Electronic Energy Levels of Atoms - Part 2

Distribution of electrons and protons in an atom can be imagined like this. An atom is like a tiny bee hive. The bee hive itself is the nucleus and the electrons are like bees flying around it. Similarly atoms consist of almost 90% empty space. Why is that? Have we ever wondered why electrons are distributed over a large space while protons are confined to a very small space?.

In the case of protons, there exists a nuclear force of attraction between them that acts at short distance only and hold the protons together. But in case of electrons, there is no such nuclear force of attraction. The is only an electrostatic force of repulsion between them. That is why electrons are distributed over a large distances from the nucleus.

This distribution can be best understood by introducing the term energy levels.There are 4 main energy levels named as K shell , L shell , M shell and N shell.K shell has an electron holding capacity of 2. L shell has a holding capacity of 8. M shell has 18 and N shell has a holding capacity of 32.The nearer an electron is to the nucleus, less energy it will have. The farther it is from the nucleus the higher the energy it will have. Each shell is further divided into subshells. Subshells consist of orbitals.

An illustration of shells and subshells is given below. As we can see the K shell is closest to nucleus and consists of an s subshell only.The second shell, which is L shell consists of an s subshell and a p subshell. The M shell consists of s, p and d subshells. The N shell consists s , p, d and f subshells. Electrons are distributed in a sequence first in the lower energy level and then in the higher energy level.

s , p , d and f subshells further consist of orbitals. Let us understand the term orbital. Electrons in an atom are moving with so much speed in such a small area that it is not possible to find the exact position of electrons. An orbital is a space around the atom where probability of finding the electron is maximum. For example, the illustration here shows that electron most probably can be found in the spherical area around the nucleus. This probability of presence of electron in a specific area is named as electron density. Why do we call it electron density and not electron? Because we are not sure about the position of an electron at specific instant so we name that area as orbital and the electron in that area as electron density.

A breakdown of shells, subshells and orbitals is shown here. K shell has one subshell called s. L shell has two subshells s and p. M shell has three subshells s, p and d. N shell has four subshells, s, p, d and f. Each orbital can hold maximum of 2 electrons.

We shall now discuss shapes of orbitals. S orbital is spherical in shape. This means that electron density is in the form of a sphere in this orbital around nucleus.

P orbitals are dumbbell shaped. In this orbital electron density is in the form of pairs of lobes on opposite sides of nucleus. P orbitals consists of Px orbital which is aligned on x-axis, Py orbital which is aligned on Y-axis and Pz orbital which is aligned on Z-axis.

The d subshell consist of 5 orbitals. The orbitals of the d subshell are illustrated here. They have complex geometry.

The f subshell consist of 7 orbitals. They are illustrated here. They have very complex geometry.

A new set of numbers were introduced to describe the presence of a specific electron, in a specific orbital, of a specific subshell, of a specific shell. For example, the numbers [2,1,-1,-1/2]. 2 means electron is in the 2nd shell which is M shell. 1 means electron is in the p subshell of M shell. -1 means electron is in the Px orbital of P subshell of M shell. -1/2 is representing the anticlockwise spin of electron. A bit confusing right? Let us study these quantum numbers in detail individually to see how they describe the electron.

There are 4 quantum numbers.Principal quantum number represented by n describes the principal shell of an atom. It describes the distance of electron from the nucleus. n can be 1,2,3 or 4. n=1 represents theK shell. n=2 represents the L shell. n=3 represents the M shell. n=4 represents the N shell. We can also find the number of orbitals in a given shell by the formula n². For example, for 2nd shell n=2 and number of orbitals will be 2², which is 4, named as s, px, py and pz.

The second quantum number is the Azimuthal quantum number represented by l. l can be 0,1,2,3. That is l=n-1. l is always 1 digit less than n. The Azimuthal quantum number describes the shapes of the subshells. l=0 describes the spherical shaped s subshell. l=1 describes the dumbbell shaped p subshell. l=2 describes the d subshell. l=3 describes the f subshell.

l always starts from n=l+1 shell.For example l=1, which is p orbital, starts from n=1 + 1 which is 2. Thus, p subshell starts from the 2nd shell. Similarly, d=2 which is d orbital, starts from n = 2 + 1 which is 3. Thus, d subshell starts from the 3rd shell. l is also known as the orbital angular quantum number.

The 3rd quantum number is the Magnetic quantum number represented by ml. It specifies the orientation of an orbital having a specific energy and shape in space. It tells us about the number of orbitals in a subshell. For a given value of l we can find the number of orbitals as ml= 2l + 1. For example, for d orbital l = 2 , so ml = 2×2 + 1, which is 5 orbitals. So d subshell has 5 orbitals oriented differently in space.Regarding the orientation of orbital, for a given value of azimuthal quantum number l value of ml ranges from -l to+l, including 0. For example, for p subshell l = 1 and value of ml will be -1,0,+1. Possible values of ml for a given value of l are given here.

A representation of magnetic quantum number for p orbital is given here.For p subshell, l = 1, and value of ml will be, -1,0,+1.

The 4th quantum number is the spin quantum number, represented by ms. Because electrons in an orbital are negatively charged, and spin around their own axis, a magnetic field is produced. So, in an orbital, if two electrons spin in the same direction, the resulting magnetic field of them will repel each other. Therefore, the atom will become unstable. To avoid this instability, electrons in an orbital spin in opposite directions to each other and their resulting magnetic fields cancel each other out. One electron spins around its own axis in the clockwise direction and the other spins in the anticlockwise direction.-1/2 is assigned to the clockwise spin of electron and +1/2 is assigned to the anticlockwise spin.

Now if we write some numbers like [2,1,-1,-1/2] it would be much clear to understand these numbers as to what they represent. The first is the principal quantum number. The second is the azimuthal quantum number. The third is the magnetic quantum number. The fourth is the spin quantum number.