# Radioactive Dating ## Carbon-14 Dating Principles - The isotope carbon-14 is the most commonly used isotope for radioactive dating purposes - Carbon-14 forms naturally in Earth's atmosphere through a nuclear reaction - Cosmic rays travelling through space knock neutrons out of atomic nuclei - These free neutrons then collide with nitrogen-14 nuclei in the atmosphere - The reaction can be written as: $^{1}_{0}\text{n} + ^{14}_{7}\text{N} \rightarrow ^{14}_{6}\text{C} + ^{1}_{1}\text{p}$

Radioactive dating uses the decay of carbon-14 to determine the age of organic samples by comparing current activity to expected initial activity

### Carbon-14 in Living Organisms - Plants absorb carbon dioxide from the atmosphere during photosynthesis - This includes carbon dioxide molecules containing the radioactive carbon-14 isotope - Animals and humans absorb carbon-14 by consuming plants in their diet - Therefore, all living organisms constantly absorb carbon-14 throughout their lifetime - The proportion of carbon-14 in living organisms remains constant - Carbon atoms are continuously replaced while the organism is alive - The ratio of carbon-14 to stable carbon-12 stays approximately the same ### Carbon-14 After Death - When an organism dies, it immediately stops absorbing any new carbon atoms - No more carbon-14 enters the dead material - The carbon-14 already present in the tissue begins to decay - The activity of carbon-14 in the organic matter gradually falls over time - This decay follows an exponential pattern with a half-life of approximately 5730 years

Carbon-14 has a half-life of 5730 years, making it suitable for dating archaeological and geological samples

The exponential decay of carbon-14 can be visualized over multiple half-lives:

### Dating Process - Scientists can determine the age of organic samples by analysis - The current amount of carbon-14 in the sample is measured - This is compared to the initial amount (based on the current ratio of carbon-14 to carbon-12 in living organisms) - Using the exponential decay equation $N = N_0 e^{-\lambda t}$, the time since death can be calculated - The decay constant $\lambda$ for carbon-14 can be found using: $\lambda = \frac{\ln 2}{t_{1/2}} = \frac{0.693}{5730 \text{ years}}$ ## Reliability of Carbon Dating - Carbon dating is a highly reliable ageing method for certain sample ages - The reliable range is approximately 1000 years old up to a maximum of around 40,000 years old - For samples outside this range, carbon dating is not the most reliable method

Carbon dating is unreliable for samples younger than 1000 years or older than 40,000 years

### Why Young Samples Are Unreliable For samples less than 1000 years old: - The activity of carbon-14 in the sample is too high - Only a small fraction of the carbon-14 has decayed - The small change in activity from the initial value is difficult to measure accurately - The difference between the sample's activity and the activity of living material is minimal - The ratio of carbon-14 to carbon-12 is too high to determine an accurate age - Small measurement errors lead to large errors in the calculated age ### Why Old Samples Are Unreliable For samples more than 40,000 years old (approximately 7 half-lives): - The activity of the sample becomes extremely small - After seven half-lives, less than 1% of the original carbon-14 remains - The count rate becomes similar to that of background radiation - It becomes difficult to distinguish the sample's activity from environmental radiation - Very few carbon-14 atoms remain in the sample - This means very few decay events occur during measurement - The ratio of carbon-14 to carbon-12 becomes too small to determine an accurate age - The signal-to-noise ratio is too low for reliable measurements ### Age Range Limitations Table | Sample Age | Number of Half-Lives | Carbon-14 Remaining | Reliability | |------------|---------------------|---------------------|-------------| | < 1000 years | < 0.2 | > 87% | Poor - too little change | | 1000 - 5730 years | 0.2 - 1.0 | 50% - 87% | Good | | 5730 - 11,460 years | 1.0 - 2.0 | 25% - 50% | Good | | 11,460 - 28,650 years | 2.0 - 5.0 | 3% - 25% | Good | | 28,650 - 40,000 years | 5.0 - 7.0 | 0.8% - 3% | Moderate | | > 40,000 years | > 7.0 | < 0.8% | Poor - too little remains | ### Historical Uncertainty - Carbon dating relies on knowing the current ratio of carbon-14 to carbon-12 - This method assumes this ratio has remained constant over time - However, scientists cannot be certain of the exact level of carbon-14 in the biosphere thousands of years ago - Cosmic ray intensity may have varied - The Earth's magnetic field strength has changed - Industrial activity has affected atmospheric carbon dioxide composition - This uncertainty makes it more difficult to accurately age very old samples - Calibration curves using tree rings and other dated materials help correct for these variations