The number of electrons that can be present in sub-shells having $m_s$ value of $\frac{-1}{2}$,for $n$ up to $3$.

The energy of an electron of $2p_y$ orbital is :

The number of radial nodes of $3s$ and $2p$ orbitals are respectively.

The azimuthal quantum number defines:

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

Consider the following statements:
$(A)$ The principal quantum number $'n'$ is a positive integer with values of $'n'=1, 2, 3, \dots$.
$(B)$ The azimuthal quantum number $'l'$ for a given $'n'$ (principal quantum number) can have values as $'l'=0, 1, 2, \dots, (n-1)$.
$(C)$ Magnetic orbital quantum number $'m_l'$ for a particular $'l'$ (azimuthal quantum number) has $(2l+1)$ values.
$(D)$ $\pm 1/2$ are the two possible orientations of electron spin.
$(E)$ For $l=5$,there will be a total of $11$ orbitals.
Which of the above statements are correct?