Which are the drawbacks of Rutherford's atomic model?

$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

The wave number of the first line of the Balmer series of $H$ atom is $15200 \ cm^{-1}$. What is the wave number of the first line of the Lyman series of $Li^{2+}$? (in $cm^{-1}$)

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

The energy (in $eV$) associated with the electron in the $1^{st}$ orbit of $Li^{2+}$ is

The wavenumber of the first line $(n_2=3)$ in the Balmer series of hydrogen is $\bar{\nu}_1 \ cm^{-1}$. What is the wavenumber (in $cm^{-1}$) of the second line $(n_2=4)$ in the Balmer series of $He^{+}$?