Explain the differences between the $1s$ and $2s$ orbitals based on their probability density plots and radial distribution.

The value of the magnetic quantum number of the outermost electron of $Zn^{+}$ ion is $.....$ .

The hydrogen-like species $Li^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light,the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
$1.$ The state $S_1$ is
$(A)$ $1s$ $(B)$ $2s$ $(C)$ $2p$ $(D)$ $3s$
$2.$ Energy of the state $S_1$ in units of the hydrogen atom ground state energy is
$(A)$ $0.75$ $(B)$ $1.50$ $(C)$ $2.25$ $(D)$ $4.50$
$3.$ The orbital angular momentum quantum number of the state $S_2$ is
$(A)$ $0$ $(B)$ $1$ $(C)$ $2$ $(D)$ $3$
Give the answer for questions $1, 2$ and $3.$

Select the correct statements for quantum numbers.
$(i)$ Magnetic quantum number $(m_l)$ gives information about the spatial orientation of orbitals with respect to the standard set of coordinate axes.
$(ii)$ Electron spin quantum number is represented by '$s$' and has values of $\pm \frac{1}{2}$.
$(iii)$ Principal quantum number $(n)$ determines the size of the orbitals and also,to a large extent,the energy of the orbitals.

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

Which among the following species has the same number of electrons in its outermost as well as penultimate shell?