Two students are studying using a plastic model of the atom to which they can easily add or remove electrons, protons, and neutrons. They build a model for the neutral \({ }_{6}^{14} \mathrm{C}\) atom. Their next job is to make the \(+2\) ion of this carbon isotope. Student \(\mathrm{X}\) removes two electrons from the atom. Student \(\mathrm{Y}\) adds two protons to the atom's nucleus. Did both students successfully construct a \(+2\) carbon-14 cation? Explain.

Understanding the carbon-14 cation begins with knowing what a cation is. In simple terms, a cation is an ion with a positive electric charge, which occurs when there are more protons than electrons in an atom.

For the carbon-14 cation, the neutral atom must lose electrons. Carbon-14 is a specific isotope of carbon where the atom has 6 protons (since carbon's atomic number is always 6) and 8 neutrons, leading to a mass number of 14. When two electrons are removed from the neutral carbon-14, as student X did in our problem, the atom becomes a cation with a +2 charge because it now has two more protons than electrons.

It's crucial to note that in creating a cation, the number of protons and neutrons remains unchanged. Only the electron count is altered, leading to the positive charge due to the imbalance. The symbol for this carbon-14 cation is ({}_{6}^{14} C^{+2}), which shows the element (carbon), its atomic number (6), its mass number (14), and its charge (+2).

Isotope notation is a shorthand way of indicating the atomic number, chemical element, and mass number of an isotope. The notation ({}_{Z}^{A} X^{q}) includes the element symbol 'X', the atomic number 'Z', the mass number 'A', and the ion charge 'q' if applicable.

For example, considering carbon-14, its isotope notation is ({}_{6}^{14} C). Here, the '6' (subscript) is the atomic number, which corresponds to the number of protons and, in a neutral atom, also the number of electrons. The '14' (superscript) is the mass number, totaling the protons and neutrons. This notation provides all necessary information to identify the isotope and to understand its nuclear composition.

The nucleus of an atom contains protons and neutrons, whereas electrons orbit around the nucleus. The number of protons (positively charged) defines the element's identity and is equal to the atomic number. An atom's electrons are negatively charged and in a neutral atom, their number is equal to the number of protons. Neutrons, which have no charge, contribute to the mass of the atom but not to its electrical charge.

In the case of the carbon-14 isotope, it has 6 protons, 6 electrons (in its neutral state), and 8 neutrons. These subatomic particles form the basis for understanding atomic structure and the behavior of ions. By changing the number of electrons, an ion is formed. Removing electrons results in a positively charged ion (cation), while adding electrons leads to a negatively charged ion (anion).

To calculate the charge of an ion, one needs to understand the balance, or imbalance, between the number of protons and electrons. The fundamental rule is that the charge equals the number of protons minus the number of electrons.

In the exercise, we saw student X create a carbon-14 cation with a +2 charge by removing two electrons from a neutral carbon-14 atom. The calculation for this is straightforward: Charge = number of protons (6) - number of electrons remaining (4) = +2 .

This calculation is essential for understanding the electric charge of ions. It is always important to remember that protons define the element's identity and that the addition of protons, like what student Y attempted, transforms the atom into a completely different element, not just an ion of the original element.