Half-Life & Carbon Dating

pg. 621-625

LO: I understand how radioactive isotopes can be used to determine the age of

matter.

Review of Radioactivity1. Why are atoms unstable?• Unbalanced nuclear forces—Electrostatic Charge Repulsion & Strong Nuclear

Force• The more protons in nucleus more neutrons needed to maintain stability.

2. Radioactive particles involvedAlpha Beta Gamma Neutron Positron

3. Types of Nuclear Reactions• Radioactive Decay• Nuclear Fusion—stars• Nuclear Fission—chain reactions (atomic bombs, etc.)

What we know about radioactivity

Radioactive (unstable) atoms exist everywhere:• Outer space bombardment into Earth’s

atmosphere• Matter on Earth• Air

All atoms above Z=83 (Bismuth) are radioactive

What is half-life?

Half Life: The time it takes for half of the parent nuclide to decay to the daughter nuclide.

100% 50% 25%

1st HL 2nd HL

50 yrs 50 yrs

Half-life time duration for isotopes

Half-Life Problem Setup

Half-Life Examples

How long does it take for a 14.2 g sample of Radon to decay to

0.8875 g?

Half-Life ExamplesCarbon-14 has a half-life of 5730 yrs. How old is the fossil if it

contains only 12.5% of the Carbon-14 relative to living organisms?

Radiocarbon Dating

Radiocarbon Dating: A technique used to estimate the ages of fossils and artifacts due to the carbon-14 contained in them. Not useful for metals.

Carbon-14: A radioactive isotope formed from nitrogen bombardment in the atmosphere by a neutron particle.

Carbon-14 dating organisms

• Plants take in Carbon-14 via photosynthesis• Living organisms eat plants which incorporate

Carbon-14 into animal tissues• Upon death, the organism stops incorporating new

Carbon-14 (half-life of 5730 yrs)• The amount (%) of Carbon-14 in the organic tissues

indicates their age (relative to living organisms)• Not dependable when dating objects beyond 50,000

years

How old is the artifact?

Question: A wooden boat discovered near Egypt had a Carbon-14 content of approximately 12.5% of that found in living organisms. How old is the boat?

Solving Half-Life Problems

Solving Half-Life Problems

A radioactive sample contains 2.45 g of an isotope with a half-life of 3.8 days. How much of the isotope in grams remains after 11.4 days?

Solving Half-Life Problems

A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 within 60.0 hours. What is the half-life of this radioactive isotope?