Problem 32 - Chemistry: An Atoms-Focused Approach

Question

Where does the \(^{14} \mathrm{C}\) found in plants come from?

Step-by-Step Solution

Answer

Short Answer: Plants contain the radioactive isotope Carbon-14 because it is formed continuously in the Earth's atmosphere through the interaction between cosmic rays and nitrogen-14. The newly formed Carbon-14 reacts with oxygen to form radioactive carbon dioxide, which then mixes with stable isotopes of carbon dioxide in the atmosphere. Plants absorb this radioactive carbon dioxide during photosynthesis and incorporate it into their tissues along with the stable carbon isotopes, resulting in the presence of Carbon-14 in plants.

Step 1: Understand the Carbon Cycle

The carbon cycle is the process through which carbon atoms circulate between the Earth's atmosphere, terrestrial biosphere (plants, animals, and microbes), oceans, and the Earth's crust in various forms. Carbon exists in many forms, including \(\mathrm{CO_2}\), hydrocarbons, carbonates, and organic compounds such as glucose.

Step 2: Photosynthesis - How Plants Acquire Carbon

Plants obtain carbon mainly in the form of carbon dioxide (\(\mathrm{CO_2}\)) from the atmosphere. During a process called photosynthesis, plants convert \(\mathrm{CO_2}\) and water (H\(_2\)O) into glucose (C\(_6\)H\(_{12}\)O\(_6\)) and oxygen (O\(_2\)) using light energy. The glucose is then used by the plant as a source of energy and as a building block for producing other organic molecules. The general equation for photosynthesis is: $$\mathrm{6CO_2 + 6H_2O} \xrightarrow{light} \mathrm{ C_6H_{12}O_6 + 6O_2}$$

Step 3: Formation of Carbon-14 in the Atmosphere

Carbon has three naturally occurring isotopes: \(^{12} \mathrm{C}\), \(^{13} \mathrm{C}\), and \(^{14} \mathrm{C}\). The radioactive isotope \(^{14} \mathrm{C}\) is formed continuously in the Earth's atmosphere through the interaction between cosmic rays and nitrogen-14 (\(^{14} \mathrm{N}\)). When high-energy cosmic ray particles enter the atmosphere, they interact with atmospheric atoms, producing a cascade of secondary particles, including neutrons. These neutrons can then react with \(^{14}\mathrm{N}\) via the following nuclear reaction: $$^1_0 \mathrm{n} + ^{14}_7\mathrm{N} \rightarrow ^{14}_6 \mathrm{C} + ^1_1 \mathrm{p}$$ This process results in the production of \(^{14}\mathrm{C}\).

Step 4: Incorporation of Carbon-14 into Plants

The newly formed \(^{14} \mathrm{C}\) reacts with oxygen to form carbon dioxide (\(^{14}\mathrm{CO_2}\)). This radioactive carbon dioxide is mixed with the stable isotopes of carbon dioxide (\(^{12}\mathrm{CO_2}\) and \(^{13}\mathrm{CO_2}\)) in the atmosphere. When plants absorb atmospheric carbon dioxide during photosynthesis, they also assimilate the radioactive \(^{14}\mathrm{C}\) along with the stable isotopes. As the plants convert carbon dioxide into glucose and other organic molecules, the \(^{14}\mathrm{C}\) becomes integrated into their tissues, which is how plants end up containing \(^{14}\mathrm{C}\).