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.