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# Draw a neat labeled energy level diagram and explain the different series of spectral lines for the hydrogen atom.

Last updated date: 08th Sep 2024
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Hint: The electrons are transited from higher energy level to the lower energy levels. This causes the spectral lines of different wavelengths. The single electron orbiting around the nucleus of the hydrogen atom is explained by the Bohr model of the atom.

The energy level diagram of the hydrogen atom is given below.

When the electron transits from a higher energy level to a lower energy level photon is emitted. The energy of the photon is the difference in the energy of the states. The photon will emit with a frequency corresponding to the energy difference of the final and initial energy states. The energy of each state remains the same. Hence the emitted photon will always have the same frequency always.
The spectral lines are classified into series. The expression connecting the wavelength and the difference between the energy levels is described by the Rydberg formula.
$\dfrac{1}{\lambda } = {Z^2}R\left( {\dfrac{1}{{n_f^2}} - \dfrac{1}{{n_i^2}}} \right)$.
Where $\lambda$ is the wavelength, $Z$ is the atomic number, $R$ is the Rydberg constant, ${n_f}$ is the principal quantum number of the final state, and ${n_i}$ is the principal quantum number of the initial state.
The spectral lines including the transition of the electron to $n = 1$ energy state from the higher energy levels are called Lyman series. That is ${n_f} = 1$ and ${n_i} > 1$.
The spectral lines including the transition of the electron to $n = 2$ energy state from the higher energy levels are called Balmer series. That is ${n_f} = 2$ and ${n_i} > 2$.
The spectral lines including the transition of the electron to $n = 3$ energy state from the higher energy levels are called Paschen series. That is ${n_f} = 3$ and ${n_i} > 3$.
The spectral lines including the transition of the electron to $n = 4$ energy state from the higher energy levels are called Brackett series. That is ${n_f} = 4$ and ${n_i} > 4$.
The spectral lines including the transition of the electron to $n = 5$ energy state from the higher energy levels are called Pfund series. That is ${n_f} = 5$ and ${n_i} > 5$.

Note:
The wavelength will be higher for the transitions between adjacent energy levels. The Balmer series have wavelengths similar to the visible light. Hence they are visible. And the Paschen lies in the infrared region.