An archaeological team discovers charcoal fragments at the site of an ancient campfire in a cave. They send a sample to a laboratory for carbon-14 dating. C...

(a) Type of radiation emitted [1]

Carbon-14 decays by beta-minus emission. [1] In this decay, a neutron in the carbon-14 nucleus converts to a proton, and a high-energy electron (beta particle) is ejected.

(b) Nuclear equation [2]

\(^{14}_{6}\text{C} \rightarrow \,^{14}_{7}\text{N} + \,^{0}_{-1}\text{e}\)

Conservation check:

• Mass number: 14 = 14 + 0 [1]
• Atomic number: 6 = 7 + (-1) [1]

The carbon nucleus gains a proton (Z increases from 6 to 7) and becomes nitrogen, while the mass number remains 14.

(c) Estimating the age from the graph [2]

The charcoal sample has an activity of 0.19 Bq/g. On the graph, locate 0.19 on the y-axis and draw a horizontal line across to the curve. [1] From the intersection, drop a vertical line down to the time axis. The reading gives approximately 2200-2400 years. [1]

This is consistent with the mathematical approach: the fraction remaining is \(\frac{0.19}{0.25} = 0.76\), and using \(0.76 = (0.5)^{t/5730}\), solving gives \(t \approx 2300\) years.

(d) Principle of carbon-14 dating [3]

1. While an organism is alive, it continuously absorbs carbon-14 from the atmosphere (through photosynthesis in plants, or through the food chain in animals), maintaining a constant level of carbon-14 activity. [1]
2. When the organism dies, it stops absorbing carbon-14. The carbon-14 atoms already present undergo radioactive decay, so the activity decreases over time. [1]
3. By comparing the current activity of the sample with the known activity of living material, the number of half-lives that have elapsed can be determined, and hence the age of the sample can be calculated. [1]

(e) Two reasons the estimated age might differ from the true age [2]

1. The concentration of carbon-14 in the atmosphere may not have been constant throughout history (e.g. due to variations in cosmic ray intensity or volcanic activity), so the assumption of a fixed initial activity may be incorrect. [1]
2. The sample may have been contaminated by more recent carbon-containing material (e.g. plant roots, groundwater carrying dissolved carbon), making the measured activity higher and the apparent age younger than the true age. [1]