Physics data booklet
First assessment 2016
Annotated by Boaz V.
Diploma Programme
Physics data booklet
Published June 2014
Revised edition published January 2016
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4082
Contents
Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Equations—AHL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Physics data booklet
Physics data booklet
Fundamental constants
Quantity
Symbol
Approximate value
Acceleration of free fall
(Earth’s surface)
g
9.81m s
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
Boltzmann’s constant
kB
1.38 × 10−23 JK −1
1
5.67 × 10−8 W m−2 K −4
Stefan–Boltzmann constant
Coulomb constant
2
k
8.99 × 109 Nm2 C−2
Permittivity of free space
0
8.85 × 10−12 C2 N−1 m−2
Permeability of free space
0
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
1
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
10 –6
micro
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
2
Physics data booklet
Electrical circuit symbols
cell
battery
ac supply
switch
voltmeter
V
ammeter
resistor
variable resistor
lamp
potentiometer
light-dependent
resistor (LDR)
thermistor
transformer
heating element
diode
capacitor
Physics data booklet
A
3
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
Sub-topic 1.3 – Vectors and scalars
If: y = a ± b
then: ∆y =
y = Result.
a, b, c = Quantities.
then:
∆y
=
y
A
AV
AH = Horizontal
component.
Multiplying/dividing quantities: %
uncertainties of quantities are added
together to obtain % uncertainty in result.
ab
c
If: y
Δ = Uncertainty.
Adding/subtracting quantities:
uncertainty in result will be sum
∆a + ∆b of uncertainties of quantities.
AV = Vertical
component.
∆a ∆b ∆c
+
+
a
b
c
AH
an
If: y
then:
Powers of quantities: % uncertainty of
quantity is multiplied by power to obtain
% uncertainty in result.
∆y
= n
y
v = Final velocity.
∆a
a
AH = A cos θ
A V = A sin θ
F = Resultant force.
Sub-topic 2.1 – Motion
u = Initial velocity.
v = u + at
Sub-topic 2.2 – Forces
F
1 2
at
2
a = Acceleration (‘g’
for gravitational).
s = ut +
s = Displacement.
v 2 = u 2 + 2as
t = Time elapsed.
s=
Equations applied to
uniform motion (known as
‘suvat’ equations).
Ff = µdR
Frictional force on a static object.
Frictional force on a dynamic object.
s = Displacement.
EK
1
mv 2
2
Work done.
Kinetic energy.
m = Mass.
1
Ep = k ∆ x 2
2
v = Velocity.
∆Ep = mg ∆h
Gravitational potential energy.
EP = Potential energy.
power
Power.
k = Spring constant
efficiency
Fv
Elastic potential energy (in a spring).
Sub-topic 2.4 – Momentum
and impulse
p
mv
F=
∆p
∆t
μs = Coefficient of
static friction.
μd = “ dynamic “.
EK
p2
2m
R = Normal reaction
force.
p = Momentum.
Resultant force due to momentum.
m = Mass.
v = Velocity.
Kinetic energy.
F = Force.
impulse = F ∆t = ∆p
t = Time.
useful work out
total work in
EK = Kinetic energy.
h = Height.
4
a = Acceleration.
Momentum.
useful power out
total power in
g = Earth’s gravity.
m = Mass.
Ff = Frictional force.
W = Fs cos θ
x = Extension.
Acceleration due to resultant force
(Newton’s 2nd law of motion).
(v + u ) t
2
F = Force.
EK = Kinetic energy.
ma
Ff ≤ µsR
Sub-topic 2.3 – Work, energy
and power
W = Work done.
Trigonometric rules of triangles are
applied when taking components of
vector quantities.
Physics data booklet
p = Pressure.
F = Force.
A = Area.
Q = Energy/heat.
m = Mass.
c = Specific heat
capacity.
Sub-topic 3.1 – Thermal concepts
Energy/heat given/received in changing
an object’s temperature.
Q = mc ∆T
Q
mL
Energy/heat given/received in changing
an object’s phase.
T = Temperature.
L = Specific latent
heat.
f = Frequency.
T
λ = Wavelength.
1
f
Period (time taken to complete 1
oscillation).
