This question is asking for the electron configuration of chlorine. From the periodic table, we can see that chlorine is found in group seven as one of the halogens. Furthermore, it is found on the third row of the table.

Recall that as one progresses, one element at a time, through the periodic table, one proton and one electron are added each time. For chlorine, because it is found in the seventh column of the table, we know that it has seven valence electrons.

Moreover, when writing the electron configuration of the elements, it's often useful to use a shorthand to make things easier. This shorthand consists of using the last noble gas to indicate the electron configuration of all the inner shell electrons. In the case of chlorine, all of its inner shell electrons are equivalent to neon.

So instead of writing out all of the electrons in each of their shells and subshells (which can get very long), it's useful to put the last noble gas in brackets to indicate the inner shell electrons. After the bracket, the valence shell electrons are shown.

Also, it's important to remember that shells of a lower energy level are filled before higher level energy shells. Because p orbitals are always higher in energy than s orbitals, the s orbitals of the chlorine atom will fill first, followed by the p orbitals. Thus, the correct electron configuration for chlorine can be shown as .

For any n, the energy level can hold 2n² electrons, since there are two electrons for each orbital.

The azimuthal quantum number is the second quantum number, designated by the letter l. It gives the shape and number of subshells in a principal energy level (shell). 

The sets of quantum numbers needs to follow the following rules: n (principal quantum
number) needs to be a positive integer, l can have any integral value from 0 to n – 1, and ml can range from –l to l. The only quantum numbers that follows these rules are (a).

The energy of an electron is related to the quantum number by the equation E = -R/n², where R is constant. The negative charge make it so that as n increases, the numerical value of the energy becomes less negative, approaching zero. Thus the energy increases as n increases.

First, we will write out the electron configuration for the ground state Manganese atom, considering only the valence electrons:

The orbitals highest in energy will be filled last, so our highest energy orbitals are orbitals.

The angular momentum quantum number describes the shape of the orbital, with orbitals corresponding to , orbitals corresponding with , and orbitals corresponding to , and so on.

We are considering a orbital, so .

The principle quantum number, , must always be an integer greater than zero.

The angular momentum quantum number, , can have values from zero up to .

The magnetic quantum number, , ranges from  to .

The spin quantum number, , must be  or .

To total, a set of quantum numbers follows the pattern: 

The only answer option that presents an invalid set of quantum numbers is . In this option, the angular momentum quantum number, , has an illegal value; it must be between zero and , and thus cannot be equal to 3.

The aluminum atom has its furthest electrons in the 3p shell. We know this because aluminum is in the third row of the periodic table, and is in the p-block. The possible quantum numbers for any valence electron are: 

There are four quantum numbers; l indicates the type of orbital (s, p, d, f), which describe the shape of the orbital. An s orbital is spherical, p orbitals are dumbbell shaped, d and f orbitals are slightly more elongated than p orbitals. The n quantum number denotes the energy level, and can be positive integers only. The magnetic quantum number, m_l denotes the specific subshell within an electron shell. Lastly, the spin number, m_s denotes the spin of a specific electron. Since only two electrons can occupy any one orbital, this number is usually represented as an up arrow or a down arrow (or a positive sign or a negative sign). 

Ammonium is NH₄₊. It is formed by the association of NH₃ with H+. Thus, NH3 acts as a Lewis base, and H+ is a Lewis acid. This is a coordinate covalent bond, and there is one of these in the molecule. The remaning three bonds are polar covalent (N–H bonds).