In the hydrogen spectrum,if an electron transitions from the $6^{th}$ orbit to the $3^{rd}$ orbit through multiple steps,what is the total number of spectral lines in the $U.V.$ region?

$A$: Thomson's atomic model is known as the plum pudding model.
$R$: The atom is considered as a positively charged sphere in which electrons are embedded.

The wavelength of the radiation emitted,when in a hydrogen atom an electron falls from infinity to stationary state $n=1$,would be ............... $nm$ (Rydberg constant $= 1.097 \times 10^7 \ m^{-1}$)

The work function of a metal is $4.2 \, eV$. If radiation of $2000 \, \mathring{A}$ falls on the metal,then the kinetic energy of the fastest photoelectron is:

When a hydrogen atom in an excited state undergoes electronic transitions to the ground state,$5$ spectral lines are observed in the ultraviolet region. How many spectral lines will be observed in the infrared region due to transitions from the same excited state?

How does the energy gap between successive energy levels in an atom vary from low to high $n$ values?