Sub-topic 4.2 – Travelling waves
c = Velocity.
f = Frequency.
p
n
c = fλ
Speed of a wave.
Sub-topic 4.3 – Wave characteristics
N
NA
N = Number of
atoms.
Pressure.
NA = Avogadro’s
constant.
Number of moles of a substance.
nRT
EK
3
kBT
2
I
A = Amplitude.
I ∝ x −2
x = Distance from
source.
I = I 0 cos2
Intensity of a wave’s radiation at a certain
distance from the source.
Transmitted intensity of light incident
on a polariser (Malus’s law).
V = Volume.
R = Gas constant.
Ideal gas law.
3 R
T
2 NA
T = Temperature.
Average kinetic energy per
molecule of a gas.
EK = Kinetic energy.
kb = Boltzmann’s
constant.
Sub-topic 4.4 – Wave behaviour
n1 sin θ 2 v 2
=
=
n2 sin θ1 v1
s=
λD
d
Refraction when a wave crosses a
boundary between 2 media
(Snell’s law).
n1/n2 = Index of
refraction.
θ = Angle of
incidence/refraction.
Fringe spacing in double slit diffraction.
v = Wave velocity.
Constructive interference:
path difference = nλ
Intensity of a wave vs. amplitude.
I = Intensity.
A2
F
A
pV
Sub-topic 4.1 – Oscillations
T = Period.
n = Number of moles.
Sub-topic 3.2 – Modelling a gas
Destructive interference:
⎛
⎝
s = Fringe spacing.
Maxima/minima on
screen in double slit
diffraction.
λ = Wavelength.
1⎞
D = Distance to
screen.
path difference = ⎜ n + ⎟ λ
2
⎠
d = Slit spacing.
I0 = Original
intensity.
n = Any integer (order
of minimum/
maximum).
θ = Angle of
polarizer.
Physics data booklet
5
I = Current.
q = Charge.
t = Time.
Sub-topic 5.2 – Heating effect of
electric currents
Sub-topic 5.1 – Electric fields
F = Force.
I=
∆q
∆t
r = Separation
distance.
F
qq
k 122
r
ε0 = Permittivity of
free space.
k
k = Coulomb
constant.
V = Potential.
W = Work done.
E = Electric field
strength.
n = Number of
charges per unit
volume.
Coulomb constant.
W
q
Potential difference.
E
F
q
Electric field strength.
nAvq
Current in a wire.
V
R
P
v = Drift velocity.
ε = I (R + r )
I = Current.
Emf of a cell.
=
1
1
+
+ ...
R1 R2
RA
L
Power supplied/dissipated.
L = Length.
Total resistance of resistors
in series.
Total resistance of resistors
in parallel.
Resistivity of material of a wire.
F = Force.
F = qvB sin θ
F = B IL sin θ
R = Resistance.
V
R
Sub-topic 5.4 – Magnetic effects of
electric currents
Sub-topic 5.3 – Electric cells
ε = Emf.
I 2R
2
Rtotal = R1 + R2 + ...
Rtotal
ρ = Resistivity.
A = X-sectional area.
VI
1
P = Power.
Resistance.
I
ρ=
A = X-sectional area.
R = Resistance.
ΣI = 0 (junction)
0
V
I
I = Current.
ΣV = 0 (loop)
Force experienced by 2 charges
(Coulomb’s law).
1
4
Kirchhoff’s circuit laws:
Current.
V = Potential.
Force on a charge moving through a
magnetic field.
Force on a current-carrying wire in a
magnetic field.
q = Charge.
v = Velocity of charge.
B = Magnitude of
magnetic field.
θ = Angle with field.
r = Internal resistance.
Sub-topic 6.2 – Newton’s law of
gravitation
Sub-topic 6.1 – Circular motion
v = Velocity.
v = ωr
ω = Angular velocity.
r = Radius of circle.
Velocity of body travelling in circle.
v 2 4 π2 r
a=
= 2
r
T
a = Acceleration.
T = Period of
rotation.
F=
F = Force.
Centripetal acceleration.
mv 2
= mω 2 r
r
Centripetal force.
F
G
g
F
m
g
G
Mm
r2
Force experienced by 2 masses
(Newton’s law of gravitation).
Field strength as experienced by a
mass in the field.
