Question

What is h in $\text{mvr = }\dfrac{\text{nh}}{\text{2 }\!\!\pi\!\!\text{ }}$?

Answer 1

Hint: The formula that is mentioned in the question represents the formula of Angular momentum of electron orbitals. The formula was proposed by Neil's Bohr. To know what the quantities in the formula represent, we are required to know the main aim of the formula.

Complete step-by-step answer:
Before moving on to the formula, we are required to know the meaning of angular momentum, by the angular momentum of a rigid object we mean the product of the moment of inertia and the angular velocity.
In the formula, $\text{mvr = }\dfrac{\text{nh}}{\text{2 }\!\!\pi\!\!\text{ }}$
m represents the mass of the electrons,
v represents the velocity of the electrons,
n represents the orbit in which the electron is present
r represents the radius of the nth orbit
And he represents the Planck constant.
By Planck constant we mean that it is a quantum of electromagnetic action that relates a photon’s energy to its frequency. The Planck constant when multiplied by a photon’s frequency is equal to the energy of the photon.
The main use of the Planck constant is in the blackbody radiation spectrum, which indicates that energy is carried by light in discrete amounts. It is also used to calculate the photoelectric effect.

According to Bohr’s atomic model the angular momentum of the electron which is orbiting around the nucleus is quantized. The electron which is moving in its circular orbit always behaves like a particle wave. So, the formula $\text{mvr = }\dfrac{\text{nh}}{\text{2 }\!\!\pi\!\!\text{ }}$ is used to find the angular momentum of the free moving electrons, h being the Planck constant.

Note: We know that electrons in free space can carry quantized orbital angular momentum which is projected along the direction of propagation. This orbital angular momentum corresponds to helical wavefronts, or equivalently a phase proportional to that of the as azimuthal angle.