The Age of the Solar System

1
The Age of the Solar System
2
Three Things to Think About

• What does it mean to grow old?
• Consider the cows of the forgetful farmer
• Is New York City dangerous to your health?

3
People Aging Made Manifest
4
More Than Just Appearances

• Aging implies a greater chance of things breaking
  down and failing. Your chances of dying in the
  next decade (say) increase as you age.

5
The Farmers Dilemma
6
and the Solution
7
The Atom
8
Atomic Number (Z)

• Z number of protons in the nucleus.
• Hydrogen 1 proton
• Helium 2 protons
• Carbon 6 protons
• Uranium 92 protons
• Determines the type of atom

9
Atomic Mass Number

• Number of protons number of neutrons atomic
  mass number
• (The mass of the neutron the mass of the
  proton.)

10
Isotopes

• Adding neutrons changes the mass but not the
  fundamental type of atom. Thus
• 1 proton Hydrogen
• 1 proton 1 neutron heavy hydrogen (a.k.a.
  deuterium). Found in heavy water.
• 1 proton 2 neutrons even heavier hydrogen
• (tritium)

11

12
Similarly

• U235 92 protons (so its U!) 143 neutrons
• U238 92 protons (its still U!) 146 neutrons

13
Radioactivity!

• Some nuclei are unstable, and spit out smaller
  pieces (releasing energy in various forms).
• 1. Kinetic Energy of the moving pieces, which
  can heat the surrounding material. (Pickering!)

14
Generating Electricity
15
.and Also

• 2. Radiant energy (electromagnetic radiation, or
  light), typically very energetic gamma rays.
• These two can cause tissue damage for better
  (therapy) or worse.

16
Radiation Therapy
17
Three Kinds of Radioactivity

• Discovered by accident (serendipity!) in the late
  1800s not understood for many years
• So, called a, ß, ? - alpha, beta, gamma

18
Alpha Particle Decay

• Example U 238 ? Th 234
• What is lost? 4 units of mass, 2 of which are
  protons.
• The emerging lump is an alpha particle

19
Beta Decay

• Example Th234 ? Pa234
• No mass is lost, but one extra proton appears.
  How?

20
Charge is Conserved

• If a new proton appeared, with a charge,
  there must be a new - to go with it!
• In effect one neutron spits out an electron, and
  turns into a proton, in a process known as beta
  decay.
• n ? p () e (-)

21
Gamma Rays

• Many decays also yield gamma rays very
  energetic electromagnetic radiation (light!).
  Dangerous!

22
There areCascades to Stable Elements(Uranium
ends up as Lead)
23
Life and Death in New York City
24
A Sociological Thought

• Why are there so many deaths in New York? (The
  obituary pages are much more extensive than in
  Kingston!)
• Its simple where there are more people, there
  are bound to be more deaths! It isnt
  necessarily any more dangerous.
• Similarly Where there are more atoms, there are
  more radioactive decays!

25
Now Think About ClocksConsider Two Isolated
Communities

• Imagine a Club Med cruise ship full of
  thousands of healthy 20-year-olds. Suppose it
  runs aground, stranding them on an idyllic island
  with no hope of rescue, ever.

26
Doomed to a Tropical Paradise
27
One Special Condition

• On the island, assume plenty of food, and no
  predators but no births! (Perhaps its a
  unisex population, as in the picture.)
• So the starting population is fixed in size.

28
Alternatively

• Consider a small meteorite containing a trace
  (umpteen trillion atoms) of Uranium.

29
The Important Question How will these
populations change as time passes?
30
In Both Cases

• In the far distant future, all the people on the
  island will have died and all the U atoms in the
  rock will have transformed into lead.
  Thereafter, there will be no more changes. So
  extremely old populations face exactly the same
  fate.
• But before we reach that point, can we somehow
  monitor the ongoing deaths to provide a stable,
  reliable clock?

31
1. On the Island

• For a long time, no one dies (its a young,
  healthy population). Perhaps 1 die in the first
  decade, say, from random illnesses and
  infections.
• BUT as the years and decades pass, the
  fractional death rate among the survivors
  increases.
• If you have a group of 90-year-olds left, its a
  pretty safe bet that theyll all be gone within
  the coming decade.

32
2. In the Meteorite

• The atoms do not individually age. All of them
  are equally robust. But some of them have the
  bad luck to die its purely random, like a
  car accident.
• During any given brief interval, some fixed
  fraction of those U atoms still present will
  decay. Since there are progressively fewer atoms
  left, theres a steady decline in the number of
  deaths.
• So radioactive rocks become less so with time.
  But the decreased level of radioactivity is not
  how we create the clock.

