
0
νe
νµ
ντ
All leptons have a lepton number
of 1 and antileptons have a lepton
number of –1
All quarks have a strangeness number
of 0 except the strange quark that has
a strangeness number of –1
Particles
experiencing
Particles
mediating
Gravitational
Weak
Electromagnetic
Strong
All
Quarks,
leptons
Charged
Quarks,
gluons
Graviton
W + , W − , Z0
γ
Gluons
Sub-topic 8.2 – Thermal energy
transfer
Sub-topic 8.1 – Energy sources
power =
energy
time
P = eσ AT 4
power =
1
Aρv 3
2
λmax (metres) =
I=
power
A
albedo =
8
2.90 × 10−3
T (kelvin)
total scattered power
total incident power
Physics data booklet
Equations—AHL
Sub-topic 9.1 – Simple harmonic
motion
ω=
2π
T
Sub-topic 9.2 – Single-slit diffraction
θ=
λ
b
a = −ω 2 x
Sub-topic 9.3 – Interference
x = x0 sin ω t ; x = x0 cos ω t
nλ = d sin θ
v = ω x0 cos ω t ; v = −ω x0 sin ω t
1

Constructive interference: 2dn =  m +  λ
2

v = ±ω ( x0 2 − x 2 )
Destructive interference: 2dn = mλ
EK =
1
mω 2 ( x0 2 − x 2 )
2
ET =
1
mω 2 x0 2
2
pendulum: T = 2π
l
g
mass-spring:T = 2π
m
k
Sub-topic 9.4 – Resolution
θ = 1.22
R=
λ
b
λ
= mN
∆λ
Sub-topic 9.5 – Doppler effect
 v 
Moving source: f ′ = f 

 v ± us 
 v ± uo 
Moving observer: f ′ = f 

 v 
∆f
f
Physics data booklet
=
∆λ
λ
≈
v
c
9
Sub-topic 10.1 – Describing fields
W = q ∆Ve
W = m∆Vg
Sub-topic 10.2 – Fields at work
GM
r
Ve =
∆Vg
∆r
E=−
Vg = −
g=−
Ep = mVg = −
Fg =
10
GMm
r2
v esc =
2GM
r
v orbit =
GM
r
kQ
r
∆Ve
∆r
GMm
kQq
=
Ep qV
=
e
r
r
Fe =
kQq
r2
Physics data booklet
Sub-topic 11.1 – Electromagnetic
induction
Φ = BA cos θ
∆Φ
∆t
ε = −N
ε = Bv l
Sub-topic 11.3 – Capacitance
C=
q
V
Cparallel = C1 + C2 + ...
1
Cseries
ε = Bv l N
1
1
+
+ ...
C1 C2
=
A
Sub-topic 11.2 – Power generation and
C =ε
transmission
d
I0
Irms =
E=
2
V0
Vrms =
1
CV 2
2
τ = RC
2
V0
V
R = = rms
I 0 Irms
q = q0 e
Pmax = I 0V0
I = I0e
1
I 0V0
2
V = V0 e
P=
−
−
t
τ
t
τ
−
t
τ
ε p Np I s
=
=
ε s Ns I p
Sub-topic 12.1 – The interaction of
matter with radiation
Sub-topic 12.2 – Nuclear physics
1
E =hf
R = R0 A 3
Emax = h f − Φ
N = N0 e − λ t
E=−
13.6
eV
n2
mvr =
nh
2π
A = λ N0 e − λ t
sin θ ≈
λ
D
2
P (r ) = ψ ∆V
∆ x∆p ≥
h
4π
∆E ∆t ≥
h
4π
Physics data booklet
11
Equations—Options
Sub-topic A.1 – The beginnings of
relativity
x′ = x − v t
Sub-topic A.2 – Lorentz
transformations
1
γ=
1−
u′ = u − v
Sub-topic A.3 – Spacetime diagrams
v 
θ = tan−1  
c
v2
c2
x′ = γ ( x − vt ); ∆ x′ = γ ( ∆ x − v ∆t )
vx 
; ∆t ′ = γ
c 2 


t′ = γ t −
v∆x 

 ∆t − c 2 


u −v
uv
1− 2
c
u′ =
∆t = γ ∆t0
L=
L0
γ
(ct ′)2 − ( x′)2 = (ct )2 − ( x )2
Sub-topic A.4 – Relativistic mechanics
(HL only)
E = γ m0 c 2
E0 = m0 c 2
EK = (γ − 1) m0 c 2
p = γ m0v
E 2 = p 2c 2 + m0 2c 4
Sub-topic A.5 – General relativity
(HL only)
∆f
=
g ∆h
c2
Rs =
2GM
c2
f
∆t =
∆t0
1−
Rs
r
qV = ∆EK
12
Physics data booklet
Sub-topic B.1 – Rigid bodies
and rotational dynamics
Γ = Fr sin θ
I = ∑ mr 2
Γ = Iα
ω = 2πf
ωf = ωi + α t
ω f2 = ω 2i + 2αθ
1
θ = ωi t + α t 2
2
L = Iω
EKrot =
1 2
Iω
2
Sub-topic B.3 – Fluids and fluid
dynamics (HL only)
Sub-topic B.2 – Thermodynamics
Q = ∆U + W
3
nRT
2
U=
∆S =
∆Q
T
5
pV 3 = constant (for monatomic gases)
W = p∆V
η=
useful work done
energy input
ηCarnot = 1 −
Tcold
Thot
Sub-topic B.4 – Forced vibrations and
resonance (HL only)
energy stored
energy dissipated per cycle
B = ρ fVf g
Q = 2π
P = P0 + ρ f gd
Q = 2π × resonant frequency ×
energy stored
power loss
Av = constant
1 2
ρv + ρ gz + p = constant
2
FD = 6πη rv
R=
vr ρ
η
Physics data booklet
13
Sub-topic C.1 – Introduction to
imaging
1
f
=
1 1
+
v u
Sub-topic C.2 – Imaging
instrumentation
fo
fe
M=
1
P=
Sub-topic C.3 – Fibre optics
f
n=
h
v
m= i =−
ho
u
M=
attenuation = 10 log
θi
θo
Mnear point =
1
sin c
D
f
+ 1; Minfinity =
Sub-topic C.4 – Medical imaging
(HL only)
D
f
I
I0
LI = 10 log
I1
I0
I = I0e − µ x
µ x 1 = In2
2
Z = ρc
Sub-topic D.1 – Stellar quantities
d (parsec) =
1
p (arc-second)
L = σ AT 4
b=
Sub-topic D.2 – Stellar characteristics
and stellar evolution
λmaxT = 2.9 × 10−3 mK
L ∝ M 3 .5
L
4πd 2
Sub-topic D.3 – Cosmology
Sub-topic D.5 – Further cosmology
(HL only)
z=
∆λ v
≈
λ0 c
v=
4πG ρ
r
3
z=
R
−1
R0
ρc =
3H 2
8πG
v = H0 d
T ≈
14
1
H0
Physics data booklet