CBSE Class 11-science Answered

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 (m_l)

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

            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.