The quantum numbers $n$ and $l$ for four electrons are given as: $(1) \, n = 4, l = 1; \, (2) \, n = 4, l = 0; \, (3) \, n = 3, l = 2; \, (4) \, n = 3, l = 1$. Arrange them in increasing order of their energy.

Write about $p$-orbitals.

For hydrogen-like atoms,the average distance of an electron from the nucleus for the orbitals belonging to the $4^{th}$ orbit is minimum for:

The number of unpaired electrons in the $p$-subshell of oxygen atom is

The orbital angular momentum of an electron in $2s$-orbital is

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