Lecture 2
Big Bang Time Line
The Birth of the Quantum
• Max Planck
– The energy contained in radiation is related to
the frequency of the radiation by the
relationship
E  nhf
• n is a positive integer called the quantum number
• f is the frequency of the oscillation
– A discreet packet of energy, later to become
known as “a photon”
Implications of Planck’s Law
• The energy levels of
the molecules must be
discreet
• Only transitions by an
amount E=hf are
allowed
• The implication is that
light is discreet or
quantised
energy
n
4hf
3hf
2hf
1hf
0
4
3
2
1
0
These quantum levels are
known as number states
Spectroscope
Three Types of Spectra
Spectral Analysis of the Elements
Studying the light emitted by an object
in order to know something about that object!
Continuous Spectrum: a collection all possible
wavelengths/ frequencies of light
Emission Spectra
Pattern of bright spectral lines
produced by an element.
Absorption Spectra
Pattern of dark spectral lines
where light within a number of
narrow frequency ranges has been
removed.
Hydrogen
Helium
Argon
Neon
Krypton
Wavelength
Bright Line Emission Spectra
Kirchoff’s Laws
• 1st law: A luminous solid or
liquid, or a sufficiently dense
gas, emits light of all
wavelengths and produces a
continuous spectrum of
radiation.
• 2nd law: A low-density hot
gas emits light whose
spectrum consists of a series
of bright emission lines which
are characteristic of the
chemical composition of the
gas.
• 3rd law: A cool thin gas
absorbs certain wavelengths
from a continuous spectrum,
leaving dark absorption lines
in their place superimposed
on the continuous spectrum.
Spectra and Background
Type of spectrum seen depends on the temperature of the
thin gas relative to the background temperature.
TOP: thin gas cooler than background, absorption lines seen.
BOTTOM: thin gas hotter than background, emission lines seen.
Studying the Stars:
Analyzing the light from a star can tell us:
1. The composition of the star.
2. The relative motion & rotation of the star.
3. The star’s temperature.
Shows limited Range of Light Energies Reaching Earth’s Surface
Hubble’s Discovery of the
Expanding Universe (1929)
• Spiral nebulae known to
have redshifted spectra
• Hubble and Humason
carry out quantitative
study
• Hubble shows velocity of
recession is proportional
to distance
Instrument of Discovery:
Hooker 100” Telescope
Mount Wilson Observatory
The Hubble Law
• Hubble’s original
data showing the
galaxy velocities
to be proportional to their
distance
v=HoR
The Hubble Law
• Improved data
showing that the
Hubble law holds to
much larger distances
v=HoR
H 0 = 75km/s/Mpc
1Mpc  106 pc  3x106 light year
Cosmic Distance Ladder
Objects
Remote Galax.
METHOD
Supernovae
Remote Clusters
Spiral Galaxies
Cepheid Var. Stars
Star Clusters
Britest Galx. In Cluster
Rotation Velocity
Period-Lum. Relat.
Color-Mag Rel.
Useful Distance
1010 Light years
1010 Light years
108 Light years
5x107 Light years
106 Light years
Stat. Parallax
1000 Light years
Hyades Star Cluster Moving Cluster
120 Light years
Planets & Stars Parallax
100 Light years
light minutes
Nearby Planets Radar
Stellar Parallax
Parallax is the annual shift in a star’s apparent
position in the sky due to the Earth’s orbital
motion.
The parallax angle is half the annual shift.
The parallax angle of the nearest star, Proxima
Centauri, is 0.77 arcseconds.
𝐴. 𝑈.
𝑑=
𝑝
Parsec
An object with a parallax of 1 arcsecond is located
at the distance of 1 parsec.
1 pc = 3.26 light-years = 3.09 1013 km
1
d (in parsecs) = -------------------------p (in arcseconds)
Parallax
Background
Stars
Earth
Sun
A.U.

2x Parallax (p) in arcsecs
360 deg
 57 deg  57 x60arc min 
2
2 radians in circle = 360 deg ==>
57 x60 x60arc sec  206000arc sec
1rad 
A.U. = Astronomical Unit = Earth-Sun Distance = 1.5x1011m
Parsec = pc = distance when parallax is 1 arcsec:
1AU
. .
d

1arc sec
1AU
. .
 206000 AU
. .  3.1x1016 m
1
rad
206000
The Hubble Law

V  H 0d 
H 0 = 75km/s/Mpc
R
d
R
The Expansion of the Universe
The Expansion of the Universe:
One should consider the galaxies
located on the surface of the
sphere which expands with time.
As the sphere expands all lengths,
including that of light increase.
That means all the photons
redshift. The redshift increase
with the distance.
Raisin Cake Model
Like raisins in rising raisin cake, galaxies move away
away from each other in our expanding universe.
Cosmology
• Hubble Time
• The age of the universe if the expansion has been
constant.
• t = 1/Ho = ?
• The expanding universe probably originated
in an explosion called the Big Bang
between 12 and 18 billion years ago.
1billion  109
Big Bang Timeline
We are here
Big Bang Timeline
• GUT period -age of quarks and gluons:
Dense concentration of matter and antimatter;
gravity a separate force, more quarks than
antiquarks
• Inflationary period: rapid expansion,
strong force separate from electroweak
force
Big Bang Timeline
• Electroweak era; age of leptons: Leptons distinct from
quarks; W  and Z 0 bosons mediate weak force (1012 s) ;
• Particle era:
• Age of nucleons and antinucleons: quarks bind together to
form nucleons and antinucleons; energy too low for
nucleon- antinucleon pair production at 10 2 s .
• Age of nucleosynthesis: stable deuterons; matter 74% H,
25% He, 1% heavier nuclei
• Age of ions: expanding, cooling gas of ionized H and
He.
Big Bang Timeline
• Recombination era: age of atoms; neutral
atoms form, pulled together by gravity;
universe becomes transparent to most light.
• Age of stars and galaxies
Thermonuclear fusion begins in stars, forming
heavier nuclei
• Present era 15x109 years