The Energy Levels of Molecules

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The Energy Levels of Molecules

The phenomena of chemistry cannot be understood thoroughly without a firm grasp of the principle concept of quantum mechanics. When talking about energy levels, quantisation has to be considered, and this quantisation is the basic assumption of Quantum theory. This is when all the energy levels are quantised meaning that they can have only discrete values. This quantisation is defined through a quantum number, which usually have integers or half integers as values. These quantum numbers can only be fixed values whereas a classical particle can have any value when changing from one energy level to another. The molecule normally accepts one quantum of energy and the size of this quantum must be exactly the same as the difference between these two levels. Therefore this statement describes us the quantisation of energy. An element can only be present in certain energy levels corresponding to various quantum states (as shown below), but the energy of an electron cannot be found between any shown levels. Energy quantisation is universal because it holds for all kinds of systems like atoms, nuclei, molecules or electrons in solids.

The principle energy levels of electrons

Shell

Principle Quantum Number

Period (horizontal row)

Maximum Number of Electrons = 2n2

Energy sublevels

K

2

S

L

2

2

8

S p

M

3

3 - 4

8

S p d

N

4

4 - 6

32

S p d f

O

5

5 - 7

32 (2n2 = 50)

S p d f

P

6

6 - 7

8 (2n2 = 72)

S p d *

Q

7

7

* *Man-Made

* Elements

S *

Kinetic Energy

There are three different forms of Kinetic Energy in molecules, as follows:

> Translational Energy - This is when single diatomic molecules move at a certain velocity in a straight line.

> Rotational Energy - This is when single diatomic molecules can rotate around their centre of gravity.

> Vibrational Energy - This is when single diatomic molecules at the end of the bonds can move relative to each other. There are approx. 1012 oscillations per second i.e. the frequency of vibration is 1012 s-1.

The above are classified as forms of Kinetic Energy because they are forms of energy
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due to their movement. Each of the above energy levels are quantised, but the molecule can change its speed, it's rotational frequency or vibrational frequency to other allowed values and therefore the change in the energy stored in this mode. The molecule also has the equivalent Potential energy i.e. the energy due to the arrangement of the electrons in the molecule, therefore the following energy must be taken into account, Electronic Energy.

The sum of these four types of energies must be equivalent to the total energy in the molecule, as follows:

ETotal = ETranslational + ...

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