Identify an orbital with the quantum numbers $n=4, \ell=3, m=0$.

Explain,giving reasons,which of the following sets of quantum numbers are not possible.
$(a)$ $n=0, l=0, m_{l}=0, m_{s}=+\frac{1}{2}$
$(b)$ $n=1, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$
$(c)$ $n=1, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$
$(d)$ $n=2, l=1, m_{l}=0, m_{s}=-\frac{1}{2}$
$(e)$ $n=3, l=3, m_{l}=-3, m_{s}=+\frac{1}{2}$
$(f)$ $n=3, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$

The quantum numbers $+1/2$ and $-1/2$ for the electron spin represent

Explain the differences between the $1s$ and $2s$ orbitals based on their probability density plots and radial distribution.

The total number of atomic orbitals in the fourth energy level of an atom is

The maximum number of electrons in a $p$-orbital with $n = 5$ and $m = 1$ is