Half-Life
Pg. 870-874
Half-Life
• Half-life = the time needed for half of the
radioisotope sample to decay into products
• Half-live can have varying lengths
• May be a fraction of a second
• Can last billions of years
•Examples:
•Carbon-14 = 5730 years
•Potassium-40 = 1.25x109 years
•Radon-22 = 3.8 days
•Thorium-230 = 75,400 years
•Thorium-234 = 24.1 days
Calculating Half lives
• There are 2 ways to solve these problems:
• Continually divide by 2
• Use the equation below
N = No (1/2) n
Calculating Half-Life
• Nitrogen-13 emits beta radiation and decays to carbon13 with a half-life (t1/2) of 10 min. Assume a starting
mass of 2.00g of nitrogen-13.
• How long is three half-lives?
• How many grams of the isotope will be present at the end of
three half-lives?
Calculating with Half lives
• If the passing of 5 half lives leaves 25.0mg
of strontium-90 sample, how much was
present in the beginning?
Examples of Uses of Half-Life
1. Can be used to determine the age of
an artifact (carbon-14 dating)
2. Artificial isotopes tend to have short
have lives
- Used in medicine
- Don’t pose long-term hazards to patients
asymmetric scan
indicates disease
normal
Radiocarbon dating
• AKA: Carbon-14 dating
• Carbon-14 is produced in the
atmosphere when high-energy
neutrons from space (cosmic
rays) collide with nitrogen-14
14
7
N  n C H
1
0
14
6
• Carbon-14 decays by bparticle production
C e N
14
6
0
1
14
7
1
1
Carbon Dating
• Carbon-14 is continuously produced in the
atmosphere and it continuously decomposes by βdecay
• The two opposite processes have come into
balance, so the amount of carbon-14 present in the
atmosphere is approximately constant.
Carbon Dating
• Carbon-14 dating can be
used to date wood and
cloth artifacts
• A living plant consumes
carbon dioxide in the
photosynthesis process
• Some carbon dioxide
contains the C-14 isotope
• When the plant uses
carbon dioxide with C-14, it
is incorporated into the
molecules in the plant
Carbon Dating
• While it is alive, the C14 in the plant
molecules is equal to
that in the atmosphere.
• When the tree is cut,
there is no more
incoming source of C14 to balance the C-14
that is decaying.
• The C-14 content
decreases.
Carbon Dating
• Using the known half-life of
5730 years for C-14,
archaeologists compare the
amount of C-14 in an artifact
to the amount currently in
trees and figure out the age.
• A wooden bowl with half as
much C-14 as a current living
tree would have been through
one half life and would
therefore be 5730 years old.
Carbon dating made by
Thomas Athol Rafter
Half life Activity
• You must get the data today
• Class data will be posted on
Moodle tonight
• Lab due Monday