33
The Half-Life

• The radioactive element produces an end product,
  like the cow produces droppings. The steady
  accumulation of material is the clock.
• Each decay cascade has a well-defined
  determinable half-life the time taken for half
  the remaining atoms to decay away to a final,
  stable form.

34
The Atoms Dont Vanish!

• As the original material dwindles away, the
  stable daughter product accumulates.

35
The Proportions Give the Age

• Note that we only need to measure the chemical
  composition (say, how much U is left, compared to
  how much lead has accumulated).
• We do not need to monitor the rock for continuing
  changes, or measure any radioactivity at all!

36
What Do We Need?

• Only a knowledge of the half-life!
• We get this beforehand from independent
  laboratory tests on pure samples not from the
  mineral whose age is being determined.

37
A Perfect (Canadian) Analogy!
38
Playoff Time

• Imagine 32 NHL teams, playing in 16 best-of-seven
  series.
• Suppose the NHL schedules each one to start on a
  Monday and end as late as the following Sunday,
  after 7 full games.

39
Steady Progress

• Monday May 1 32 teams start round 1
• Monday May 8 16 teams start round 2
• Monday May 15 8 teams start round 3
• Monday May 22 4 teams start round 4
• Monday May 29 2 teams start round 5
• Monday June 5 1 team has a victory parade!

40
How Unlikely is This Outcome?
41
The Analogy

• Half-life 7 days. (The number of teams is
  halved every week.) You already know this from
  (say) reading the NHL league rules, or watching
  it last year.
• In week 1, there are 16 series going on lots of
  activity!
• By week 3, that has been reduced to 4 series by
  week 5, there is only one series. The activity
  steadily dies away.
• (Of course, real fans will find the later series
  more intense than the opening ones! But less is
  actually happening!)

42
Determining Ages

• You awake from a coma on May 15 and see that
  there are 24 idle teams, with 8 about to start a
  new series. Since only ¼ of the teams are still
  active, you deduce instantly that 2 half-lives
  have gone by.
• Note you dont have to watch even a single game
  the relative number (the proportions) of
  surviving and eliminated teams immediately gives
  you the answer!
• Deduction The playoffs started 2 weeks ago (
  the age!)

43
Problem 1 Contaminants

• We have to be able to determine the likely
  original composition of the rock. Perhaps it
  already contained a bunch of lead from the very
  start.
• (Did the cows walk into a field already filled
  with manure?)
• Chemistry helps study the mix of non-radioactive
  isotopes to figure out the original recipe.

44
Conversely
45
Problem 2 Losses

• In minerals will the daughter atoms inevitably
  stay behind to be counted?
• (Did the dung beetles or a heavy rain sweep away
  some of the daughter product?)
• K ? Ar can be a problem. Ar is a gas.

46
Resetting the Clock
47
Ages Since When?

• The age of a rock is the time since the latest
  melting and re-crystallization, because that
  shuffles atoms around in different proportions
  according to chemical reactions undergone, their
  melting points and fluid mobility, etc.
• When the elements and minerals coalesce in new
  proportions, the clocks are re-set.

48
Useful Radioisotopes

• This depends on the timescale of interest. They
  are not just used as clocks!

49
First Range

• Short timescales (minutes, say)
• Example radioactive Iodine
• - used diagnostically or therapeutically
• - decays away in minutes
• - we want a strong signal for a while, but not
  for long!
• - needs to be created afresh each time

50
Thyroid Health
51
Second Range

• Middling perhaps centuries (Archaeology)
• - the famous Carbon dating
• - half-life of 5700 years
• - radioactive C14 maintained in atmosphere
• - ingested and incorporated into living bodies
  (plants, animals)

52
CarbonDating
53
Historical Calibration
54
How Do We Get the Age of Stonehenge?
55
Third

• Long Timescales Geological
• - K40 ? Ar40 (1.3 Billion yrs)
• - Rb87 ? Sr87 (47 Billion yrs)
• - U235 ? Pb207 (700 Million yrs)
• - U238 ? Pb206 (4.5 Billion yrs)

56
Some Results
57
The Age of the Solar System

• Earth rocks are near 4 B.y. old
• Moon rocks, Mars rocks and meteors are up to
  4.6 B.y.
• Sun is 4.5 B.y. (by a different method!)