Limitation of Bohr's Theory
1) According to Bohr, the radiation results when an electron jumps from one energy orbit to another energy orbit, but how this radiation occurs is not explained by Bohr.
2) Bohr Theory had explained the existence of various lines in H-spectrum, but it predicted that only a series of lines exist. At that time this was exactly what had been observed. However, as better instruments and techniques were developed, it was realized that the spectral line that had been thought to be a single line was actually a collection of several lines very close together (known as fine spectrum). Thus for example, the single H¥-spectral line of Balmer series consists of many lines very close to each other.
3) Thus the appearance of the several lines implies that there are several energy levels, which are close together for each quantum number n. This would require the existence of new quantum numbers.
4) Bohr's theory has successfully explained the observed spectra for hydrogen atom and hydrogen like ions (e.g. He+, Li2+, Be3+ etc.), it can not explain the spectral series for the atoms having a large number of electrons.
5) There was no satisfactory justification for the assumption that the electron can rotate only in those orbits in which the angular momentum of the electron (mvr ) is a whole number multiple of h/2pi, i.e. he could not give any explanation for using the principle of quantisation of angular momentum and it was introduced by him arbitrarily.
6) Bohr assumes that an electron in an atom is located at a definite distance from the nucleus and is revolving round it with definite velocity, i.e. it is associated with a fixed value of momentum. This is against the Heisenberg's Uncertainty Principle according to which it is impossible to determine simultaneously with certainty the position and the momentum of a particle.
7) No explanation for Zeeman effect: If a substance which gives a line emission spectrum, is placed in a magnetic field, the lines of the spectrum get split up into a number of closely spaced lines. This phenomenon is known as Zeeman effect. Bohr's theory has no explanation for this effect.
8) No explanation of the Stark effect: If a substance which gives a line emission spectrum is placed in an external electric field, its lines get spilt into a number of closely spaced lines. This phenomenon is known as Stark effect. Bohr's theory is not able to explain this observation as well.