Problem 24 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Why do we use the carbon dating to calculate the age of the fossil? \([2006-5 \mathrm{M},-2]\) (a) Rate of exchange of carbon between atmosphere and living is slower than decay of \(\mathrm{C}^{14}\) (b) It is not appropriate to use \(\mathrm{C}^{14}\) dating to determine age (c) Rate of exchange of \(\mathrm{C}^{14}\) between atmosphere and living organism is so fast that an equilibrium is set up between the intake of \(\mathrm{C}^{14}\) by organism and its exponential decay (d) none of the above

Step-by-Step Solution

Answer

Carbon dating is possible because of the rapid equilibrium of \\(\mathrm{C}^{14}\\) exchange, as explained in option (c).

Step 1: Understanding Carbon Dating

Carbon dating is a technique used to determine the age of ancient artifacts and fossils. It relies on the decay of carbon-14, a radioactive isotope of carbon. When a living organism dies, it stops taking in carbon-14, and the isotope starts to decay at a known rate, allowing scientists to calculate how long it has been since the organism's death.

Step 2: Analyzing the Given Options

Let's consider each option: (a) claims the exchange rate is slower than decay, which would not help set an accurate baseline for measurement. (b) states that \(\mathrm{C}^{14}\) dating is not appropriate for determining age, which contradicts its scientific use. (c) explains that the exchange rate is fast, allowing for equilibrium and making the technique viable, which matches how carbon dating operates. (d) simply dismisses all options, providing no information.

Step 3: Selecting the Correct Option

The correct understanding of carbon dating aligns with option (c). The rapid exchange rate allows living organisms to reach a constant \(\mathrm{C}^{14}\) level, making it feasible to measure the reduction after death. This equilibrium ensures that carbon dating can accurately measure the time since death using the decay curve of \(\mathrm{C}^{14}\).

Key Concepts

Radioactive Isotopes

Radioactive isotopes are atoms with an unstable nucleus that emit radiation as they decay to a stable form. This process, known as radioactive decay, can take various amounts of time depending on the isotope.
Radioactive isotopes have a wide range of applications, from medical imaging to determining the age of archaeological findings.
One of the key characteristics of radioactive isotopes is their half-life, which is the time required for half of the radioactive atoms in a sample to decay. This predictable decay rate enables scientists to use them as natural clocks.

• Example of Radioactive Isotope Usage: Medical isotopes are used for diagnosing and treating diseases.
• Calculation of Age: Dating techniques like carbon dating utilize the decay rates of isotopes to determine ages.

Carbon-14

Carbon-14 is a specific type of radioactive isotope of carbon.
It naturally forms in the upper atmosphere through the interaction of cosmic rays with nitrogen-14.
With a half-life of about 5,730 years, carbon-14 is particularly useful for dating organic material that is thousands of years old.

• Formation Process: Cosmic rays smash into atmospheric nitrogen, transforming it into carbon-14.
• Role in Living Organisms: Carbon-14 is absorbed by living things through carbon dioxide. As long as the organism is alive, the ratio of carbon-14 remains constant.
• Decay Process: After death, carbon-14 decays while the other carbon isotopes do not, altering the carbon ratio.

The constant intake and decay reach an equilibrium during life, which makes carbon-14 an effective tool for radiocarbon dating.

Fossil Age Determination

Fossil age determination involves techniques like carbon dating to estimate the time frame during which an organism lived.
In the case of carbon dating, the technique hinges on measuring the remaining amount of carbon-14 in an organic specimen and comparing this to the consistent decay rate.
The key factor in determining the age of a fossil using carbon dating is the rapid exchange rate of carbon-14 between the organism and its environment while the organism is alive.

• Understanding the Method: When an organism dies, it stops absorbing carbon-14, so the ratio of remaining carbon-14 to other carbon isotopes provides a timestamp.
• Applicability: Suitable for dating objects up to around 50,000 years old. Beyond this, the remaining carbon-14 is too sparse to measure accurately.
• Common Use: Archaeologists and paleontologists use carbon dating to timestamp organic remains with reasonable accuracy.