Molecular orbital theory(MOT) is a quantum mechanical approach to bonding. This theory considers an orbital as a wave function(ψ).In order to understand MOT, it is imperative that we know the basic principles of wave superimposition.
What is a wave?
A wave is a disturbance that transfers energy through matter or space from one point to other. So, a wave can be thought of as an energy transport phenomenon.
e.g. – Sunlight reaches earth in the form of light waves. The heat and light energy from the sun is transported across space via these waves. This heat and light energy is the reason we have life on our planet!
Waves consist of – Crests and troughs.
Crest → The point on the wave with the maximum value of upward displacement/the highest point in the cycle.
Trough → The point on the wave with the maximum value of downward displacement/lowest point in the cycle.
Wavelength → Distance between successive crests or successive troughs.
Amplitude → Height of the wave from equilibrium position either upwards or downwards. The higher the energy of the wave, the higher is its amplitude and vice versa.
Interference and superposition of waves.
When two or more waves meet, they superpose, to form a resultant wave and the phenomenon is called interference of waves.
Principle of superposition of waves –
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
This means that when two waves traveling independently meet, the resultant that is generated will have an amplitude which is the algebraic sum (addition) of the amplitudes of those waves at that location. (This concept is explained with examples below).
Interference is of two types –
1)Constructive interference
2)Destructive interference
CONSTRUCTIVE INTERFERENCE – In this type of interference, both interfering waves have the same displacement in the same direction at the same point of time i.e they are in phase. So, when they meet, the crest of one wave superposes with the crest of another wave, and the troughs coincide too. This has an additive effect and thus the resultant wave has a higher amplitude than the parent waves.
|
For Figure Above |
A1 |
A2 |
Aresultant |
|
crest meets crest |
+1 |
+1 |
+2 |
|
trough meet trough |
-1 |
-1 |
-2 |
DESTRUCTIVE INTERFERENCE – When both interfering waves are out of phase i.e they have displacement in opposite direction or they are traveling in the opposite direction, they destructively interfere with each other. These two waves cancel each other if they have the same amplitude. Thus, the resultant is a straight line.
|
For Figure Above |
A1 |
A2 |
Aresultant |
|
crest meets trough | +1 | -1 |
0 |
|
trough meets crest | -1 | +1 |
0 |
However, if the two-parent waves are not similar, then, the amplitude of the resultant wave is less than that of the highest amplitude parent wave.
|
For Figure Above |
A1 |
A2 |
Aresultant |
|
crest meets trough | +1 | -0.4 | +0.6 |
|
trough meets crest | -1 | +0.4 |
-0.6 |
(In the above tables, the numerical values given to A1 and A2 are randomly chosen as examples).
With our understanding of waves, we will learn the MOT in our next post. Till then,
Be a perpetual student of life and keep learning…
Good Day!
Image source –
References and Further Reading –
1.https://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves
2.https://www.physicsclassroom.com/class/waves/Lesson-2/Energy-Transport-and-the-Amplitude-of-a-Wave
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