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

The shortest wavelength of hydrogen atom in Lyman series is $\lambda$. The longest wavelength in Balmer series of $He^{+}$ is

The ratio of the difference between the $1^{st}$ and $2^{nd}$ Bohr orbits energy to the difference between the $2^{nd}$ and $3^{rd}$ Bohr orbits energy is:

The energy of an electron in a hydrogen atom when present in $n=1$, $n=2$, and $n=3$ will be in the ratio of:

The figure that is not a direct manifestation of the quantum nature of atoms is:

The correct representation of the wavelength-intensity relationship of an ideal black body radiation at two different temperatures $T_{1}$ and $T_{2}$ (where $T_{2} > T_{1}$) is: