Energy of Orbitals

As the study in the field of chemistry furthered over the centuries, scientists preferred rationalizing the otherwise anomalous behavioral patterns of atoms and molecules, thus introducing the Periodic Table put forward by Mendeleev and the Atomic Structure by Ernest Rutherford, later corrected by Bohr. The idea of the atomic structure much like a solar model is flawed in many ways. Still, the perk here is it can give the fundamental understanding of the Nucleus posing as the Sun at the center and the Electrons orbiting the Nucleus matching planets with the disparity that the Electrons populate the regions of space, which are called the Orbitals and the orbitals have varied orbital energy levels.


What is Principal Quantum Number (N)?

The foundation of orbitals chemistry starts with Bohr who established that electron orbitals represent an energy level in terms of their distance from the Nucleus. The Orbitals are named K, L, M, N… or 1, 2, 3, 4… in ascending order. These numbers are the Principal Quantum Numbers. A Principal Quantum number is denoted as 'n'. For example, for the K-orbital n = 1, for L-orbital n = 2, for M-orbital n = 3.


What is The Azimuthal Quantum Number (L)? 

Arnold Sommerfeld delved deeper into the orbitals chemistry, he viewed every orbital energy level or shell is made up of many subshells. He imagined that other than the circular orbits that Bohr established, there are elliptical orbits as well. The Azimuthal or Subsidiary quantum number helps to determine the ellipticity of the subshells. It is generally denoted as ‘l’.


To Denote the Value of 'l' Instead of 1, 2, 3… Some Spectroscopic Symbols are Used -


l

0

1

2

3

4

Spectroscopic Symbol

s

p

d

f

g


It should be noted that the subshells are energy levels as well, called Subsidiary orbital energy levels, so if we sort the subshells in ascending order in terms of their energy levels, it would be s < p < d < f.


Calculating the Energy Level of an Orbital

In a single electron, Hydrogen-like atom, the orbital energy i.e. the energy of that one electron depends just on the principal quantum number (n). In orbitals chemistry when it comes to filling up the atom with electrons, the Aufbau principle tells the lower energy level orbitals always come first. The order followed here is 1s <2s < 2p < 3s <3p < 4s… To easily memorize this anomalous behavior I strongly suggest following this diagram-

(image will be uploaded soon)

  • Since the electrons are negatively charged particles, they repel each other. The stability of an atom depends on the attraction between the electrons, positively charged Nucleus and repulsive force within the electrons. The particle can only be stable if the total attractive interaction is more than the whole repulsive interaction. 

  • As we go down the periodic table, the atomic number increases and another factor comes in to play here, i.e., shielding. Due to the presence of electrons in the inner shells, the total positive charge exerted by the Nucleus (Ze) is slightly hindered for the electrons in outer shells. The net positive charge felt by the electrons in the outer shells are termed as an effective nuclear charge (Zeffe ). 

  • The closer the orbital is to the Nucleus more tightly bound it would be. So an s-orbital electron will be more tightly bound to the Nucleus of that atom than a p-orbital.

  • The s-orbital particles will be of a lesser charge as it has a lower orbital energy, which means it would be a more negative charge than the electrons in the p-orbital, which will have smaller energy for its higher orbital energy compared to the d-orbital electrons.

  • In some cases, two orbitals may have the same n+l value; in those instances, the orbital with a lower n (principal quantum number) count will have low energy.

  • In some cases two orbitals may have the same n+l value; in those instances the orbital with a lower n (principal quantum number) will have a low energy. 


Solved Examples 

Q. Which of these orbitals has a lower orbital energy level 3d or 4s?

The n + l value of 3d orbital is (3 + 2) = 5, Similarly the (n + l) value of 4s is (4 + 0) = 5.

So the 4s orbital has a higher (n+l) value, thus has a higher orbital energy level. 


Ans. 3d


Q. Which of these orbitals has a higher orbital energy level 3d or 4p?

The (n+l) value of 3d orbital is (3+2) = 5, and 4p orbital is (4+1)=5. Both have the same (n+l) value with 3d having a lower n-count; thus, it is weaker and has a lower orbital energy level. 


Ans. 3d 


Fun Facts

The letters s, p, d ,f represent the shape of the orbitals. The s-orbital is spherical, and the Nucleus is in its center. The p-orbital has a form of a pair of lobes on each side of the Nucleus, somewhat has a dumbbell kind of structure.

FAQ (Frequently Asked Questions)

What Determines Orbital Energy?

The electrons spin around the Nucleus in orbit, and the energy level of the electron depends on the distance of the orbit from the Nucleus that is the foundation of orbitals chemistry. Each orbit has a given set of quantum numbers, such as the Principal Quantum Number (n), Azimuthal Quantum number (l) etc. Each orbital has many subshells, like 's,' 'p', 'd','f', 'g', having the value of 0,1,2,3,4, respectively. The energy level of an orbit is determined by the (n+l) value of that particular orbit. To calculate the energy level of 5s orbital, we need to calculate the (n+l) value that is (5+0) = 5.

What are 4 Types of Orbitals?

In Orbitals Chemistry, each principal orbit is made up of many subshells. There are mainly four types of orbitals; they are termed as s-orbital, p-orbital, d-orbital, f-orbital, the names represent, Sharp, Principal, Diffuse, and Fundamental respectively. Each orbital has its quantum number that is the Azimuthal quantum number (l). The s-orbital has the azimuthal quantum number value of 0, the p-orbital has a value of 1, and the d-orbital has two and f-orbital 3. The orbital energy levels of these are varied, s-orbital having the lowest energy level and f-orbital being the highest, summed up as s < p < d < f.