M
r2
Field strength at a certain
distance from body.
F = Force.
G = Gravitational
constant.
M = Mass of body.
m = Mass of body (in
a field).
r = Separation
distance of bodies.
g = Gravitational
field strength
m = Mass.
6
Physics data booklet
E = Energy.
Sub-topic 7.1 – Discrete energy and
radioactivity
h = Planck’s constant.
f = Frequency.
λ = Wavelength.
c = Speed of light.
E
hf
λ=
hc
E
∆E = ∆mc 2
Energy of a photon.
E = Energy.
Sub-topic 7.2 – Nuclear reactions
m = Mass.
Energy released when nucleons are
assembled into nucleus.
c = Speed of light.
Wavelength of a photon.
Sub-topic 7.3 – The structure of matter
e = Elementary
charge.
u = Up.
d = Down.
c = Charm.
s = Strange.
t = Top.
Charge
2
e
3
1
e
3
Baryon
number
Quarks
u
d
c
s
t
b
Charge
–1
1
3
0
Leptons
e = Electron.
e
e
νµ
u = Muon.
ντ
τ = Tau.
All leptons have a lepton number
of 1 and antileptons have a lepton
number of –1
1
3
ν = Neutrino.
All quarks have a strangeness number
of 0 except the strange quark that has
a strangeness number of –1
b = Bottom.
Particles
experiencing
Particles
mediating
Gravitational
Weak
Electromagnetic
Strong
All
Quarks,
leptons
Charged
Quarks,
gluons
Graviton
W + , W − , Z0
Sub-topic 8.2 – Thermal energy
transfer
Sub-topic 8.1 – Energy sources
A = Area swept out
by turbine blades.
ρ = Air density.
v = Wind speed.
power
energy
time
1
power = Aρv 3
2
P = eσ AT 4
Power available from a wind
turbine.
power
A
albedo
P = Power.
Power radiated by a body.
2.90 × 10−3
λmax (metres) =
T (kelvin)
I
Physics data booklet
Gluons
e = Emissivity.
σ = Stefan-Boltzmann
constant.
Wavelength at
which intensity of
radiation is at a
maximum.
A = Area.
Intensity of radiation.
T = Temperature.
λ = Wavelength.
total scattered power
total incident power
I = Intensity.
7
Equations—AHL
Sub-topic 9.1 – Simple harmonic
motion
ω = Angular
frequency.
ω=
T = Period.
2π
T
Angular frequency of oscillation.
a = −ω 2 x
a = Acceleration.
Displacement of
object in SHM.
x0 = Maximum
displacement.
v = ω x0 cos ω t ; v = −ω x0 sin ω t
t = Time elapsed.
v = ±ω ( x0 2 − x 2 )
Velocity of
object in
SHM.
Velocity of object in SHM.
EK = Kinetic energy.
EK =
ET = Total energy.
l = Length of
pendulum.
1
mω 2 ( x0 2 − x 2 )
2
1
ET = mω 2 x0 2
2
g = Gravitational field
strength.
Kinetic energy of object in
SHM.
l
g
θ = 1.22
b = Slit width/
diameter.
R=
R = Resolvance
Δλ = Smallest
possible resolvable
wavelength
difference.
λ
b
λ = Wavelength.
b = Slit width.
nλ = d sin θ
Path difference between slits for a
diffraction grating (constructive/
destructive interference).
1⎞
⎛
Constructive interference: 2dn = ⎜ m + ⎟ λ
2⎠
⎝
Destructive interference: 2dn = mλ
Interference patterns for thin-film
interference.
n = Any integer (for
diffraction grating).
λ = Wavelength.
d = Slit spacing (for
diffraction grating).
θ = Angle.
d = Thickness of
medium (for TFI).
n = Refractive index
of medium (for TFI).
m = Any integer (for
TFI).
Period of oscillation of
a mass on a spring in
SHM.
First minimum for diffraction in a circular
aperture.
λ
= mN
∆λ
θ = Angle.
Sub-topic 9.3 – Interference
Sub-topic 9.4 – Resolution
λ = Wavelength.
b
Angle at which first minimum occurs
in single-slit diffraction.
Period of oscillation of
a pendulum in SHM.
m
mass-spring:T = 2π
k
θ = Angle.
