The maximum number of possible electrons in a subshell with $n=3$ and $l=2$ is

The maximum number of electrons that can be accommodated in a shell with $n=4$ is:

How many nodal (angular) planes are present in the $d_{xy}$ orbital? Which are they?

Identify which of the following sets of quantum numbers are not possible and explain why.
$(a) n = 0, l = 0, m_l = 0, m_s = +1/2$
$(b) n = 1, l = 0, m_l = 0, m_s = -1/2$
$(c) n = 1, l = 1, m_l = 0, m_s = +1/2$
$(d) n = 2, l = 1, m_l = 0, m_s = -1/2$
$(e) n = 3, l = 3, m_l = 3, m_s = +1/2$
$(f) n = 3, l = 1, m_l = 0, m_s = +1/2$

Five valence electrons of $P^{15}$ are labelled as $\boxed{AB}_{3s} \,\boxed{X|Y|Z}_{3p}$. If the spin quantum numbers of $B$ and $Z$ are $+\frac{1}{2}$,the group of electrons with three of the quantum numbers $(n, l, m)$ the same are:

Maximum number of electrons possible with spin quantum number $+\frac{1}{2}$ with principal quantum number $n=4$ in an atom is