What is principal quantum number, azimuthal quantum number & magnetic quantum number?

### Asked by chinjalsoni911 | 16th Oct, 2018, 06:14: PM

**Principle Quantum Number (n)**

- The principle quantum number (n) is related to the size and energy of the main shell. “n” has positive integer values of 1, 2, 3,….
- The principal quantum number determines the size and to large extent the energy of the orbital. For hydrogen atom and hydrogen-like species (He
^{+}, Li^{2+}.... etc.) energy and size of the orbital depends only on ‘n’. - The principal quantum number also identifies the shell.

- All the orbitals of a given value of ‘n’ constitute a single shell of an atom and are often represented by the letters K, L, M, … For each ‘n’ value there is one main shell.

**Azimuthal Quantum Number ( l)**

- The Azimuthal quantum number. ‘
*l*’ is also known as orbital angular momentum or subsidiary quantum number. - It defines the three-dimensional shape of the orbital.
- For a given value of n,
*l*can have n values ranging from 0 to n –*l*, that is, ‘*l*’ has integer values from 0 to n-*l*for each value of ‘n’. Each ‘*l*’ value represents one sub-shell.

Each value of ‘*l*’ is related to the shape of a particular sub-shell in the space around the nucleus.

**The Magnetic Quantum Number (m**_{l}**)**

- Magnetic orbital quantum number. ‘ m
’ gives information about the spatial orientation of the orbital with respect to a standard set of co-ordinate axis._{l } - The magnetic quantum number (m
) has integer values between –_{l}*l*and*l*, including zero. Thus for a certain value of*l*, there are (2*l*+ 1) integer values of mas follows:_{l}

m* _{l}* = -

*l*, (-

*l*+ 1)…, -1, 0, 1, …(+

*l*-1), +

*l*

- When
*l*= 0, (2*l*+ 1) = 1 and there is only one value of m_{l}, thus we have only one orbital that is, 1s. - When
*l*= 1, (2*l*+ 1) = 3, that means m_{l}has three values, namely, -1, 0, and 1 or three p orbitals, with different orientations along x, y, z-axes. These are called as p_{x}, p_{y}, p_{z}.

### Answered by Varsha | 17th Oct, 2018, 12:08: PM

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