Protons and neutrons are found in the nucleus of atoms, while electrons are found in orbitals around the nucleus.

First, start off by finding S (sulfur) on the periodic table. According to the period table, the atomic number for sulfur is 16. That means that sulfur (in it's uncharged, unionized state) has 16 protons, and 16 electrons. Since this ion has a negative two charge, we know it has picked up two extra electrons. Thus  contains 18 electrons.

A diatomic element is an element that will spontaneously bond with itself if it isn't already part of a compound. This is done to increase stability. The seven diatomic elements are hydrogen, oxygen, nitrogen, fluorine, chlorine, bromine, and iodine. Note that all of these except iodine are gasses at room temperature. Helium is a noble gas, which means it has a full valence shell. Helium does not need to bind to anything to increase its stability.

An atom's valence electrons are the electrons on the outermost shell surrounding the atom. For the first shell, the number of valence electrons can be at most 2. For all subsequent shells, the maximum is 8. To determine the number of valence electrons around a neutral atom, you match the atom with its group number. As you can see from the picture below, fluorine has a group number of 7. Therefore, it has 7 valence electrons.

We rank the order of orbital filling in order of increasing energy given the probability of an electron occupying a given space. Take into consideration the Aufbau principle, which states that electrons fill electron orbitals from most to least stable. Recall that eight electrons constitutes a full valence shell for all orbitals except for the first one, which has a maximum occupancy of two electrons. The order in which electrons are filled is as follows:

We rank the order of orbital filling in order of increasing energy given the probability of an electron occupying a given space. Take into consideration the Aufbau principle, which states that electrons fill electron orbitals from most to least stable. Recall that eight electrons constitutes a full valence shell for all orbitals except for the first one, which has a maximum occupancy of two electrons. The order in which electrons are filled is as follows:

We rank the order of orbital filling in order of increasing energy given the probability of an electron occupying a given space. Take into consideration the Aufbau principle, which states that electrons fill electron orbitals from most to least stable. Recall that eight electrons constitutes a full valence shell for all orbitals except for the first one, which has a maximum occupancy of two electrons. The order in which electrons are filled is as follows:

Quantum numbers are used to describe the location of an electron within the electron cloud. The first quantum number corresponds to the energy level, which matches with the period of the periodic table in which the element is usually found. The second quantum number describes the electron subshell, corresponding to the s, p, d, and f subshells. The third quantum number tells the orbital within the subshell that holds the electron. Finally, the fourth quantum number describes the spin of the electron as either positive or negative. Each orbital can only carry two electrons.

The first quantum number is a positive integer:

The second quantum number is any integer greater than zero and less than the first quantum number:

The third quantum number is an integer between the value of the second quantum number and its inverse:

The final quantum number can only carry a value of positive or negative one-half:

The answer choice that gives an impossible set of quantum numbers has a negative second quantum number. The first and second quantum numbers will always be greater than or equal to zero.

The ground state electron configuration for calcium is:

The question asks us to give the  value for the valence electrons in calcium. Valence electrons are located in the outermost shell, the shell with the highest principle quantum number. For calcium, the outermost shell is 4s. The  value that corresponds to 4s is . 

The other answer choices are incorrect because they describe the  value for the location of non-valence electrons.

The, principal quantum number, , tells us the energy shell that is represented as the leading coefficient in electronic configuration. We can see that the given orbital has a leading coefficient of .

The angular momentum (azimuthal) quantum number, , tells us the shape of the orbital. Each shape corresponds with a numerical value of  and a letter. The values for  and their corresponding subshells are listed below:

We are given an orbital with a p subshell, indicating that the angular momentum quantum number must be .