Transcript The Age of the Solar System

Unit 7 – The Age of the Solar System
ASTR 101
Prof. Dave Hanes
Think About Clocks
They are designed to measure and mark the passage of time, by
monitoring some regular, repeated mechanical action.
There are Other Ways!
Here, we watch while something gets used up. (When the
sand has run out of the top of the egg-timer, your boiled
egg is done.) Radioactive chronometers work this way.
Now Think About Getting Old
More Than Just Appearances
For people, “aging” brings with it a greater chance of
things breaking down and failing. Your chances of dying
in the next decade (say) increase as you age.
Actuarial Tables Quantify This
The older you get, the more likely you are
to die in the coming year (statistically).
Different Consequences
The number of deaths depends
on the current distribution of
ages.
If you have 100 people in (say)
a retirement home, not all of
them will be around for a
reunion in five years time.
If you have 100 people in a firstyear university class, the odds
are very good that they will all
be available.
Radioactive Age-Dating
By contrast to people, atoms do not age.
An atom that has been around for ten billion
years is indistinguishable from one that has
just been formed.
Flipping Coins: It’s Random Chance
If you were to ‘flip’ all these coins, about half would come
up heads, half tails. It doesn’t depend on when the coin
was minted (its individual age). Nor can you tell which of
the coins will come up heads – it is pure chance.
Pick Me a Winner
Similarly Radioactive Elements
If you have a sample of Uranium atoms, a given fraction of them
will radioactively transmute to some other form in (say) the
coming decade – but you don’t know which specific atoms will
do so, only the statistical odds.
A million years from now, there will be fewer U atoms left (which
means of course that the level of overall radioactivity declines as
more of the original atoms decay away) but the same fraction of
them will transmute in the successive decade. Their individual
chance of ‘dying’ does not increase as time passes.
Only Statistical!
If you flip 1000 coins, you are unlikely to get precisely 500 heads.
But you will be close!
With umpteen trillions of atoms in a typical sample of
radioactive material, the statistical precision of the
changing proportions is very reliable indeed.
The ‘Half-Life’
Each radioactive decay process has a characteristic half-life – the
time over which half the atoms transmute to another form.
Imagine a piece of pure uranium. After one half-life, 50% of it
has turned to lead; 50% is still uranium.
After a second half-life, 50% of the remaining uranium has
turned to lead. It is now 25% uranium, 75% lead. And so on…
The proportions of Uranium and Lead steadily change, in a
statistically predictable way.
The Atoms Don’t Vanish!
Here, radioactive Potassium becomes Argon
As the original material dwindles away, the stable
‘daughter product’ accumulates.
The Proportions Give the Age
We do not need to
(a) monitor the rock for continuing changes,
(b) measure the radioactivity at all.
Note that we only need to measure the chemical
composition.
For example, if a sample is 25% Uranium and 75%
Lead, we may conclude that it’s been around for
two half-lives.
Age Since When?
The “age” of a rock is the time
since the latest melting and
re-crystallization that formed
that mineral.
The atoms themselves may have been around for a very
long time, but a slurry of magma in a volcano may
create some new mineral with a fresh starting ratio of
Uranium to Lead, say. Once ‘frozen in’ to some mineral,
that ratio will progressively and predictably change.
Three Essential Pieces of Information
To work out the age, we need to know:
1.
2.
1.
The half-life of the relevant decay process.
Whether the original sample had any daughter
product in it from the very start.
Whether any of the daughter product is lost
over the passage of time.
The First Requirement
We need to know the relevant half-life. We don’t
determine it ourselves from our sample; instead,
we simply look up a value that someone else
worked out earlier, in a laboratory.
Here is how: they took a lump of ultra-pure Uranium. Its weight told
them how many atoms it contained. Its radioactivity told them what
fraction of them were breaking down in a given time. This allowed
them to calculate the time it would take for half of it to disappear.
No need to wait for that to happen (which can take millions or billions
of years for some radioactive elements)!
