For the Balmer series in the spectrum of H atom,$\stackrel{-}{v}=R_H\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$the correct statements
among (I) to (IV) are:

I) As wavelength decreases, the lines in the
series converge
II) The integer n₁ is equal to 2

III) The lines of longest wavelength corresponds to n₂ = 3
IV) The ionization energy of hydrogen can be calculated from wave number of these lines

 

$\stackrel{-}{v}=R_H\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$

Here n=2 since Balmer series, the transition is between some energy level  n₂  

and n₁=2.

As the wave length decreases, the wave number increases. This implies that the difference$\frac{1}{2^2}-\frac{1}{n_2^2}$also increases or ultimately n₂ increases. As n₂increases , the lines in the series converge. Ionization energy of hydrogen can be calculated from wave number of lines in lyman series as the electron is present in n=1.Longest wave length.

corresponds to minimum difference betweeen $\frac{1}{2^2} \mathrm{and} \frac{1}{{\mathrm{n}}_2^2}$ this is for n₂=3