Problem 129 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following option is correct? (a) In living organisms, circulation of \({ }^{14} \mathrm{C}\) from atmosphere is high so the carbon content is constant in organism. (b) carbon dating can be used to find out the age of earth crust and rocks (c) radioactive absorption due to cosmic radiation is equal to the rate of radioactive decay, hence the carbon content remains constant in living organism (d) carbon dating can not be used to determine concentration of \({ }^{14} \mathrm{C}\) in dead beings. [IIT 2006]

Step-by-Step Solution

Answer

Options (a) and (c) are correct.

Step 1: Analyzing Option (a)

Let's analyze option (a). It states that in living organisms, the circulation of \( ^{14}C \) from the atmosphere is high, which keeps the carbon content constant. This statement is partially true, as living organisms constantly exchange carbon with the atmosphere while they are alive, which keeps the \( ^{14}C \) content relatively stable during their lifetime. Thus, this option can be considered correct.

Step 2: Analyzing Option (b)

Now let's examine option (b). It claims carbon dating can be used to determine the age of the Earth's crust and rocks. Carbon dating is used to date formerly living things, containing organic material. Rocks and the Earth's crust do not fall into this category, so carbon dating is not used for this purpose. This option is incorrect.

Step 3: Analyzing Option (c)

This option suggests that radioactive absorption due to cosmic radiation equals the rate of radioactive decay, keeping the carbon content constant in living organisms. This is true; living organisms maintain a steady level of \( ^{14}C \) because the rate of new \( ^{14}C \) atoms introduced by cosmic rays balances the decay rate of \( ^{14}C \). Hence, option (c) is correct.

Step 4: Analyzing Option (d)

Option (d) states that carbon dating cannot determine the concentration of \( ^{14}C \) in dead beings. This option is incorrect because carbon dating precisely measures the remaining \( ^{14}C \) in dead organic material to estimate its age. Therefore, it is used to determine \( ^{14}C \) concentration.

Key Concepts

Radioactive Decay

Radioactive decay is a natural process where unstable atomic nuclei lose energy by emitting radiation. This process is predictable, which makes it very useful for scientific purposes. During radioactive decay, an atom of one element transforms into a different element. For instance, carbon-14 ( C^{14} ), a radioactive isotope of carbon, decays into nitrogen-14 over time. This decay occurs at a consistent rate, known as the half-life. The half-life of carbon-14 is about 5,730 years, which means after this period, only half of the original carbon-14 remains in a sample.
This consistent decay rate is what makes carbon dating possible. Scientists can measure how much carbon-14 remains in a sample to determine how long ago an organism died. Therefore, understanding the process of radioactive decay is crucial for radiocarbon dating techniques used in archaeology and geology.

Cosmic Radiation

Cosmic radiation is high-energy radiation that originates from outer space and solar activity. When these cosmic rays enter Earth's atmosphere, they interact with nitrogen atoms to produce carbon-14.
- This formation process is continuous. - As a result, the Earth constantly has a certain level of carbon-14 in the atmosphere. - Living organisms absorb this carbon-14 during their lifespans, maintaining a consistent ratio with stable carbon isotopes.
Once an organism dies, it stops absorbing carbon, and the carbon-14 begins to decay without replacement by new carbon from the atmosphere. The interplay between cosmic radiation and carbon cycle is integral in understanding how carbon dating works, providing the basis for measuring the time elapsed since the organism's death.

Living Organisms

Living organisms are in a constant exchange with their environment. They take in carbon, including carbon-14, through processes like photosynthesis and feeding. While alive, the intake of carbon from the atmosphere or food keeps the amount of carbon-14 in these organisms relatively stable.
- This exchange means that the carbon-14 in a living organism is constantly being refreshed, maintaining a balance with that in the atmosphere. - It is this balance that allows scientists to use carbon dating to estimate the time since an organism's death.
Understanding this constant intake and output is crucial because once an organism dies, it stops this exchange, and the carbon-14 content begins to decrease at a known rate, making it possible to determine how long ago the organism died.

Carbon-14

Carbon-14 is a radioactive isotope of carbon. Unlike the more common carbon isotope, carbon-12, carbon-14 is unstable. This instability leads to its radioactivity, and eventually, it decays to nitrogen-14 with a known half-life of about 5,730 years.
- In living organisms, continual absorption from the environment keeps carbon-14 levels in balance with the atmosphere. - Carbon-14 is created in the atmosphere through cosmic radiation interactions with nitrogen. - This constant creation means that despite its decay, a steady amount is present in the atmosphere and absorbed by living organisms.
Because carbon-14 decays at a predictable rate, scientists can measure the amount remaining in a dead organism. This measurement provides an estimate of when the organism stopped absorbing carbon-14, hence, revealing the time of death. Therefore, carbon-14 plays a crucial role in radiocarbon dating, enabling scientists to date ancient organic materials with high precision.