The location of a given electron is described by a set of four quantum numbers. Of these, the magnetic quantum number () gives the orientation of the orbital in three-dimensional space.

The principle quantum number, , gives the energy level of the electron. It essentially describes the size of the electron shell, and can be any integer value.

The azimuthal (angular momentum) quantum number, , refers to the subshell of the energy level. Each subshell has a different shape, corresponding to spdf configurations. can be any value from zero to .

The magnetic quantum number, , gives the orientation of the subshell given by the azimuthal quantum number. For example, a p orbital has three different orientations based on three different values for the magnetic quantum number. These values correspond to orientations along the x-axis, y-axis, or z-axis. Each orientation constitutes a different orbital and can hold exactly two electrons. The magnetic quantum number can be any integer greater than and less than , with the total number of possible orbitals given by .

 is the electron spin quantum number. This number is used to distinguish between the two electrons in a single orbital.

() is not a quantum number. This is a formula that allows us to determine the possible values of  for every principal quantum number.

 is the correct configuration for a neutral sodium atom.

A neutral sodium atom contains eleven electrons, so you can eliminate  and  which contain twelve and ten electrons, respectively.

Next,  can be eliminated because of the Aufbau principal, which states that electrons are placed into orbitals from the lowest to highest energy. In this answer choice, the  (lower energy) orbital is not completely filled, containing only five out of the possible six possible electron that it can hold. This orbital must be filled completely before electrons can be placed in the  (higher energy) orbital.

 is incorrect because there are seven electrons in the  orbital. This is impossible, as p orbitals hold a maximum of six electrons.

The noble gas electron configuration for fluorine, , in its ground state is  . We can see from this configuration that there are seven valence electron in its outer shell of  

When an element gains or loses charge, becoming a cation or an anion, it is either gaining or loosing electrons. Anions (negatively charged ions) have gained electrons and cations (positively charged ions) have lost electrons. 

The  ion has gained one electron, increasing its total valence electrons by one. The new noble gas electron configuration for the ion will be , with eight valence electrons. The ion is now isoelectronic to the noble gas neon, and satisfies the octet rule.

To write the noble gas configuration of an element, choose the noble gas in the row above the element to put in brackets. For sulfur, that is the noble gas neon, .

Then, you write the rest of the configuration beginning on the same row as the given element. Sulfur is in the third row, or period, which means that it must start with the orbital. Continuing to fill the orbitals, we get the configuration .

Writing electron configuration this way can save time, and easily tells us how many valence electrons an element has. Sulfur has six valence electrons, shown by the number of electrons in the third energy level.

In its ground state, phosphorous has five valence electron.

We can determine the number of valence electrons by examining the ground state electron configuration of an element. The ground state electron configuration of phosphorous is:

From this configuration we can see that the outermost shell is . In its outer shell there are two electrons in the  subshell and three electrons in the  subshell, giving us a total of five valence electrons. Keep in mind that the different subshells correspond to different orbitals in the same energy level. When determining valence electrons, all electrons in the highest energy level must be included.

A noble gas electron configuration is achieved when an atom has an octet electron configuration, indicating its most stable state. For example, sulfur (S), at its ground state, has 6 valence electrons. When it gains two electrons (-2 charge), it has eight electrons, fulfilling the octet.

All of the answer choices, except , have octet/noble gas electron configurations. Phosphorus (P), at its ground state, has 5 valence electrons. A -2 charge will create an ion with 7, not 8, electrons.

Carbon is an element with six protons (atomic number six), and most commonly has six neutrons. This brings the total mass of carbon to twelve atomic mass units (12amu). There are isotopes of carbon with seven or eight neutrons, which are radioactive. These isotopes correspond to carbon-13 and carbon-14. The true atomic mass of carbon on the periodic table is 12.011amu, accounting for small contributions by these heavier isotopes.

Carbon-6, cabron-7, carbon-8, and carbon-9 imply isotopes with zero, one, two, and three neutrons respectively. Though these isotopes could theoretically exist, they would be extremely unstable and do not occur in nature.

Isotopes are variations of an element that differ by the number of neutrons in the nucleus. Neutrons are neutrally charged, so adding or removing them from a nucleus does not alter the charge of the atom. The atomic number is the number of protons in an atom, and the mass number is the sum of both protons and neutrons in the nucleus. As a result, the mass number will change by adding a neutron.

The number of protons is equal to the atomic number of the element. Adding or subtracting protons will change the element's identity. Ions can be created by changing the number of electrons and isotopes can be created by changing the number neutrons, but changing the number of protons changes the element.

Ions are atoms that have gained or lost electrons. This results in an atom with a charge. Atoms with a neutral charge have an equal number of protons and electrons. Changing the electron number will result in a charge on the atom.

For example, adding an electron to chlorine creates a chlorine anion.

Two atoms are isoelectric if they each have the same number of electrons. Ions of an element will vary in the number of electrons, but isotopes will vary in the number of neutrons only. In its ground state, fluorine has 9 electrons, equal to the number of protons in order to have a neutral atom. Any ground state isotopes of fluorine will also have 9 electrons, making them isoelectric.