Bohr Second Postulate of Quantisation: Overview, Questions, Preparation

After conducting scientific experiments, De Broglie came to a conclusion that particles like electrons can also exhibit wave like properties under certain conditions. Electrons who orbit the nucleus have the ability to form a standing wave around the orbit. The wavelength of this electron can be denoted as:

λ=h/p​=h/mv​

Where,

λ = De Broglie wavelength

h = Planck's constant

p = momentum of the particle

m = mass of the particle

v = velocity of the particle

The wave must be a standing wave if it wants to be stable in the orbit. For this to be possible, the circumference of the orbit must be a multiple of electron’s wavelength. This is exactly what leads to quantized angular momentum. Mathematically, it can be represneted as:

2πr=nλ

Where n = 1,2,3......

Now, Substitute De Broglie’s formula with λ

2πr=n*h/mv

mvr=n*h​/2π

L=mvr=nℏ

This is what Bohr’s postulate states.

Hence = Proved

This theory turned out to be revolutionary in proving the wave nature of the electron. De Broglie helped provide a strong evidence to Bohr’s model of atom and helped understand why to assume the quantized angular momentum. It also offered the base for foundation of quantum mechanics by connecting the bridge between classical and quantum mechanics, and brought a revolution in the field of physics.

Here are a few core conclusions that the above derivation jumped on to:

• Particle must form a standing wave around the nucleus in order to be stable and fit in the orbit.
• Electron will only revolve in certain fixed orbits, the ones who are an integral multiple of the wavelength.
• We do not randomly require assuming that angular momentum is quantized; this theory helped offer the connection of Bohr postulate to De Broglie’s statement.