Transcript Evolution and the Big Bang, ET Life Lec. 6, Jan 18, 2002

Radioactive Dating
Lecture Sixteen, Feb. 21, 2003
Last Time: Distance to nearest star
• Was a very long quest. Finally we were
able to measure the parallax of nearby
stars such as Alpha Centuri.
Very distant star
Nearby star
Earth’s orbit
Cepheid Variable Stars
• Oscillate with a regular period. Intrinsic
•
•
•
brightness of star is proportional to its period.
Measure the period of the variable star and its
apparent brightness and infer the stars actual
distance.
Need to calibrate the relation with Cepheids at
known distances.
Finally, Hubble telescope can resolve individual
Cepheid variable stars at cosmological distances.
Hubble resolves Cepheids in M100
Spiral galaxy M100
Allows accurate determination of distance
Hubble’s Law Gives Expansion Rate
of Universe
• Distant galaxies are moving away with velocity
•
•
•
•
•
v=Hd
Easy to measure velocity v from redshift of
spectral lines.
Distance d was very hard!
Hubble constant is now H=v/d.
Distance divided by velocity is a time:
d/v=T=1/H= Age of Universe!
Age of Universe 13 B. years follows form 1/H.
Timeline
• Big bang.
• Creation of galaxies and first stars.
• Creation of chemical elements.
• Creation of solar system: Sun, earth and
planets.
• Origin of life on Earth.
• Evolution and mass extinctions.
Radioactive dating
• Measure present amount of a radioactive isotope.
• Have some way to infer the initial amount.
• Compare the decrease to the known rate of radioactive
•
•
•
•
•
decay to infer an age.
Rate of radioactive decay of an isotope characterized by
its half life.
Example 14C has a half life of about 5000 years.
After 5000 years half of the original 14C is gone and after
10,000 years ¾ of original amount has decayed.
Note, need to chose an isotope with a half life
comparable to the age you are trying to measure.
Cant use 14C to measure 4.6 Billion year age of earth.
Radioactivity, a Tour
• * DANGER - SEVERE RADIATION
* ENTER AT YOUR OWN RISK
* Enjoy Your Visit
Our Safety Inspector Homer Simpson will
now take you on a tour of the Springfield
Nuclear Power Plant.
• Can you feel it? That tingling in your bones?
Well, yes, that's partly because of the radiation,
but mainly it's because you're in Burns territory
now! The Springfield Nuclear Power Plant
dominates the landscape here, from its main
office to its giant turbines to the cut-off valve
that I once plugged with my ample frame, thus
averting a nuclear meltdown.
And then there's the fuel rod and nuclear waste
storage areas. Is it me, or does the Springfield
Isotopes baseball field (property of C.
Montgomery Burns) seem to be just a bit too
green?
Radioactivity a Primer
• Atoms have an electron cloud around a nucleus
•
•
which is made of protons and neutrons.
A free neutron decays with a half-life of 10.6
minutes into a proton (p) an electron (e) and an
antineutrino ().
n! p + e- + 
Protons and electrons have opposite charges
while neutron and antineutrino are uncharged.
Electric charge is conserved in all reactions.
Initial charge = 0 = Final charge = +1 + -1 + 0
Half-Life
• Nuclear reactions are probabilistic. A given
•
•
nucleus could decay instantly or it could survive
for the age of the Universe.
The half-life is the amount of time one has to
wait until the probability of decay is 50%.
If you start with 8lbs of radioactive material.
After one half-life 4lbs remain, after two halflives 2lbs remain and after 3 half-lives only one
lb is left. Thus only ¼ of the initial # of
neutrons will be left after 20 minutes because
the neutron half-life is 10 minutes.
Antiparticles
• According to relativity, every particle has an antiparticle
•
•
•
•
with the same mass but opposite electric charge.
When particles and antiparticles meet they annihilate
into gamma rays.
Example, the anti-electron is known as a positron (e+)
and has a positive charge but the electron’s mass. [The
proton is 2000 times more massive than an electron.]
Antihydrogen is an atom made from a positron and an
anti-proton. It is the simplest atom of antimatter.
Science Fiction writers have speculated that antimatter
would make a very efficient rocket fuel.
Radiocarbon dating
• Carbon 14 (14C) is an isotope of carbon with 6
•
•
protons and 8 neutrons in the nucleus. One of
these bound neutrons decays with a half-life of
5000 years converting 14C! 14N + e- + 
With a half-life of only 5000 years, almost all of
the primordial 14C has long since decayed.
