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

If $n=2$ for $He^{+}$ ion,then what is the wavelength in $\mathring{A}$?

Which of the following statements is $NOT$ correct regarding the Bohr model?

In the Balmer series of lines of the hydrogen spectrum,the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?

The ratio between the radii of $He^{+}$ ion and $H$ atom is:

When an electric discharge is passed through hydrogen gas,the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
$\bar{v} = 109677 \left[ \frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}} \right] \ cm^{-1}$
What points of Bohr's model of an atom can be used to arrive at this formula? Based on these points,derive the above formula,giving a description of each step and each term.