Idea of quantization of energies
The bright line spectrum shows that the energy levels in an atom are quantized.
These lines corresponds to definite wavelengths and are obtained as a result of electronic transitions between the energy levels. Hence, the energies of electron in these levels are quantized.
Classical mechanics ignores the concept of dual nature of matter; thus, it is not able to explain the working of microscopic objects like electrons, atoms, and molecules, etc. but quantum mechanics considers this dual behavior of atom.