All About Energy Levels

As we all know, an atom consists of protons, neutrons, and electrons. Protons and neutrons reside in the nucleus of an atom, and electrons spin around the nucleus. Electrons can move around, jump around and bind with other atoms. But they cannot do so in any manner and any position. They have fixed energy levels in which they can do so. We can create an analogy of energy levels with the staircase steps. As in the staircase, you can stand on one step or another at a time but not in the space between them. Similarly, electrons can be in any energy level but not in the space between energy levels.

We can call energy levels atomic orbitals for electrons in an atom. However, electrons do not have the freedom to choose any energy levels of an atom. They are allowed to be at certain energy levels.

So, an electron in an atom will exist in any one of the allowed energy levels in Bohr’s atomic model and not in between energy shells. If an electron is residing in the first energy level, it must have exactly -13.6eV of energy. Similarly, if it is in the second energy level, then it will have -3.4eV of energy, and therefore it cannot have values like -9eV or -7eV or any other value in between.

So, whenever an electron wants to jump from one energy level to another, it will emit the energy or be required to gain it. We suppose that an electron in a neutral hydrogen atom wants to jump from its first energy level, i.e., n=1, to its second energy level, i.e., n=2. Since the second energy level has greater energy than the first energy level, an electron will be required to gain energy to jump from the first to the second energy level. The energy required to jump will be equivalent to (-3.4) – (-13.6) = 10.2 eV. This energy required can be absorbed from light by electrons. 

Now, if an electron in a hydrogen atom wants to jump back from the second energy level n=2 to the first energy level n=1, then it must emit some energy. This energy exchange is done in discrete units known as photons, and these photons have definite energy. Therefore, while making a transition from the first to second energy level, an electron will be required to get a photon of exactly 10.2eV. If the electron is coming back to the first energy level, it will emit the photon of 10.2eV. 

Electrons in an atom of an element are always added to its lowest energy levels until the maximum number of electrons possible for that level is filled. When the lowest level is filled, the electrons are filled in subsequent energy levels of the atom. The maximum number of electrons possible to be filled in a particular orbit is dependent on the number of orbitals. Electrons present in the outermost orbital or energy level are known as valence electrons. They play a major role in understanding many properties of the atom, including the reactivity of the atom.

As we know, energy levels are also known as atomic orbitals. But these energy levels are known to be Quantized. An electron is a three-dimensional wave-particle with no precise location and is delocalized over space. Our periodic table arranges elements with electrons from the lowest energy level to the highest energy levels. Bound electrons are delocalized in three-dimensional quantized energy levels of Bohr’s explanation of energy levels.

Mathematically, to calculate the energy of these atomic orbitals:

En = – 2π2 me4 Z2 / h2 n2

Where,

n = 1 is the first level (the ground state)

n = 2 is the second level (the first excited state, 1st level above the ground state)

n = 3 is the third level (the second excited state, 2nd levels above the ground state)

The above equation is valid for hydrogen or hydrogen-like species. Example: H, He+ , Li2+, etc. 

We will be required to have more complicated equations for other situations. 

Orbitals are also known as wave functions and help to correctly identify the region of the space occupied by an electron. We can also find nodes-regions with a 0% probability of finding an electron.

We define quantum numbers to name the energy levels or the orbitals.

n is known as the principal quantum number and helps to determine the energy, size, shell, row of an electron

l is known as the Azimuthal Quantum Number and helps to know about the shape of the energy level.

ml  is known as a magnetic quantum number, specifies an orbital, gives the orientation of the orbital, and gives direction.

ms  is known as spin orientation quantum number and it gives the orientation of the electron, “up” or “down”.

We can have a unique address for every electron in an atom in Bohr’s atomic model with the help of the above-mentioned quantum numbers.