Answer to Question #165703 in Physical Chemistry for Raj

Question

Explain how different quantum numbers related to each other

Answer 1

There are four quantum numbers which describe an electron in an atom completely. They are :

1) Principal Quantum Number (n): It describes the electron shell energy level of an atom, or simply, the shell number of an electron in an atom. The principal quantum number is always a positive integer value. The values of principal quantum number can be n = 1, 2, 3... and so on.

2) Azimuthal Quantum Number (l): It is known as the angular momentum quantum number. It describes the sub-shell and gives the magnitude of orbital angular momentum. The azimuthal quantum number tells us the orbital in which an electron is present in a shell, whether in the s,p,d or f orbital. The values of angular momentum are l = 0, 1, 2...(n−1). For example, for n = 3, l = 0 to (3−1) = 0 to 2 = 0, 1, 2. 

For different values of l, the orbitals are :

l = 0, orbital = s

l = 1, orbital = p

l = 2, orbital = d

l = 3, orbital=f

3) Magnetic Quantum Number (m): It describes and yields the projection of the orbital angular momentum along a specified axis. The values of m are from −l to +l. For example, for l = 2, m = −2, −1, 0, +1, +2.

4) Spin Quantum number (s): It describes the intrinsic angular momentum of the electron in an orbital and the projection of the spin angular momentum along the specified axis. every orbital can accommodate a maximum of only two electrons with opposite spins. The values of s are +$\frac{1}2$ and -$\frac{1}2$ ​. The  +$\frac{1}2$ spin represents the clockwise spin of an electron, while the -$\frac{1}2$​ spin represents the anti-clockwise spin of an electron.