Question

The difference in angular momentum associated with the electron in two successive orbits of hydrogen atom is $\dfrac{{xh}}{{2\pi }}$.
The value of x is:

Answer 1

We need to remember that the rotational counterpart of linear momentum is angular momentum (rarely momentum or rotational momentum). In physics, it is an essential parameter since it is a conserved quantity; a closed system's total angular momentum remains constant.
We know that the orbit usually refers to a trajectory that repeats periodically, but it can also refer to a trajectory that does not repeat.

Complete step by step answer:
$mvr = n\left( {\dfrac{h}{{2\pi }}} \right)$ difference in angular momentum associated with the electron in two successive orbits of hydrogen atom is $\dfrac{h}{{2\pi }}$ . So, x is 1.
We need to remember that the angular momentum is a quantity of vectors (more specifically, a pseudovector) representing the product of the rotational inertia of a body and the rotational velocity (in radians/sec) around a specific axis. However it is necessary to discard the vector essence of angular momentum and consider it as a scalar momentum if the particle's trajectory lies in a single plane (more precisely, a pseudoscalar).
Therefore, the value of x is 1.

Additional information:
While the language of angular momentum can be replaced by Newton's laws of motion in classical mechanics, it is especially helpful for central potential motion, such as planetary motion in the solar system. The planet's orbit in the solar system is therefore determined by its energy, its angular momentum and the angles of the major axis of the orbit relative to the coordinate frame.

Note:
We need to know that the electron is a particle that is subatomic, a symbol e− or β−
Electrons belong to the first generation of the lepton particle family, and are generally considered to be elementary particles because they have no recognised components or substructure. The electron has a mass of approximately $\dfrac{1}{{1836}}$ that of the proton.