Question

Carbon- 14 dating is a method used to determine the age of historical artifacts by examining the ratio of two isotopes of carbon (carbon- 14 and carbon-12). A living plant consumes carbon dioxide in the photosynthesis process and incorporates the carbon, including \({ }^{14} \mathrm{C}\), into its molecules. As long as a plant lives, the \({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\) ratio in its molecules remains the same as in the atmosphere because of its continuous uptake of carbon. However, as soon as a tree is cut to make a wooden bowl or a flax plant is harvested to make linen, the \({ }^{14} \mathrm{C}^{12} \mathrm{C}\) ratio begins to decrease because of the radioactive decay of \({ }^{14} \mathrm{C}\left({ }^{12} \mathrm{C}\right.\) is stable). By comparing the current \({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\) ratio to the presumed ratio when the artifact was made, one can estimate the age of the artifact. For carbon-14 and carbon- 12 , how many protons and neutrons are in each nucleus? Assuming neutral atoms, how many electrons are present in an atom of carbon- 14 and in an atom of carbon-12?

Short answer

In summary, for carbon-14 and carbon-12 isotopes, both have 6 protons and 6 electrons in their respective atoms. The difference lies in the number of neutrons, with carbon-14 having 8 neutrons and carbon-12 having 6 neutrons.

Step-by-step solution

Understanding atomic structure and isotopes

: An atom is composed of a nucleus (which contains protons and neutrons) and electrons that orbit around the nucleus. The number of protons in an atom is called its atomic number (Z), while the sum of protons and neutrons is called its mass number (A). Isotopes are atoms of the same element (having the same atomic number) but with different mass numbers due to a different number of neutrons.

Find the atomic number (Z) for carbon

: The atomic number of carbon is denoted as Z, which is the number of protons in its nucleus. By looking at the periodic table, we find that the atomic number of carbon (C) is 6, meaning that all carbon atoms have 6 protons.

Determine the mass number (A) for carbon-14 and carbon-12

: For carbon-14, the mass number (A) is given as 14, while for carbon-12, the mass number (A) is given as 12. This indicates that carbon-14 has 14 nucleons (protons and neutrons) in its nucleus, while carbon-12 has 12 nucleons in its nucleus.

Find the number of neutrons for each isotope

: To find the number of neutrons in each isotope, we need to subtract the atomic number (number of protons) from the mass number (number of protons and neutrons). For carbon-14: \(n_{14} = A_{14} - Z = 14 - 6 = 8\) For carbon-12: \(n_{12} = A_{12} - Z = 12 - 6 = 6\) Hence, carbon-14 has 8 neutrons and carbon-12 has 6 neutrons.

Find the number of electrons for each isotope

: Since the atoms of carbon-14 and carbon-12 are neutral, the number of electrons is equal to the number of protons in each isotope. Recall that carbon has an atomic number of 6, which means that all carbon atoms, regardless of their isotopic forms, have 6 electrons. Thus, both carbon-14 and carbon-12 have 6 electrons each. By following these steps, we have determined that carbon-14 has 6 protons, 8 neutrons, and 6 electrons, while carbon-12 has 6 protons, 6 neutrons, and 6 electrons.

Key concepts

Isotopes

Isotopes are different forms of the same element. They all have the same number of protons in their nuclei but differ in the number of neutrons. This means they have the same atomic number but different mass numbers.
For example, carbon has several isotopes, with carbon-12 and carbon-14 being the most studied. Carbon-12 has 6 protons and 6 neutrons, making its mass number 12. Carbon-14, on the other hand, has 6 protons and 8 neutrons, making its mass number 14.
In isotopes, the chemical properties remain the same because the protons and electrons, which determine the chemical behavior, are not different. However, the physical properties, such as atomic mass, do change due to the different number of neutrons.

Atomic Structure

Atomic structure refers to the composition of an atom, which includes a nucleus and orbiting electrons. The nucleus is made up of protons, which are positively charged particles, and neutrons, which carry no charge. Surrounding the nucleus, electrons move in orbits or shells with a negative charge.
Each element is defined by its number of protons, known as the atomic number. For carbon, this number is 6. This means every carbon atom has 6 protons. The sum of protons and neutrons is called the mass number. This is what differs in isotopes.
By understanding the atomic structure of an element, you can determine how it will engage in bonding and interactions with other atoms. For carbon-12 and carbon-14, both isotopes have the same number of electrons as protons. This balance maintains their neutrality.

Radioactive Decay

Radioactive decay is a process by which unstable atomic nuclei lose energy. This happens by emitting particles or electromagnetic waves. Carbon-14 is a radioactive isotope, which means it is unstable and gradually transforms into a different element through decay.
This decay occurs at a predictable rate, known as the half-life, which is roughly 5,730 years for carbon-14.
In carbon dating, scientists use this predictable decay to determine the age of artifacts that contain organic material. By measuring the ratio of carbon-14 to carbon-12, scientists can backtrack to find out when the organism stopped incorporating carbon, which happens when it dies.

Photosynthesis

Photosynthesis is a fundamental process used by plants to convert light energy into chemical energy, stored in glucose. During this process, plants absorb carbon dioxide from the atmosphere.
While absorbing carbon dioxide, carbon isotopes—including carbon-14—are incorporated into the plant. This means that living plants maintain a constant proportion of carbon isotopes, similar to that in the atmosphere.
Once the plant dies or is harvested, the intake of carbon stops, and the ratio of carbon isotopes starts to change due to the decay of carbon-14. This premise is the basis for carbon-14 dating, where scientists can pinpoint when a plant or animal was alive by examining its carbon isotope ratios.