(Advice about healthy living
is given in the pdf file
Basic facts about the known universe:
There are hundreds of billions of stars
in a typical galaxy, like our galaxy, the Milky Way.
The largest galaxies contain more than a trillion stars.
Small galaxies, called "dwarf galaxies," contain
as few as a million stars.
There are hundreds of billions
of galaxies in the known universe.
So if there are 1011 galaxies and an ordinary galaxy
has 1011 stars, then there must be
something like 1022 stars
in the known universe. Our sun is an average star.
An average star, like our sun, burns hydrogen
forming helium. This burning is a fusion process
and it takes place in the central third of the star
at a temperature of about 15 million degrees Kelvin
(0 K or absolute zero is -273 Celsius,
so the two temperature scales are effectively
the same at high temperatures). Since one degree Kelvin
is one degree Celsius is 9/5 = 1.8 degrees Fahrenheit,
the center of the sun is about 27 million degrees F.
Why the Sun Shines
The net reaction that liberates energy in an average star
is that four protons and four electrons
(that is, four hydrogen atoms) turns into
two protons and two neutrons and two electrons
and two neutrinos,
in such a way that the two protons and the two neutrons
are tightly bound together into a helium nucleus
(also called an alpha particle).
If the two protons and the two neutrons did not
form a nucleus of helium, this reaction would soak up
rather than liberate energy.
Instead, the mass of a helium atom is
6.644 × 10-27kilograms,
while the mass of four hydrogen atoms
is 6.908 × 10-27kilograms.
The difference is 0.0468 × 10-27kilograms
or 4.68 × 10-29kilograms.
Since the speed of light c = 3 × 108 meters
Einstein's formula, E = mc2, gives for
the energy released the value
4.68 × 10-29kg
× (3 × 108 m/s)2
= 42.12 × 10-13Joules or
4.212 × 10-12J in mks units.
Now one Joule = 6.2415 × 1018
electron Volts, so the burning of four H atoms
releases 4.212 × 10-12
× 6.2415 × 1018 eV
= 26.3 × 106 eV or
That's a lot of energy from only four atoms.
In fact, the burning
of the hydrogen atoms in 100 drops of water
would produce enough energy to light
a 40 Watt bulb for a century.
In 1938, Hans Bethe explained the detailed
nuclear reactions that occur in a star like our Sun
when hydrogen is burned to helium,
work for which he won the Nobel prize in 1967.
He died on March 6th of 2005 at the age of 98.
During WWII, Bethe first worked on radar at MIT
and then on the atomic bomb;
he lead the theoretical group
at Los Alamos. After the war,
he argued that hydrogen bombs should
not be built. He lost that argument.
With Linus Pauling, Bethe
argued that nuclear weapons
should not be tested in the atmosphere.
They won that argument when the
Limited Test Ban Treaty was passed in 1963
during the Kennedy administration.
Bethe has long argued that the number of nuclear weapons
possessed by Russia, China, and other states
should be fewer than a few hundred per state.
Current nuclear arsenals are in the thousands.
Bethe has been a firm supporter of the
use of nuclear power for the generation
The Early Universe and the Big Bang
Some 14 billion (14,000,000,000
= 1.4 × 1010) years ago,
the universe was much hotter than the center of the sun,
which is about 15 million degrees K.
The universe has been expanding and cooling
since this Big Bang.
In the first instants after the Big Bang,
space is believed to have expanded rapidly
in one or more very brief intervals.
This superluminal expansion is called inflation.
Unlike evolution, inflation is a theory.
But its consequences seems to be true.
Inflation would have made space flat.
(Imagine rapidly blowing an
enormous amount of air into an unbreakable,
infinitely expandable balloon.
The surface of the balloon would expand and
This consequence of inflation seems to be
verified by recent experiments.
If the whole known universe inflated from
a very tiny sphere that was in thermal equilibrium,
then the whole known universe now should
be homogeneous on very large scales
and should look the same in all directions,
should be isotropic.
These consequences of inflation also seem to be
verified by recent experiments.
The First Three Minutes
After inflation, the universe cooled and
continued to expand.
It was a very hot plasma
of all kinds of particles and antiparticles
in thermal equilibrium.
After about three minutes,
most of the particles and antiparticles
that could annihilate into photons
had done so,
leaving a small residue of protons, neutrons,
and electrons and lots of photons
and neutrinos and particles that
cannot annihilate into photons.
The protons, neutrons, and electrons
later became gas, stars, dust, and galaxies.
The particles that could not annihilate into photons
do not interact with light; they constitute an unknown
form of matter called "dark matter," which cannot be photographed
because it does not interact with light.
