Age of fossil may be found out by determining the ratio of two isotopes of carbon. The isotopes are

To determine the age of fossils using isotopes of carbon, we typically refer to carbon-14 (C-14) and carbon-12 (C-12). The process relies on the principle of radioactive decay.

Breakdown of the Problem

1. Identify the Isotopes: The two isotopes are C-14 (radioactive) and C-12 (stable).
2. Understand the Ratio: The age determination relies on measuring the ratio of C-14 to C-12 in a fossilized sample.
3. Radioactive Decay: C-14 decays to nitrogen-14 (N-14) over time, which allows scientists to estimate the elapsed time since the organism's death.

Relevant Concepts

1. Half-life of C-14: The half-life of carbon-14 is about 5,730 years. This means that every 5,730 years, half of the C-14 in a sample will have decayed into N-14.
2. Decay Equation: The decay of a radioactive isotope can be expressed as: $N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$ where:
   • $N(t)$ is the remaining amount of C-14 at time $t$,
   • $N_0$ is the initial amount of C-14,
   • $T_{1/2}$ is the half-life of C-14.

Analysis and Detail

1. Measurement: Scientists measure the current ratio of C-14 to C-12 in the fossilized remains.
2. Calculate Age: Using the ratio and the known half-life, they can calculate how many half-lives have passed since the organism died and thus estimate the age of the fossil.

Verify and Summarize

• Carbon dating is effective for materials up to about 50,000 years old.
• The method relies on assumptions about the initial C-14 levels and the constancy of C-14 production in the atmosphere.

Final Answer

The two isotopes used to determine the age of fossils are carbon-14 (C-14) and carbon-12 (C-12).