The first quantum mechanical model of the atom was proposed by ........

Based on equation $E = -2.178 \times 10^{-18} \ J \ \frac{Z^2}{n^2}$,certain conclusions are written. Which of them is not correct?

What is the ratio of the wave number of the first line (lowest energy line) of the Balmer series of the $H$ atomic spectrum to the first line of its Brackett series?

For the Balmer series in the spectrum of $H$ atom,$\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$,the correct statements among $(I)$ to $(IV)$ are:
$(I)$ As wavelength decreases,the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$.
$(III)$ The lines of longest wavelength corresponds to $n_{2}=3$.
$(IV)$ The ionization energy of hydrogen can be calculated from wave number of these lines.

Which of the following provisions of the Bohr atomic model of hydrogen turned out to be false?

Given the energy equation $E_n = -313.6/n^2$,if $E_n = -34.84$,which of the following could be the value of $n$?