The number of quantum numbers required to describe an electron in an atom completely is

When the value of azimuthal quantum number is $l = 3$,the magnetic quantum number $m_l$ can have values:

The ground state energy of a hydrogen atom is $-13.6 \ eV$. Consider an electronic state $\Psi$ of $He^+$ whose energy,azimuthal quantum number,and magnetic quantum number are $-3.4 \ eV$,$2$,and $0$ respectively. Which of the following statement$(s)$ is(are) true for the state $\Psi$?
$(1)$ It has $2$ angular nodes
$(2)$ It has $3$ radial nodes
$(3)$ It is a $4d$ state
$(4)$ The nuclear charge experienced by the electron in this state is less than $2e$,where $e$ is the magnitude of the electronic charge.

The five valence electrons of $_{15}P$ are represented as shown in the figure. If the spin quantum number of $B$ and $Z$ is $+1/2$,which of the following groups has three identical quantum numbers?

The maximum number of electrons accommodated in $5f$ orbitals are

According to the Aufbau principle,which of the three $4d$,$5p$,and $5s$ will be filled with electrons first?