Absolute Dating Using half-lives to study past-lives Notes #26
What is radioactivity? (notes) Some atoms have an unstable nucleus Over time, these nuclei* fall apart, creating two smaller atoms (radioactive decay) They release energy and particles in the process *Nuclei is plural for nucleus
Radioactivity is Random (not notes) Whether a particular nucleus will break down is completely random Due to the Law of Large Numbers, it tends toward the average chance Think of it like flipping a coin: it is random every time but if you were to flip billions of coins it would average out to 50% heads and 50% tails *There are approximately 50 quintillion (50,000,000,000,000,000,000) atoms in a grain of sand. So that s a lot of chances.
Alpha, beta, and gamma radiation (not notes) Early on scientists observed three different types of radiation. They didn t know what they were so they called them alpha, beta, and gamma Nowadays we know what they are: Alpha is 2 protons and 2 neutrons Beta is an electron Gamma is high-energy light
Alpha, beta, and gamma radiation (not notes) In terms of strength alpha is the weakest (stopped by a sheet of paper), beta is medium (stopped by thin metal), and gamma is very powerful (requires several inches of metal)
All matter has some radioactivity (notes) There are unstable atoms in all matter* By measuring the amount of unstable atoms remaining in a substance, we can calculate its age * Radioactive isotopes
Dangerous Radioactivity (not notes) The main difference between normal radioactivity in matter and dangerous radioactivity is the amount and energy By refining materials that are radioactive we concentrate the unstable atoms Enriching uranium is a process of concentrating the more radioactive versions of uranium; it is important for making nuclear weapons and power plants
Half-Life (notes) A half-life is defined as how long it takes for half of the radioactive atoms in a substance to decay In science the Greek letter lambda is used to signify the half-life of a substance.
Halving Half-Lives (not notes) If you start out with 100% of a substance after one half-life you will have 50% 1 λ
Halving Half-Lives (not notes) After two half-lives you will have 25% (half of 50%) 2 λ
Halving Half-Lives (not notes) After three half-lives you will have 12.5% (half of 25%) Repeat as many times as you like 3 λ
Half-Life Graphs (not notes)
Calculating the half-lives (not notes) To figure out how many half-lives have gone by divide the half-life into how much time has passed: Example: if a substance has a half-life of 50 years and 150 years have passed, how many half-lives is this? 3 half-lives (150 years / 50 years) Example: if 1,000,000 years have passed and a substance has a half-life of 1,000 years, how many half-lives is this? 1,000 half-lives (1,000,000 years / 1,000 years)
Using half-lives to calculate amount (not notes) Take the number of half-lives and multiple your original value by ½ that many times. Example: If you started with 24 grams of radioactive material, how much would you have after one half-life? 24g * (1/2) = 12g Example: If you started with 24 grams of radioactive material, how much would you have after two half-lives? 24g * (1/2) * (1/2) = 6g Example: And now 24g after 3 half-lives? 24g * (1/2) * (1/2) * (1/2) = 3g
Going Backward (not notes) Scientists usually want to know the age of the rock, not the amount So they run the same process, but backward: Example: A rock sample has 25% of the starting amount of radioactive material. How many half-lives have passed since that rock formed? 2 half-lives (Half of 100% is 50%, then half of 50% is 25%) Example: If the same radioactive material above has a half-life of 10,000 years, how old is the rock? 20,000 years (2 half-lives * 10,000 years)
Going Backward (not notes) Another: Example: Strontium-90 has a half-life of 28 years. If only 12.5% of the original amount remain, how old is the sample? Step 1: How many half-lives? 3 (100->50->25->12.5%) Step 2: How many years? 84 years (3 half-lives * 28 years)
Rates of Decay (notes) Elements decay at different rates This means that some are good for measuring shorter time spans, while others are better for longer ones Example half-lives: Lithium-4: 0.000000000000000000000324 seconds Thorium-234: 24.1 days Argon-39: 259 years Carbon-14: 5,730 years Uranium-235: 710,000,000 years Potassium-40: 1,248,000,000 years Uranium-238: 4,468,000,000 years Tellurium-128: 160 trillion times longer than the age of the universe
Carbon-14 (notes) Carbon-14 is found in all living things Carbon-14 is useful for dating recent* objects but decays too quickly to be used for older ones *Recent in geology means a few 10 s of thousands of years, like Ötzi the Iceman
Uranium-238 (notes) U-238 is the most common form of uranium and is found in small quantities in many rocks Its half-life is approximately the age of the Earth, making it good for dating the oldest rocks