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Physics data booklet
First assessment 2016
Annotated by Boaz V.
Diploma Programme
Physics data booklet
Published June 2014
Revised edition published January 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
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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
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