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

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

Expert Answer:

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+, Li2+.... 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 (ml)

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

            ml = - l, (-l + 1)…, -1, 0, 1, …(+ l -1), + l

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


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