Who modified Bohr's theory by introducing elliptical orbits for electron path?

The number of absorption lines in the given figure will be .......

Find the wavelength of the third line in the Brackett series of the hydrogen spectrum.

An electromagnetic radiation of wavelength $331.5 \ nm$ is made to strike the surface of a metal. Electrons are emitted with a kinetic energy of $1.2 \times 10^5 \ J \ mol^{-1}$. The work function (in $eV$) of the metal is (given: $h=6.63 \times 10^{-34} \ Js$, $N_{A}=6 \times 10^{23} \ mol^{-1}$, $1 \ eV = 1.6 \times 10^{-19} \ J$)?

When electromagnetic radiation of wavelength $300 \, nm$ falls on the surface of sodium,electrons are emitted with a kinetic energy of $1.68 \times 10^{5} \, J \, mol^{-1}$. What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?

Evaluate the following ratios for the energy of the electron in a particular orbit:
[Kinetic $:$ Potential] and [Total $:$ Kinetic]