32.THE ATOMIC STRUCTURE- Understanding de broglie’s thesis,Wave Mechanics vs Quantum Mechanics

321In the last post we discussed how the de broglie’s hypothesis was validated by experimental data obtained from ,the double-slit experiment,performed by Davisson and Germer.

When examined on an sub-atomic scale, the concepts of particles and waves melted together.Why is it then,that on the macroscopic scale i.e in our day-to-day lives,such behaviour is not observed? If we throw a ball at a wall , it will always travel in a straight line and hit the wall at a specific point.This means it shows particle like behaviour and its behaviour is nowhere like a wave! How do we explain this?

The answer to this question is hidden in the de broglie’s relation –

λ = h/p = h/mv.
λ  = constant/mv.
λ ∝ 1/mv.

The above relation implies that the wavelength (λ) is inversely proportional to the mass of the object(m) and its velocity(v).

Case 1 –  If the object is at rest ,v=0.

If v=0 , then λ  = constant/m×(0).
∴ λ = ∞, which means the wavelength has no finite value i.e the wave doesn’t exist.Thus,

Particles do not exhibit wave-like properties when at rest.Matter waves exist only when the particle is in motion.

Case 2 – For moving objects,velocity and mass of the moving particle is inversely proportional to its wavelength.The velocity of the ball thrown at the wall is ridiculously lesser than the velocity of an electron orbiting around the nucleus.

Velocity of a free electron accelerated through 100 volts = 5.9×106 m/s = 5900000m/s.
Velocity of a ball = 40m/s.

Also,the mass of everyday objects is very large compared to that of an electron.

Mass of an electron = 9.11×10-31kg = 0.000000000000000000000000000000911 kg
Mass of a ball = 15 ×10-2kg =0. 15kg

Do you see the difference?

Let us now calculate de broglie’s wavelength for both the ball and the electron.

de broglie’s wavelength for an electron accelerated through 100 volts,

λ= h/mv
λ= [6.626 ×10-34 J.s]/[(9.11×10-31kg) ×(5.9×106 m/s)]
= 1.2 ×10-10 m     Note -[ J=kg m2 / s2.]
∴ λ=0.12nm = 1.2Å for the electron.This wavelength is comparable to the electron’s surroundings i.e diameter of an atom which is approximately  1-10Å.

Now for the ball ,

λ = [6.626 ×10-34 J.s]/[(0.15kg) ×(40 m/s)]
= 1.1 ×10-34 m.This wavelength is so so so very small when compared with the it’s surroundings(the ground which may be 1km = 1000m in diameter!).

 Thus,the wavelength of the moving ball  is so negligible compared to its surroundings , that it is never seen and thus not considered and the ball appears to move in a straight line.

Thus, for everyday objects, the de broglie’s wavelength is very small and thus, their wave-like behaviour is never seen.Thus, de broglie’s equation suggests that every moving particle(microscopic/macroscopic) has a wavelength associated with it.Only for larger objects, this wavelength is so small that it is never seen.This line of thought is calledWAVE MECHANICS‘.

(Mechanics ⇒ the branch of applied mathematics that deals with motion and forces that produce motion.Simply put, it is the science of motion of the bodies.)

Thus, wave mechanics is a branch of physics which studies the wavelike properties of matter.

Thus, taking Einstein’s work, de broglie introduced a concept of ‘Matter waves’ ,This concept was easier to comprehend for the scientific community,than Niels Bohr idea of ‘quantum jumps of an electron’, as they could picturize waves.Albert Einstein and de broglie thus thought that they had given the world a much better idea than Niels Bohr.

However, Niels Bohr was not ready to accept his defeat just yet! In 1916, he returned to his native land ,Copenhagen(Denmark).Here,he was considered as a celebrity .The Carlsberg brewery offered him a huge funding ,with which he built his research institute.This institute became a leading centre of research in theoretical physics and it started attracting a whole lot of young talent, who desperately wanted to work with Niels Bohr.

Thus, the theoretical physicists were now divided into two groups –

GROUP 1 ⇒Scientists who believed in Albert Einstein and de broglie’s WAVE MECHANICS.

&

GROUP 2 ⇒Scientists who believed in Niels Bohr and Pauli’s QUANTUM MECHANICS.

WAVE MECHANICS = Electrons behaves as waves.
QUANTUM MECHANICS = Electrons show quantum jumps from one orbit to other/discretisation of orbits.

The rivalry between these two groups intensified and both started outwitting each other .This competition lead to further research and produced two great physicists , one from each group, who totally loathed each other.Both these scientists were giants in the world of nuclear physics.They were – ERWIN SCHRÖDINGER and WERNER HEISENBERG!!

SCHRÖDINGER was a supporter of de broglie &

 HEISENBERG was a supporter of Niels Bohr.

Thus, the conflict between Einstein and Bohr intensified and became much like a war between Schrödinger and Heisenberg.This war lead to many inetersting discoveries.We shall start talking about these great scientists,their disputes and discoveries, in our coming posts.Till then,

Be a perpetual student of life and keep learning…

Good day !

References and further reading :

1.hyperphysics.phy-astr.gsu.edu
2.Clash of Titans – A BBC documentary.
3.http://www.spaceandmotion.com/Physics-Quantum-Theory-Mechanics.htm

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