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

With increasing principal quantum number,the energy difference between adjacent energy levels in $H$ atom

Choose the correct option regarding: Assertion: Energy of the orbital decreases with increase of $n$.
Reason: Energy is required in shifting away the negatively charged electron from the positively charged nucleus.

The radius of the second excited state of $Li^{2+}$ is ................ $\mathring{A}$.

The wavelength of a spectral line emitted by a hydrogen atom in the Lyman series is $\frac{16}{15 R} \ cm$. What is the value of $n_2$? $(R = \text{Rydberg constant})$

Which of the following statements are correct?
$I$) The energy of hydrogen atom in its ground state is $-13.6 \ eV$
$II$) On the basis of Bohr's model,the radius of the $3^{rd}$ orbit of hydrogen atom is $158.7 \ pm$
$III$) The order of radius of the first orbit of $H, He^{+}, Li^{2+}$ and $Be^{3+}$ is $H > He^{+} > Li^{2+} > Be^{3+}$