ASTR 209 Lecture Notes - Solar Wind, Frederick Reines, Gamma

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25 Jan 2013
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Astr 209
Lecture 3c
October 2 2010
Details about the fusion of hydrogen in the Sun
The
HeH4
has three stages.
The nucleus of a hydrogen atom is also called a proton (p).
( )
ν
+++ +
+
++ epnpp
(2 of these) (1)
( ) ( )
γ
++ ++
+
+ppnppn
(2 of these) (2)
( ) ( ) ( )
++
++++++ +++ ppppnnppnppn
(3)
Equation (1) requires considerable description (a, b, c, and d below).
a) the protons
The two hydrogen nuclei have a property called electrical charge. You can
at least become aware of the effects of this property by playing with long
strips of adhesive tape.
i) Stick one long strip to the top of a table. Stick another strip
on top of the first. Rip the bottom piece off the table, so
that the two strips of tape are still stuck together.
Pull the two strips apart, and hold them far apart. Now
bring them closer together; they are attracted to each other.
This is the same behavior exhibited by clothes that you take
out of a dryer when you have forgotten to use a sheet of
Fleecy. Notice also that, if you are taking the laundry out of
the dryer in the dark, when you pull the socks off your shirt
you see sparks and hear crackling. Light and sound involve
the transfer of energy.
ii) Stick a fresh piece of tape to a table-top. Stick another
piece to a different part of the table-top. Pull both strips off
the table, and hold them apart. When you bring the strips
close to each other, they repel each other. These two strips
are analogous to the two protons in step (1) above.
MANY observations like (i) and (ii) have convinced us that there are two
(and only two) types of electrical charge. In case (i), you have done
something different to the two strips, so they have different properties
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(different types of charge). It turns out that when two objects carry
different types of charge, they attract each other.
In case (ii), you have done the same thing to the strips, so they have the
same property (same type of electric charge). It turns out that two objects
with the same type of electrical charge repel each other.
(What sort of observation might you expect if there are more than
two type of charge? This isn’t an idle question. It turns out that the
constituents of protons and neutrons [called QUARKS] have a
property analogous to electric charge. We call this property
“color” - American spelling for an American idea. “Color” is just
the name of a property; it has nothing to do with the everyday
meaning of colour. A quark can have one of two types of electric
charge (positive, negative); a quark can have one of three colors
(call them red blue, and green if you like). The quark-quark
interactions are considerably more complicated than proton-
proton interactions.)
One source of electrons is a hot wire, like a toaster filament.
(J. J. Thomson in 1897 actually discovered electrons by studying what is
somehow emitted by hot wires.) In the late 1800s and very early 1900s we
learned that electrons are natural “parts” of matter. It turns out that
electrons all carry the same amount of one type of charge (called
negative). When electrons are emitted by (expelled from) matter, what
remains carries the other type of charge (called positive). We have found
that this division of charge applies to individual atoms. (The smallest
amount of an element is an atom.) A hydrogen atom is the simplest atom;
it is composed of one negative electron and one positive proton. (J.J.
Thomson in 1906 discovered that a hydrogen atom has only one electron.)
If you can figure out how to strip electrons from matter, you have removed
electrons from individual atoms. In the case of hydrogen, each atom has
become a proton. Two protons carry the same type of charge, so they repel
each other. To get them close to each other, you must somehow make the
protons travel very rapidly towards each other; as the inter-proton distance
decreases, the speed decreases. This is another example of POTENTIAL
energy increasing, and KINETIC energy decreasing. (In this case
ELECTRICAL potential energy increases as two similarly-charged
protons get closer to each other. Recall that you must push two similarly-
charged strips of tape together.)
It turns out that the temperature of something tells you about the average
speed of that thing’s atoms and molecules.
For instance, the speed of sound is higher on a hot day than on a
cold day. The sound energy is conveyed from one molecule
(oxygen, nitrogen) to the next in a collision. That means that the
speed of sound is determined by the speeds of the molecules.
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Another example. On a hot day, your molecules are vibrating back
and forth, in place, a little faster than on a cold day.
If protons must be travelling very fast to fuse, the temperature at the core
of the Sun must be very high. It turns out that the temperature must be at
least 10 million kelvins (107 K). Fusion therefore can only happen in the
core of the Sun.
Why does the core have a high temperature? The outer layers of the Sun
push on the inner layers, so that the pressure in the core is very high. We
calculate a pressure of about 1011 time the pressure of Earth’s atmosphere.
Using more-or-less the IDEAL GAS LAW that describes familiar gases on
Earth, we calculate that the temperature in the core is about 15 million K.
This is more than the minimum required for proton-proton fusion. (This
doesn’t prove that fusion happens, just that the right conditions are present
in the core.)
When two protons get “close enough”, they are actually attracted to each
other, and stick together. In the process, one of the protons turns into a
neutron (n), a positron (
+
e
) and a neutrino (v; the symbol is the Greek
letter “nu”, the equivalent of our letter “n”).
The protons sticking together is an example of what has come to be called
the strong nuclear force: “strong” because the attractive force is stronger
than the repulsive electric force, and “nuclear” because this force is only
important when distances are as small as a nucleus (about 10-15 m, almost
1 millionth the size of an atom, so we don’t need to understand nuclear
forces to understand atoms).
The transformation of a proton into a neutron, a positron, and a neutrino is
an example of the weak nuclear force. “Weak” in this case means the
reactions are slow compared with reactions involving the strong nuclear
force.
b) the neutron (a vague description):
It is “like” the proton, but with a mass 0.1% larger than the proton’s mass.
It has no charge
The bound state of a proton and a neutron is called a deuteron, a type of
(an ISOTOPE of) hydrogen. The Greek word “deuteros” means “second,
as in Deuteronomy, the second book of the bible; deuterium is the second-
heaviest nucleus.
c) the positron: