First question I'm going to answer is how old is the solar system?
And the answer is it's rather old. it's easy to look at me and see that I'm
old. But how do you look at a astronomical
system and notice that it's old? Well, it turns out you date the rocks.
We find on Earth some rocks that are as old as 4.4 billion years.
We abbreviate that giga years such rocks are rare on Earth.
Most of the rocks we find on Earth are tens or hundreds of millions of years
old. But on the moon, rocks, old rocks are far
more common and the oldest moon rocks are as old as four and a half billion years
old. The meteorites meteors that fall onto
Earth, we'll talk about that later on space rocks can be as old as a little
older than that, 4.54 billion years, we sense a pattern.
And indeed, our best estimate for the age of the solar system is about 4.56 billion
years. So, 4.56 billion years ago is when the
solar system formed. That's a pretty ambitious statement.
How do you know how long ago the solar system formed?
The answer, of course, is more physics. And the, technology that we use to figure
out the age of a rock is called radioactive dating and to understand how
we date rocks we're going to have to carry our understanding of the structure
of the atom deeper in and we're going to have to look inside the atomic nucleus
that rather for discovered, carries the entire mass of an atom.
And remember, that a species of atom is identified by its atomic number, the
positive charge in the nucleus and what rather for discovers is at that charge is
carried basically by a number Z of positively charged massive particles we
now called protons, we just call them hydrogen nuclei.
a proton is nothing other than the nucleus of a hydrogen atom.
And so, inside the nucleus are Z Hydrogen nuclei.
This is a discovery by Rutherford in 1917.
This accounts for approximately half of the mass of an average nucleus.
What is the rest? Well, the rest is obviously neutral
matter. Chadwick, in 1932, discovers the neutron.
And it's realized that the rest of the mass of an atomic nucleus besides the
protons is made up of A minus Z of these neutral particles called neutrons, that
each have about the same mass as a proton.
So helium nucleus, for example, contains two protons and two neutrons, for a total
atomic mass of four. Now, if you look up the atomic mass of
helium in the periodic table, you'll discover that it's slightly less than
four. The reason for this is that the same
combination of protons can appear with differing number of neutrons.
Note that since the protons determine the charge of the nucleus,
these, these will lead to two atoms, which have the same electron cloid and
so, are chemically indistinguishable but have different mass.
In fact, helium, for example, can appear in two forms.
There are helium nuclei with two neutrons and two protons for an atomic mass of
four. And there's a less stable isotope as it
is called, of helium, helium three with two protons, so the same electron
structure as helium, but only one neutron.
And so, Z determines the chemistry, the number A minus Z of neutrons determines
the mass, and in general, you can combine neutrons and protons in various
combinations. This all brings up a great question, of
course. Once you realize that the atomic nucleus
is all, not all in one piece, it's made up of neutral and positive particles, you
can ask, why doesn't that thing blow up? There is a whole lot of positive charge.
There are these repellent Coulomb interactions between the protons.
What is it that holds the nucleus together?
We'll get to that later, but at the moment it suggests, and you are right
that most combinations of neutrons and protons do not like to stay together and
most nuclei, most assemblies you could put together
decay and, in fact, many of those that we find in nature do decay.
And they decay, it is discovered in the late 19th, early 20th century in one of
three ways. One is a process called alpha decay.
This is the emission of what is called an alpha particle that is soon discovered to
be nothing other than a Helium nucleus. A nucleus of the stabilizer dopefolium)
of helium with two protons and two neutrons.
And so many nuclei decay by emitting, notice they emit a Helium nucleus, this
means the remaining nucleus has a different nuclear charge so you've
achieved chemical transmutation, one element is transmuted into another, the
object of alchemy is achieved. sadly, lead is more often the product
than the initial part of this and turning lead to gold is not yet a commercial
enterprise. the other species of decay, continuing
the order is beta decay. the beta rays that nuclei emit are
discovered to be nothing other than electrons and a nucleus can emit an
electron. I said that electric charge is conserved
and indeed, the emission of an electron is found to be associated with the
conversion of a neutron to a proton. So, in a sense a neutron decays into a
proton and electron, the proton remains in the nucleus,
the electron escapes. The net result is that the total number
of nucleons in the nucleus is unchanged, A is unchanged, but Z increases by one so
again, you've changed the element. There is also positive beta decay in
which the, the particle emitted has the same
mass as the electron but positive charge as opposed to the electron's negative
charge and this is accompanied by the conversion of a proton to a neutron, so
again, A is unchanged in beta decay but in this kind of beta decay, Z in fact
decreases by one. many heavy elements also spontaneously
undergo fission, which is a more dramatic thing where a
heavy nucleus basically splits up into two smaller nuclei, often throwing off a
couple of alpha particles as well. And this is a process in which, again,
you start with a heavy nucleus and end with two smaller ones.
And all of these are, in general, accompanied by the emission of high
energy photons gamma rays. So, this process go on, what is all that
got to do with dating the solar system? Well, we'll see that in a minute and
radioactivity however, has lots of applications and it contributes much to
our life, let's start with something we know.
And remember, helium, we said. was a rare element on Earth, it was first
discovered on the sun. if you did your homework last week you
might understand what's going on. At the temperatures in the Earth, so, so,
helium is lighter than air. Helium, if we pop a helium balloon, then
the helium without the balloon will float in the Earth's atmosphere up to the top,
to the outer atmosphere, to something called the exosphere.
And at the temperatures of about 1,000 or 1,500 degree Kelvin that obtain there,
the kinetic energy of helium atom with its small mass, means that its velocity
is about a sixth, if you computed last week, of the escape velocity at that
altitude. That means the hotter, faster.
And remember, there's a statistical distribution.
This is only an average kinetic energy. The faster helium atoms evaporate and
escape Earth, [COUGH] and so, in fact, Earth does not
have the mass needed to retain an atmosphere of helium.
This explains why despite the fact that hydrogen and helium are the most common
species of atoms in the solar system, our atmosphere is not comprised of hydrogen
and helium. Hydrogen and helium, hydrogen molecules
with an atomic mass of two and helium atoms with an atomic mass of four move
fast enough to escape the Earth's gravity.
we still have lots of hydrogen on earth because hydrogen binds and is found in
things like water. Helium, being a noble gas, does not bind
anything, so any atom of helium will eventually evaporate.
In fact, earth loses large quantities of helium to space all the time.
So, where, you ask, do we find helium to fill our helium balloons?
Earth having been around, they claim for four billion years, would have been
completely free of helium were it not for the fact that helium is being produced
inside the Earth, and escaping out to the atmosphere at a constant rate, and helium
is being produced as alpha decay, so every bit of helium, every atom of helium
you've ever put in a birthday balloon is the result of radioactive decay inside
the Earth, primordial helium is long gone.
In addition, this process both the helium nuclei, the alpha particles, the beta
particles, the gamma rays, escape from the nucleus with lots of energy.
They plow into the surrounding medium distribute this energy.
What this ends up doing is dumping energy in the surroundings.
This is bad if the surroundings are your lungs but in the inside the Earth, this
turns out to be a source of internal heat.
So, there is, at the inside the Earth, an ongoing process of radioactive decay.
We see it's mostly happening in the core and mantel and this heats the inside of
the earth. That's something that radioactivity can
do. but for our purposes, what do you want to
understand is how we use radioactivity to date a rock.
So, the idea is that radioactive decay is a random process.
Any given atom is independently, or any given nucleus will decay independently
with a probability per unit time that is constant.
What this amounts to is that if you have a sample within some prescribed time
dependent on the species of nucleus that you are studying half of all the atoms
will have decayed. And then, within that same period, half
of the remaining atoms will have decayed, the process has no memory.
Once a nucleus has not decayed for some time, the clock starts over.
It's as likely to decay in the next second as it was in the previous second
given that it didn't decay. This leads to a mathematical expression
for the time dependence of the number of nuclei of a given species,
which says, that in a given time, called the half-life, t1/2, a half of the sample
will have decayed. So, if you start with some number at time
zero, when t is equal to t and to the, to t1/2, the half-life, you will have half
of the sample left, another half-life later, you will have a quarter, and so on
exponentially. And what that means is, on the other
hand, this decay say, if the predominant mode of decay is alpha decay, then you
have one nucleus that when it decays will produce another species of nucleus.
So, with time, the concentration of what is called the daughter nucleus will
increase while the parent concentration decreases.
Now, if you knew the initial concentrations of
daughter and parent, if you could, and for some reason know what you started
with, then you could compare the initial concentration to the current
concentration and extract from that, the amount of time
that has passed. The best way to do this in dating rocks
though there are other forms, carbon dating, where you make a different
comparison. But imagine that you have a process where
the daughter nucleus is a chemical element.
Remember, these are different chemical elements whose chemistry is such that it
escapes, it boils out of liquid rock, and therefore, is not contained within a
freshly solidified rock. So, when a piece of rock solidifies,
there are no daughter nuclei, but the parent nucleus is trapped,
is bound, can be bound within the crystal.
Then, once the rock is solid the parent nuclei start to decay and they produce
concentrations of the daughter, the ratio of concentrations is then
dependent on time like this. If you can measure both of these, you can
and you know the half-life, then you can extract the length of time that has
passed. can we find such candidates?
Surely the beautiful thing is that the degree of instability of various nuclear
species varies wildly from fractions of a second to billions of years for the
half-life. In particular, many of the isotopes of
uranium decay. They decay by various processes but the
end product of many of the processes is lead.
And it turns out that a mineral called zircon binds uranium when it forms, but
not lead, so when a zircon rock forms it will contain essentially no lead but it
might contain trace amounts of uranium, that uranium will decay with half-lives
of the order of a few billion years. And so, if you find lead in a chunk of
zircon, it was produced there by radioactivity.
If you compare the concentration of lead to the concentration of uranium, you can
figure out how long that rock has been sitting there.
This is tricky because lead can in fact escape.
Lead is not completely trapped and so, you might find less lead than should be
there. In the case of lead and uranium, we're
fortunate there are two different isotopes of uranium produced two
different isoptoes of lead as their final
product. And with slightly different half-lives, and so, you can compare the
relative concentration of the two isotopes of lead and the two isotopes of
uranium. And in this beautiful diagram, you see
sort of the plots by age of the predicted ratios of concentrations.
You see that the samples have lost some lead.
Their lead concentration is lower. then the uranium concentration you would
predict but they lie along this line and the intersection of the two lines gives
you the age these rocks. And
this is the way that we date the solar system.
This is how we know that the oldest rocks we find in the solar system are four and
a half billion years old.