In a hydrogen atom,if an electron transitions from an $n$-th orbit to the ground state,and the total number of spectral lines observed is $10$,then the value of $n$ is:

The energy difference of two stable orbits of Hydrogen is $214.68 \ kJ \ mol^{-1}$. If the transition of an electron takes place,find the emitted frequency. (Note: $v = \Delta E/h$ and $h = 6.626 \times 10^{-34} \ J \ s$)

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

According to Bohr's theory,the angular momentum of an electron in the $5^{th}$ orbit is ....... (in $h/\pi$)

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

The energy of a photon is calculated by ......