Did Bohr's model account for the splitting of line spectra of a hydrogen atom into finer lines ?

What is the use of a line spectra?

The Bohr's model of atoms:

In Bohr model of atom :

The number of spectral lines in hydrogen atom are

a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2 and 3 levels.

What are the limitations of Bohr's theory of hydrogen atom?