Angular Momentum of an Electron
Understanding the chemical properties of elements and the structure of atoms depends significantly on the electron’s angular momentum. It describes the reasons behind atoms absorbing or releasing light at specific wavelengths and why some elements exhibit specific chemical reactions. This knowledge forms the basis for areas such as chemistry, physics, and also materials science.
De Broglie’s Explanation to the Quantization of Angular Momentum of Electron
Expanding on Bohr’s research, Louis de Broglie later proposed the concept that electrons exhibit characteristics of both particles and waves during motion. This duality was a crucial development in comprehending how electrons behave on a quantum scale.
De Broglie applied his hypothesis to the Bohr model of the atom. he said that if electrons behave like waves, then for an electron to exist in a stable orbit around the nucleus, the circumference of its orbit must accommodate an integer number of wavelengths.
This can be shown by this formula, 2πr=nλ. Here, if we substitute λ by h/p where p = mv, we get
2πr = nh/p
and if we use the formula of angular momentum L = mvr and rearrange the expression we get,
L = nh/2π
In terms of mathematics, the formula for the angular momentum of an electron can be expressed as:
The angular momentum is equal to the product of mass, velocity, and radius, which is also equivalent to half of the reduced Planck constant divided by 2 times pi.
L = mvr = nh/2π
Where
- Angular momentum is represented by L.
- The mass of the electron is denoted by m.
- v represents the speed at which the electron is moving.
- r represents the size of the orbit.
- n is the main quantum number that indicates the orbit in which the electron can be found.
- Planck’s constant is denoted by h.
This equation also serves as a foundational principle for contemporary comprehension of atomic structure.
Angular Momentum of Electron
In the world of physics, angular momentum helps us understand how objects behave when they rotate. It is not only limited to big objects like planets but it also helps us gain insight into the motion of smaller particles such as electrons. Let’s understand angular momentum of an electron with the basic introduction of momentum in this article.
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