λ
Total energy of object in SHM.
pendulum: T = 2π
k = Spring constant.
θ=
Acceleration of object in SHM.
x = x0 sin ω t ; x = x0 cos ω t
x = Displacement
from equilibrium.
Sub-topic 9.2 – Single-slit diffraction
Resolvance of a diffraction grating.
Sub-topic 9.5 – Doppler effect
⎛ v ⎞
Moving source: f ′ = f ⎜
⎟
⎝ v ± us ⎠
⎛ v ± uo ⎞
Moving observer: f ′ = f ⎜
⎟
⎝ v ⎠
∆f
∆λ
v
=
≈
f
λ c
Doppler effect for light.
f’ = Perceived
frequency.
f = Actual frequency.
v = Wave speed.
us = Velocity of
source.
uo = Velocity of
observer.
λ = Wavelength.
m = Diffraction
order.
v = Relative speed of
observer and source.
N = Number of slits
illuminated.
c = Speed of light.
8
Physics data booklet
Vg = Gravitational
potential.
Sub-topic 10.1 – Describing fields
W = Work done.
q = Charge.
Ve = Electric
potential.
m = Mass.
W = q ∆Ve
Work done moving a charge
between 2 points in a field.
W = m∆Vg
Work done moving a mass
between 2 points in a field.
Potential.
Field strength.
Potential energy.
Vg = Gravitational
potential.
Force.
Ve = Electric
potential.
Sub-topic 10.2 – Fields at work
GM
r
Ve
∆Vg
∆r
E=−
Vg = −
g=−
GMm
Ep = mVg = −
Ep
r
Fg
GMm
r2
Fe
kQ
r
G = Gravitational
constant.
k = Coulomb
constant.
∆Ve
∆r
qVe
M = Mass.
kQq
r
Q = Charge.
r = Separation
distance.
kQq
r2
v esc
2GM
r
Escape velocity of a planet.
v orbit
GM
r
Velocity of a body in circular orbit
around another body.
g = Gravitational
field strength.
E = Electric field
strength.
Ep = Potential
energy.
m = Mass.
q = Charge.
Fg = Gravitational
force.
Fe = Electric force.
V(esc) = Escape
velocity.
V(orbit) = velocity of
orbit.
Physics data booklet
9
Φ = Magnetic flux.
B = B = Magnitude of
magnetic field.
A = Area of coil.
Sub-topic 11.1 – Electromagnetic
induction
Φ = BA cos θ
N = Number of turns.
∆Φ
ε = −N
∆t
t = Time elapsed.
ε = Bv l
Magnetic flux.
Induced emf in a coil.
Sub-topic 11.3 – Capacitance
Capacitance of a capacitor.
Cparallel = C1 + C2 + ...
Induced emf in a conductor moving
through a field.
Induced emf in a coiled wire moving
through a field.
q = Charge.
q
V
C
1
Cseries
ε = Bv l N
l = Length of wire.
A
Sub-topic 11.2 – Power generation and
C =ε
transmission
d
I0 = Maximum current.
V(rms) = Effective pd.
I0
Irms
2
V0
Vrms
P(max) = Maximum
power dissipated.
P = Power dissipated.
ε = Emf.
N = Number of turns.
p/s = Primary/
secondary.
f = Frequency.
Φ = Work function.
n = State of atom.
m = Mass.
v = Velocity.
I 0V0
Maximum power dissipated.
1
I 0V0
2
Average power dissipated.
E
hf
Emax = h f − Φ
13.6
E = − 2 eV
n
mvr =
nh
2π
x = Position.
p = Momentum.
h
4π
h
∆E ∆t ≥
4π
Kinetic energy of freed electron
(photoelectric effect) (= e ×
stopping voltage).
Quantised energy of electron in the
hydrogen atom.
Angular momentum of the orbiting
electron in the hydrogen atom.
P (r ) = ψ ∆V
∆ x∆p ≥
Capacitance of capacitors in
series.
Capacitance of a capacitor.
1
CV 2
2
τ = RC
−
−
V = V0 e
Energy stored in a capacitor.
Exponential decrease of charge
stored for a discharging capacitor.
τ
t
Exponential decrease of current for a
discharging capacitor.
