Half-Life Pg. 870-874
Dec 31, 2015
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 carbon-
13 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-Life1. 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
• Carbon-14 decays by -particle production
NeC 147
01
146
HCnN 11
146
10
147
Carbon Dating
• Carbon-14 is continuously produced in the atmosphere and it continuously decomposes by β-decay
• 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 C-14 in the plant molecules is equal to that in the atmosphere.
• When the tree is cut, there is no more incoming source of C-14 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