However, a very small amount of 14C is
continually being made by cosmic rays
interacting with the earth’s atmosphere.
Dating old wood
• While a tree is alive it continually exchanges carbon with
•
•
•
•
the atmosphere. This replenishes the very small amount
of 14C present in the tree.
However, when the tree dies it stops exchanging C with
the atmosphere. With no new source, the amount of 14C
slowly decays.
One can date old pieces of wood by measuring how
much 14C is left. The smaller the amount, the older the
wood.
Very useful in archeology!
However, can’t measure ages much longer than 5000
year half-life.
Radioactive Dating of Rocks
• To measure the billions of year ages or rocks
•
•
•
need to use isotopes with longer half-lives.
Potassium 40 (40K) is an isotope with 19 protons
and 21 neutrons. It decays to Argon 40 with a
half-life of 1.28 billion years.
Uranium 238 has a half-life of 4.47 billion years.
The radioactive decay of 40K and 238U are
important sources of heat for the earth and help
drive plate tectonics.
Potassium Argon Dating of Rocks
• If the produced Argon (a noble gas) can not
•
•
escape from the middle of a solid rock then,
carefully measure the ratio of 40Ar to 40K in a
rock. The larger the ratio the older the rock
since K is turning into Ar slowly.
Note, if the rock is melted (for example from the
heat of a nearby asteroid impact) then the
Argon gas will escape. This “resets” the K to Ar
clock.
You are measuring the time since the rock was
last melted.
Dating the earth
• Problem: we have not found any rocks as
old as the earth. All of the earth rocks we
have been able to study have been melted
at some time in their past. Thus the
oldest known earth rocks are about 3.5
billion years.
• We can not directly radioactively date the
earth!
Meteorites
• Meteorites in general are small asteroids that have fallen
•
•
•
to earth.
Asteroids formed at the same time as the rest of the
solar system. Thus we think all of the planets, the sun,
and the asteroids and comets all have the same age.
Asteroids have circled the sun almost undisturbed for the
life of the solar system. They have not been remelted.
The radioactive age of most meteorites is 4.6 billion
years. Thus we think the earth and sun are 4.6 billion
years old because this is the age of the meteorites.
Asteroids fall as Meteorites
Radioactive Dating of Oldest Stars
• This is a new way to get the age of the universe.
• Find a star that you think is very old. Spectrum shows
•
•
•
•
very few Fe lines. Chemical elements except H, He
made in stars. Very old star has few heavy elements.
Measure abundance of Thorium and Uranium from
strength of spectral lines. Note, Uranium lines are very
faint and hard to observe.
Need very high quality spectra from long exposures at
the largest telescopes.
Asume ratio of original U to Th was the same as the
original ratio in the sun.
Infer the age of the star from the amount of U that
remains.
Independent Age of Universe
• We have found stars with radioactive ages
near 12 § 3 billion years.
• We think these formed within 1 billion
years of the big bang.
• This gives a direct age to the universe that
is independent of (but consistent with) the
“expansion age” from the rate of the
expansion of the universe.
Nuclear Power For Spacecraft
• Needed for last third of this class to explore the
•
•
•
outer solar system.
“Nuclear Batteries” have radioactive isotopes,
usually Plutonium, that decay and produce heat.
This heat is turned into electric power.
Cassini Mission to Saturn uses nuclear batteries
because it is very far from the sun so solar cells
are inefficient.
Concern that launch accident may spread
plutonium.
Nuclear Rockets
• One can use a nuclear reactor to heat
hydrogen gas to very high temperatures
and produce a rocket exhaust.
• Conventional chemical rocket carries both
H and O (note O is heavy) to burn to
make H2O.
• Nuclear rocket does not need O and can
get the H hotter and thus moving faster.
Nuclear Explosive Power
• Explode a whole series of small nuclear
weapons behind a pusher plate.
• Very high temperatures reached in nuclear
explosions accelerate debris to very high
speeds.
• This makes an incredibly powerful rocket if
your spacecraft survives.
Small Scale Test with Conventional
High Explosives in 1950s
• Orion project to build
•
powerful spacecraft
that could take large
payloads anywhere in
the solar system.
Test of model (about
1 meter in size) with
conventional ~1kg
explosive charges.