A Second Requirement
We have to understand how much daughter
product was in the original sample.
Suppose you find a rock that is 50% U and 50% Pb [lead]. (Note: this
is very unlikely! Rocks are usually complex mixtures of many
elements.) How old is it? There are two extreme possibilities:
1. Perhaps it was originally 100% U, of which 50% has now
decayed into Pb. It has been around for one ‘half-life.’
2. Perhaps it is brand-new – created, say, in a volcanic eruption
yesterday – and contained 50% Pb right from the start.
If any Pb was present to start, you will tend to overestimate the age.
A Third Requirement
We have to understand if any of the daughter
products get lost over time.
Earlier, we saw that radioactive potassium can turn into argon. But
argon is a gas, and can diffuse out of the mineral through small cracks
and holes.
If you have a sample of pure potassium, you may think that it is ‘brand
new’ since no daughter product has accumulated – but the rock may
have been sitting around for ages, losing all the new argon into the
atmosphere. You will tend to underestimate the age of the sample.
Solution
We need to determine, somehow, the original composition
of the rock, and take the losses into account.
There are ways! We can intercompare various isotopes
that obey the same chemistry to gauge the initial
composition. (The details don’t matter.)
We can avoid the problem of lost argon (say) by sampling
the deep interior of rocks out of which gases cannot
readily escape.
Useful Radioisotopes
Radioisotopes are not used just for
astronomy, or just as clocks.
Their application can depend on the
timescale of interest: short, medium,
long.
Short Half-lives: Used in Medicine
We want patients to ingest a fluid with a
radioactive ‘tracer’ that will allow us to track
metabolic behaviour by giving a strongly
detectable signal for a while. But we want it
to die away soon so that the patient is not
subjected to long-term radioactivity.
In other words, we want an isotope with a short
half-life.
Thyroid Health
A good example: a radioactive isotope of Iodine, with
a half-life of about an hour.
It is used for tracking thyroid
performance.
Goiters can be caused by
iodine deficiency; we can
track whether the iodine is
being suitably absorbed and
used by the thyroid.
Where Do We Get It?
We can’t just order it from the pharmacy!
Suppose we start with 10 trillion trillion atoms (1025) of
radioactive Iodine. That’s about 150 grams.
After ~80 half lives (just a few days) it’s all gone!
Solution:
we make it in accelerators, to supply hospital needs
http://www.triumf.ca
Intermediate Half-Lives
Cosmic rays maintain a certain level of radioactive carbon in the
atmosphere. Plants absorb that in the form of carbon dioxide,
and animals eat the plants (or other animals).
Living things thus maintain a certain average amount of radioactive
C14 within them, until they die. After that, it decays away,
with a half-life of ~5700 years, and the changing proportions
in the bones (or in dead vegetation, like wooden spears) tell us
when the metabolic processes ended (when the person died,
or a tree was cut down to make the spear).
This is the famous “carbon dating,” and is particularly useful in
archaeology.
Carbon
Dating
Historical
Calibration
We can compare
the results to
known historical
dates, tree-ring
counts, and so on.
Long Half-lives: Geological
[Important question: why do we need such long half-lives?
It is to ensure that there is still a measureable amount
of the parent element present in the sample, to work
out the ratio of parent to daughter abundances.]
Examples
- K40  Ar40 (1.3 Billion yrs)
- Rb87  Sr87 (47 Billion yrs)
- U235  Pb207 (700 Million yrs)
- U238  Pb206 (4.5 Billion yrs)
The Age of the Solar System
The oldest identifiable Earth rocks are near 4 B.y. old.
(Remember that is it geologically active: things get
‘reworked,’ so it could be somewhat older still.)
‘Genesis’ rocks from the Moon; rocks from Mars; and
meteors: all are ~ 4.6 B.y. old
Asteroid and comet samples will soon be collected
The Sun is ~ 4.5 B.y. (by a completely different method!)