The wavelength corresponding to an electronic transition between two orbits of a hydrogen atom is $912 \mathring{A}$. The wavelength (in $\mathring{A}$) for the same electronic transition in $Li^{2+}$ is

The radius of the first orbit of $Li^{2+}$ is $X \mathring{A}$. The radius of the third orbit of $He^{+}$ (in $\mathring{A}$) is (in $X$)

The ratio of the radius of the first three Bohr orbits is

If the wavelength of the limiting line of the Lyman series of the hydrogen atom is $16$ times the wavelength of the limiting line of the same series for an ion $X$,then what is $X$?

The statements
$i$. In filling a group of orbitals of equal energy,it is energetically preferable to assign electrons to empty orbitals rather than pair them into a particular orbital.
$ii$. When two electrons are placed in two different orbitals,energy is lower if the spins are parallel.
Are valid for

The electron in the $n^{th}$ orbit of $Li^{2+}$ is excited to $(n+1)$ orbit using the radiation of energy $1.47 \times 10^{-17} \ J$. The value of $n$ is $....$. Given $R_H = 2.18 \times 10^{-18} \ J$.