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According to Bohr's theory, the hydrogen atom consists of a nucleus (proton) and an electron revolving around the nucleus in fixed circular orbits. The theory assumes that the electron orbits have quantized energies and angular momenta.

According to Bohr's theory, an electron can only exist in specific energy levels, and it cannot have energy values between these levels. These energy levels are given by the expression: \[E_n = -\dfrac{13.6\, eV}{n^2}\] where \(E_n\) is the energy of the nth energy level, and \(n\) is the principal quantum number, which takes integer values \(n = 1, 2, 3, ...\)

When an electron in the hydrogen atom transitions from a higher energy level (\(n_i\)) to a lower energy level (\(n_f\)), it releases energy in the form of a photon. The energy of the emitted photon can be calculated using the energy difference between the initial and final energy levels: \[\Delta E = E_{n_f} - E_{n_i} = h\nu\] where \(\Delta E\) is the energy difference, \(h\) is Planck's constant, and \(\nu\) is the frequency of the emitted photon. This energy difference corresponds to specific wavelengths of light, leading to the formation of line spectra.

From Bohr's theory, the quantized energies of the electron in the hydrogen atom can be related to the line spectra as follows: \[\dfrac{1}{\lambda} = R_H\left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right)\] where \(\lambda\) is the wavelength of the emitted photon, and \(R_H\) is the Rydberg constant for hydrogen (\(R_H \approx 1.097 \times 10^7 \, m^{-1}\)). This equation demonstrates how the line spectra observed in the hydrogen atom can be explained by the quantized energies of the electron, as predicted by Bohr's theory. When an electron transitions between two energy levels, it emits a photon with a wavelength that corresponds to the energy difference between the levels. Since the energy levels are quantized, the emitted photon's wavelength will also be fixed, resulting in the line spectra observed in experiments.