80. Covalent Bonding(26) – Molecular Orbital Theory(1).

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!

sunlight-eps-vector_k4053185.jpg

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.

801.jpg

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.

812.jpg
Figure 1

For Figure Above

A1

A2

Aresultant

crest meets crest

+1
(upward displacement)

+1
(upward displacement)

+2
(twice the upward displacement)

 trough meet trough

-1
(downward displacement)

-1
(downward displacement)

-2
(twice the downward displacement)

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.

813.jpg
Figure 2

For Figure Above

A1

A2

Aresultant

crest meets trough

+1
(upward displacement of the crest)

-1
(downward displacement of the trough)

0
(No wave)

trough meets crest

-1
(downward displacement of the trough)

+1
(upward displacement of the crest)

0
(No wave)

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.

814.jpg
Figure 3

For Figure Above

A1

A2

Aresultant

crest meets trough

+1
(upward displacement of the crest)

-0.4
(downward displacement of the trough)

+0.6
(Wave with smaller crest amplitude than A1)

trough meets crest

-1
(upward displacement of the crest)

+0.4
(downward displacement of the trough)

-0.6
(Wave with smaller trough amplitude than A1)

(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 –

  1. https://www.gograph.com/vector-clip-art/sunlight.html

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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