Unit 7 – The Age of the Solar System

ASTR 101Prof. 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 ThisThe older you get, the more likely you are

to die in the coming year (statistically).

Different ConsequencesThe 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 first-year 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 timesince the latest melting and re-crystallization that formedthat 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. The half-life of the relevant decay process.

2. Whether the original sample had any daughter product in it from the very start.

3. Whether any of the daughter product is lost over the passage of time.

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)!

The First Requirement

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.

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Thyroid Health

A good example: a radio-active 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.

CarbonDating

Historical Calibration

We can compare the results to known historicaldates, 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!)