Degree of Freedom: Explaining n,l & m Quantum Numbers

In summary, the movement of an electron around a nucleus in 3D space requires three quantum numbers - n, l, and m - to specify its degree of freedom. These quantum numbers represent the energy levels available to the electron and the direction of its angular momentum vector. The concept of degrees of freedom refers to the number of parameters necessary to describe a system, and in this case, n, l, and m represent the dimensions of a phase space in the context of the hydrogen atom.
  • #1
mkbh_10
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An electron moves around a nucleus in 3d space so it is required that there should be 3 quantum no. each specifying its degree of freedom .

the three quantum no. are n,l & m , but n,l& m specify the energy levels avalaible to electron & m specifies the direction of angular momentum vector .

So what is actually meant by degree of freedom & how do n,l & m specify it ?
 
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  • #2
i'm not sure what you are asking, do you want a claasical explenation of what n,l and m mean?

n,l and m simply come from solving the hydrogen Schödinger equation. And from wikipedia

Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. In mathematical terms, the degrees of freedom are the dimensions of a phase space.

so this definition agrees with what n,l and m does, i guess.
 
  • #3
I studied my self and found the ans from hydrogen atom
 

FAQ: Degree of Freedom: Explaining n,l & m Quantum Numbers

1. What is the purpose of the quantum numbers n, l, and m?

The quantum numbers n, l, and m are used to describe the energy, shape, and orientation of an electron within an atom. They help to identify the specific location and behavior of each electron, which is essential in understanding the properties and behavior of atoms.

2. How does the quantum number n relate to the size of an electron's orbital?

The quantum number n, also known as the principal quantum number, indicates the energy level of an electron and is directly related to the size of its orbital. The larger the value of n, the higher the energy level and the farther away the electron is from the nucleus, resulting in a larger orbital size.

3. What range of values can the quantum number l have?

The quantum number l, also known as the azimuthal quantum number, can have values ranging from 0 to n-1. This means that for a given energy level (n), there can be l possible sublevels, each with a different shape and orientation.

4. How does the quantum number m relate to the orientation of an electron's orbital?

The quantum number m, also known as the magnetic quantum number, specifies the orientation of an electron's orbital in space. It can have values ranging from -l to +l, including 0. This means that for a given sublevel (l), there can be m possible orientations of the orbital.

5. Why is it important to understand the quantum numbers n, l, and m?

Understanding the quantum numbers n, l, and m is crucial in understanding the electronic structure and behavior of atoms. They provide valuable information about the location, energy, and orientation of electrons, which are essential in predicting chemical reactivity and physical properties of elements. Without understanding these quantum numbers, we would not have a complete understanding of the nature of matter at the atomic level.

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