There were about 2 billion photons and a similar number
of neutrinos for each proton and each neutron.
But the charge of the universe is
believed to be relatively small,
so there were almost exactly as many
protons as electrons.
This hot ionized plasma of protons and electrons
interacting with high-energy photons was
a very radioactive environment.
No structures made of protons, neutrons, and electrons
was able to survive until about 230 seconds
after the Big Bang, when
the temperature dropped below 109 K.
Deuterium is an isotope of hydrogen
consisting of one proton loosely bound
to one neutron.
When the temperature had dropped below 109 K,
deuterium could survive long enough to absorb
a neutron and another proton becoming
a tightly bound nucleus with two protons
and two neutrons -- a nucleus of helium.
Almost all the neutrons and deuterium
were quickly cooked into helium nuclei.
So after about 240 seconds, the universe
was a hot plasma consisting
mostly of ionized hydrogen (3/4) and
helium (1/4), electrons, photons, neutrinos
(and anti-neutrinos), and mysterious particles
of dark matter.
Dark Matter and Dark Energy
Paradoxically, most of the matter of the universe,
both then and now, is in unknown forms called
"dark matter," because they do not interact
And most of the energy of the universe
is in an unknown form called "dark energy."
Recent experiments indicate that the
matter we know about is only 4% of the
energy density of the universe.
Dark matter is about 29%,
and dark energy is about 67%.
After about four-hundred thousand years,
the temperature of the universe had dropped
to around 6,000 K. At this temperature,
only about one photon in 2 billion
had enough energy (13.6 eV) to ionize a hydrogen atom.
Since there are about 2 billion photons
hydrogen atoms and helium atoms are stable
at temperatures lower than about 6000 K.
So 400,000 years after the big bang,
the electrons fell into
stable orbits about the protons, forming hydrogen atoms,
and about the alpha-particles, forming helium atoms.
Since low-energy photons interact much less with
neutral atoms than with free electrons and ions,
the universe suddenly became transparent to light
at about 400,000 years after the big bang.
Most of the photons of the universe have not
been scattered since the onset of transparency.
But with the expansion of the universe,
the wave-lengths of these photons have been
stretched from hundreds of nanometers to
a few millimeters.
These photons have been red-shifted
from visible-light photons
to microwave photons, which are 4,000 times
This radiation is the same as that
inside a closed box whose walls are at
a temperature of 2.725 K.
It appears as radio noise on
sensitive antennas, and was first identified
Astronomers call transparency "recombination"
as though there had been atoms earlier, before
the Big Bang.
(Recombination is a moronic term which the astronomers
should have dropped.)
The Red Shift
The universe continues to expand.
Its present rate of expansion is
about 72 kilometers per second (km/s) per megaparsec (Mpc).
A megaparsec is about 3.1 million light years.
(It is a moronic unit which the astronomers
should have dropped a century ago.)
So two stars separated by 3.1 million light years
are moving away from each other by
about 72 kilometers per second, but
a megaparsec is too short a distance for
the expansion of the universe to dominate
random local velocities.
So it would be better to say that
two galaxies separated by 3.1 billion light years
are moving apart at the rate of 72,000 kilometers per second.
The Hubble parameter H0
is now about 72 km/s/Mpc.
H0 was decreasing over
the first 10 billion years,
but it has been increasing over the past 4 billion years
due to the dark energy.
It is not a constant, and so "Hubble constant"
is another moronic term
which the astronomers should have dropped.
Astronomers have used the Hubble Space
Telescope to make images of many distant
You may view images made by the Hubble Space
Telescope by going to this
Observations suggest that the energy density of the universe
is very nearly critical, that is, just enough to keep
the universe from collapsing.
Atoms and the other kinds of matter and energy we know
about account for only 4%
of this critical energy density.
Some 29% is due to "dark matter."
Nobody knows what dark matter is.
Very recently, however, some English astronomers
seem to have discovered the first
which they reported in the article
The main component of the critical energy density
is "dark energy." Nobody knows what this is either.
The Mid-Term Exam
The scores on the mid-term exam ran from
40% to 90%. To find your score, multiply
the number of questions you got right by 5.
The grades on the mid-term are 90% = A+,
85% = A, 80% = A-, 75% = B+, 70% = B,
65% = B-, 60% = C+, 55% = C, 45% = C-,
and 40% = C-.
The Extra-Credit, Take-Home Exam
You may download a pdf file
of the extra-credit, take-home exam.
The Final Exam
The final exam is on Monday,
the ninth of May, at 5:30 pm in Regener 103.
This was it.