τ
t
Exponential decrease of potential
difference for a discharging capacitor.
τ
Sub-topic 12.2 – Nuclear physics
R
R0 A
N = N0 e
1
3
− λt
A = λ N0 e
sin θ ≈
λ
D
− λt
Nuclear radius of an element.
Number of nuclei left in a radioactive
sample.
Activity of a radioactive sample.
d = Separation of
plates.
τ = Time constant.
R = Resistance.
t = Time elapsed.
I = Current.
I0 = Initial maximum
current.
V0 = Initial maximum
potential difference.
R = Nuclear radius.
R0 = Fermi radius
(constant).
A = Atomic mass
number.
N = Number of
nuclei.
N0 = Original
number of nuclei.
First minimum of an electron diffraction
pattern around a circular object.
Probability that an electron will be
found within a small volume ΔV.
A = Activity.
λ = Decay constant.
θ = Angle of first
minimum.
Uncertainty in momentum and
position of a particle (Heisenberg).
λ = De Broglie
wavelength.
Uncertainty in energy and lifetime of
the state of a particle (Heisenberg).
D = Diameter of
circular object.
t = Time.
10
A = Area of plates.
q0 = Original charge.
t
−
ε = Permittivity of
dielectric material.
E = Energy stored.
Time constant for a circuit.
q = q0 e
I = I0e
Capacitance of capacitors in
parallel.
V = Potential
(difference).
Ratios of emf, turns and current in a
transformer.
Energy of a photon.
2
V = Volume.
E
Sub-topic 12.1 – The interaction of
matter with radiation
r = Radius.
Ψ = Wave function.
Resistance.
ε p Np I s
=
=
ε s Ns I p
E = Energy.
h = Planck’s constant.
I0
Pmax
P
Vrms
Irms
V0
R
Effective (root mean square) potential
difference in an AC generator.
2
V0 = Maximum pd.
R = Resistance
Effective (root mean square) current in
an AC generator.
1
1
+
+ ...
C1 C2
=
v = Speed of wire.
I(rms) = Effective
current.
C = Capacitance.
Physics data booklet
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
f
=
Rs
∆t =
g ∆h
c2
2GM
c2
∆t0
1−
Rs
r
qV = ∆EK
Physics data booklet
11
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 ×
Av
energy stored
power loss
constant
1 2
ρv + ρ gz + p = constant
2
FD = 6πη rv
R=
12
vr ρ
η
Physics data booklet
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
M=
attenuation 10 log
θi
θo
Mnear point =
1
sin c
n
h
v
m= i =−
ho
u
D
f
+ 1; Minfinity =
I
I0
Sub-topic C.4 – Medical imaging
(HL only)
D
f
10 log
LI
I1
I0
I = I0e − µ x
µ x 1 = In2
2
d = Distance from
Earth to a star.
Z = ρc
p = Parallax angle.
L = Luminosity.
σ = StefanBoltzmann constant.
Sub-topic D.1 – Stellar quantities
d (parsec)
1
p (arc-second)
T = Temperature.
L = σ AT 4
Luminosity of a star.
b = Apparent
brightness.
L
b=
4πd 2
A = Area.
d = Distance to star.
z=
∆λ v
≈
λ0 c
v = Relative velocity
of light source.
z=
R
−1
R0
c = Speed of light.
v
H0 d
T
1
H0
R = Cosmic scale
factor.
R(0) =
λmaxT = 2.9 × 10−3 mK
L
M 3 .5
Apparent brightness of a star.
Sub-topic D.3 – Cosmology
z = Red shift.
λ(0) =Emitted
wavelength.
Distance to a
star in parsec.
Sub-topic D.2 – Stellar characteristics
and stellar evolution
Red shift of a star/galaxy moving
away from us.
Red shift depending on cosmic
scale factor.
Relation between
wavelength of maximum
intensity radiation of a
star and its temperature.
T = Temperature.
L = Luminosity.
Mass-luminosity relation for main
sequence stars.
M = Mass.
Sub-topic D.5 – Further cosmology
(HL only)
v=
4πG ρ
r
3
ρc =
3H 2
8πG
H(0) = Hubble
constant.
d = Distance from
Earth.
Physics data booklet
λ = Wavelength.
13