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De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation | Physics for JEE Main & Advanced PDF Download

Angular Momentum Of Electron

What is Angular Momentum of Electron?
Angular momentum of an electron by Bohr is given by mvr or nh/2π (where v is the velocity, n is the orbit in which electron is, m is mass of the electron, and r is the radius of the nth orbit).
Bohr’s atomic model laid down various postulates for the arrangement of electrons in different orbits around the nucleus. According to Bohr’s atomic model, the angular momentum of electron orbiting around the nucleus is quantized. He further added that electrons move only in those orbits where angular momentum of an electron is an integral multiple of h/2. This postulate regarding the quantisation of angular momentum of an electron was later explained by Louis de Broglie. According to him, a moving electron in its circular orbit behaves like a particle wave.

De Broglie’s Explanation to the Quantization of Agular Momentum of Electron:

The behaviour of particle waves can be viewed analogously to the waves travelling on a string. Particle waves can lead to standing waves held under resonant conditions. When a stationary string is plucked, a number of wavelengths are excited. On the other hand, we know that only those wavelengths survive which form a standing wave in the string, that is, which have nodes at the ends.

Quantization of Angular Momentum of ElectronQuantization of Angular Momentum of Electron

Thus, in a string, standing waves are formed only when the total distance travelled by a wave is an integral number of wavelengths. Hence, for any electron moving in kth circular orbit of radius rk, the total distance is equal to the circumference of the orbit, 2πrk.

2πrk = kλ
Let this be equation (1).
Where,
λ is the de Broglie wavelength.
We know that de Broglie wavelength is given by:
λ = h/p
Where,
p is electron’s momentum
h = Planck’s constant
Hence,
λ = h/mvk

Let this be equation (2).
Where mvk is the momentum of an electron revolving in the kth orbit. Inserting the value of λ from equation (2) in equation (1) we get,
2πrk = kh/mvk

mvkrk = kh/2π
Hence, de Broglie hypothesis successfully proves Bohr’s second postulate stating the quantization of angular momentum of the orbiting electron. We can also conclude that the quantized electron orbits and energy states are due to the wave nature of the electron.

The document De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation | Physics for JEE Main & Advanced is a part of the JEE Course Physics for JEE Main & Advanced.
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FAQs on De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation - Physics for JEE Main & Advanced

1. What is the formula to calculate the angular momentum of an electron?
Ans. The angular momentum of an electron can be calculated using the formula L = mvr, where L is the angular momentum, m is the mass of the electron, v is the velocity, and r is the distance between the electron and the nucleus.
2. How does De Broglie explain Bohr's second postulate of quantisation?
Ans. De Broglie explains Bohr's second postulate of quantisation by introducing the concept of wave-particle duality. According to De Broglie, electrons exhibit both wave and particle properties. He suggests that the electron's motion around the nucleus can be thought of as a standing wave, and only certain standing wave patterns are allowed, leading to quantized energy levels.
3. What is the significance of Bohr's second postulate of quantisation?
Ans. Bohr's second postulate of quantisation is significant because it explains why electrons occupy only certain energy levels in an atom. It helps to explain the stability of atoms and the discrete emission and absorption spectra observed in atomic spectra. This postulate laid the foundation for the development of quantum mechanics.
4. How does the De Broglie wavelength relate to the quantisation of electron motion?
Ans. The De Broglie wavelength is related to the quantisation of electron motion by providing a wave-like description of the electron's motion. The wavelength of the electron wave is inversely proportional to its momentum, and when the electron is confined to specific energy levels, its momentum becomes quantized. This quantization of momentum leads to the quantization of the electron's energy levels.
5. Can the angular momentum of an electron in an atom have any value?
Ans. No, the angular momentum of an electron in an atom cannot have any value. According to Bohr's second postulate of quantisation, the angular momentum of an electron is quantized and can only take on certain discrete values. These values are determined by the principal quantum number, which represents the energy level occupied by the electron.
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