According to Bohr's model, electrons in a hydrogen atom revolve only in certain permitted orbits having definite energies. When an electron transitions from a higher energy state to a lower energy state, the difference in energy is emitted as a photon. Since only specific energy levels are allowed, the emitted radiation consists of discrete frequencies, producing the line spectrum of hydrogen.
Bohr's Third Postulate
When an electron makes a transition from a higher energy level (ni) to a lower energy level (nf), where ni > nf, the energy difference is emitted as electromagnetic radiation.
Formula:
hνif = Eni − Enf
where:
- h = Planck's constant
- νif = frequency of emitted radiation
- Eni = energy of the initial state
- Enf = energy of the final state
Since ni and nf are integers, only certain frequencies are emitted. Therefore, the hydrogen atom produces a line spectrum.
Energy of the Electron in Hydrogen Atom
The total energy of an electron in the nth orbit is given by:
En = −13.6 / n² eV
Rydberg Formula
The wavelengths of the spectral lines of hydrogen are given by:
1/λ = RH (1/nf2 − 1/ni2)
where:
- RH = 1.097 × 107 m−1 (Rydberg constant)
- ni = principal quantum number of the initial orbit
- nf = principal quantum number of the final orbit
Lyman Series
In this series, electrons transition from higher energy levels to the first orbit.
Final orbit: nf = 1
Initial orbits: ni = 2, 3, 4, ...
Formula:
1/λ = RH (1 − 1/ni2)
This series lies in the ultraviolet region of the electromagnetic spectrum.
Balmer Series
In this series, electrons transition from higher energy levels to the second orbit.
Final orbit: nf = 2
Initial orbits: ni = 3, 4, 5, ...
Formula:
1/λ = RH (1/2² − 1/ni2)
This series lies in the visible region of the electromagnetic spectrum.
Paschen Series
In this series, electrons transition from higher energy levels to the third orbit.
Final orbit: nf = 3
Initial orbits: ni = 4, 5, 6, ...
Formula:
1/λ = RH (1/3² − 1/ni2)
This series lies in the infrared region of the electromagnetic spectrum.
Brackett Series
In this series, electrons transition from higher energy levels to the fourth orbit.
Final orbit: nf = 4
Initial orbits: ni = 5, 6, 7, ...
Formula:
1/λ = RH (1/4² − 1/ni2)
This series lies in the infrared region of the electromagnetic spectrum.
Pfund Series
In this series, electrons transition from higher energy levels to the fifth orbit.
Final orbit: nf = 5
Initial orbits: ni = 6, 7, 8, ...
Formula:
1/λ = RH (1/5² − 1/ni2)
This series lies in the infrared region of the electromagnetic spectrum.
Emission Spectrum
The various lines in the atomic spectrum are produced when electrons jump from higher energy states to lower energy states and photons are emitted. These spectral lines are called emission lines.
Absorption Spectrum
When an atom absorbs a photon having exactly the energy required for an electron to jump from a lower energy level to a higher energy level, the process is called absorption.
If photons with a continuous range of frequencies pass through a rarefied hydrogen gas and are analyzed with a spectrometer, a series of dark spectral lines appear in the continuous spectrum. These dark lines indicate the frequencies that have been absorbed by the atoms of the gas.
Importance of Hydrogen Spectrum
- It confirms the existence of quantized energy levels in atoms.
- It provides strong support for Bohr's atomic model.
- It played a major role in the development of modern quantum theory.
- Niels Bohr received the Nobel Prize in Physics in 1922 for his contributions to atomic structure.
Frequently Asked Questions (FAQs)
1. What is the line spectrum of hydrogen?
It is the spectrum consisting of discrete wavelengths emitted or absorbed by hydrogen atoms due to electronic transitions between different energy levels.
2. Why does hydrogen produce a line spectrum?
Because electrons in hydrogen can occupy only specific energy levels, resulting in the emission or absorption of photons of definite energies.
3. Which hydrogen spectral series is visible to the human eye?
The Balmer series.
4. What is the Rydberg constant?
The Rydberg constant is 1.097 × 107 m−1.
5. What is the difference between emission and absorption spectra?
Emission spectra consist of bright lines produced during downward transitions of electrons, whereas absorption spectra consist of dark lines produced when electrons absorb photons and move to higher energy levels.
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