For the given quantum numbers,write the name of the subshell,the values of the magnetic quantum number $(m_l)$,and the number of orbitals:
$(i) \ n = 3, \ l = 2$
$(ii) \ n = 4, \ l = 3$
$(iii) \ n = 2, \ l = 0$
$(iv) \ n = 5, \ l = 1$

Which of the following sets of quantum numbers is not possible?

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

In a multi-electron atom,which of the following orbitals have the same energy in the absence of magnetic and electric fields? $(a) n = 1, l = 0, m = 0, (b) n = 3, l = 0, m = 0, (c) n = 2, l = 1, m = 1, (d) n = 3, l = 2, m = 1, (e) n = 3, l = 2, m = 0$

The magnetic quantum number for a $d$-orbital is ...... .

An electron in the $5d$ orbital can be represented by the following $(n, l, m_l)$ values: