Question

What is the angular quantum number?

Answer 1

Hint: The quantum theory suggests that electrons in an atom are present with quantized energy. There are numbers that address the electrons in an atom that are called quantum numbers. There are 4 quantum numbers, principle, azumithul, magnetic and spin. They all give different properties of an electron.

Complete answer:
According to the modern structure of an atom, the electrons are held in an atomic orbital. These orbits have quantized energy for each orbital. There are numbers called quantum numbers that tell us about the position and the address of the electrons in a particular orbit. The 4 quantum numbers are, principle number (n), azimuthal or secondary number $(\ell )$, magnetic quantum number (m) or $(m\ell )$ and spin quantum number (s) or$(ms)$.
The principal quantum number gives the number of shells in which the electron is present. The magnetic quantum number tells the orbital and the orientation of the electron, while the spin quantum number tells the spin that is $+\dfrac{1}{2}$ or$-\dfrac{1}{2}$.
The quantum number that gives us the angular momentum of the electron is the azimuthal quantum number, $(\ell )$. It gives the angular momentum of an electron in a given sub – shell or orbital. The angular momentum is,
Angular momentum = $mvr=n\dfrac{h}{2\pi }$ or,
$mvr=\sqrt{\ell (\ell +1)}\dfrac{h}{2\pi }$where, $\sqrt{\ell (\ell +1)}$ gives number of sub – shells.
Hence, the angular quantum number is azimuthal or secondary quantum number, $(\ell )$.

Note:
Apart from giving the angular momentum of an electron, the azimuthal quantum number, $(\ell )$ also tells us the sub – shell in which the electron is present and also gives the shape of the different sub – shells (s, p, d, f) and their energies. For example, $\ell =0$, s subshell, $\ell =1$, p subshell, $\ell =2$, d sub shell and $\ell =3$, f subshell.