Carbo Dating

Carbon dating (Radiocarbon dating) is a technique used to determine the age of ancient organic materials (like wood, bones, shells, and cloth) up to about 50,000 years old. It is based on the decay of Carbon-14 (¹⁴C), a radioactive isotope of carbon.

How Carbon Dating Works:

1. Formation of Carbon-14

In the upper atmosphere, cosmic rays convert Nitrogen-14 (¹⁴N) into Carbon-14 (¹⁴C).

This ¹⁴C mixes with Carbon-12 (¹²C) and Carbon-13 (¹³C) in the atmosphere.

2. Absorption by Living Organisms

Plants absorb ¹⁴C during photosynthesis.

Animals and humans consume plants, incorporating ¹⁴C into their bodies.

3. Decay After Death

When an organism dies, it stops absorbing ¹⁴C.

The ¹⁴C in its body starts decaying into Nitrogen-14 (¹⁴N) at a fixed rate.

4. Half-Life of Carbon-14

Half-life = 5,730 years (time for half of the ¹⁴C to decay).

By measuring the remaining ¹⁴C, scientists can estimate the time since death.

Formula for Age Calculation:

t = \frac{\ln(\frac{N_f}{N_0})}{-k}

 = age of the sample

 = remaining ¹⁴C

 = original ¹⁴C

 = decay constant ( per year)

Limitations of Carbon Dating:

Only works for materials younger than 50,000 years.

Ineffective for rocks or fossils millions of years old (other dating methods like uranium-lead dating are used).

Can be affected by contamination and changes in atmospheric ¹⁴C levels.

Applications of Carbon Dating:

Dating ancient artifacts, fossils, and historical objects.

Archaeological studies (e.g., Egyptian mummies, prehistoric cave paintings).

Climate change research by analyzing old tree rings and ice cores.