Half-LifePg. 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 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

Half life Activity• You must get the data today

• Class data will be posted on Moodle tonight

• Lab due Monday