Question

The orbital angular momentum quantum number of the state ${{\text{S}}_2}$ is:
A. 0
B. $\sqrt 2 \dfrac{{\text{h}}}{{{{2\pi }}}}$
C. 1
D. $\dfrac{{\text{h}}}{{{{2\pi }}}}$

Answer 1

Orbital angular momentum number is also known as subsidiary and azimuthal quantum number (l). It gives the three-dimension shape of the orbital, and to some extent, it also determines the energy of the orbital in a multi-electron atom.

Complete answer:
In this question, we asked about the Azimuthal quantum number(i.e., l ) of the ${{\text{S}}_2}$.
We know that ${{\text{S}}_2}$ has the 3p subshell notation, and the corresponding value of l for 3p is 1.

**Hence, the correct answer is option (C) i.e., 1

Additional information:**
To distinguish between atomic orbitals on basis of size, shape and spatial orientation we use quantum numbers, each orbital can be designated with 4 quantum numbers labelled as n, l, ${{\text{m}}_{\text{l}}}$ and ${{\text{m}}_s}$.
The 4 quantum numbers that are associated with an orbital, these are;
1. Principle quantum number: Determines the size of the orbital and the energy associated with the orbital.
2. Azimuthal quantum number: 3-dimensional geometry of the orbital ( l = n – 1).
3. Magnetic quantum number ( ${{\text{m}}_{\text{l}}}$ ): ${{\text{m}}_{\text{l}}}$ gives the orientation of the orbital for a given value of l.
4. Electron spin quantum number ( ${{\text{m}}_s}$ ): ${{\text{m}}_s}$ gives the orientation of the spin of the electron.

Note:
There could be no two-electrons in an atom having the same set of 4 quantum numbers, this dramatically limits the number of electrons that can be present in a shell or subshell. The electronic arrangement of an atom can be understood by the Pauli exclusion principle and Hund’s rule of maximum multiplicity.