Explain how the different series of lines are formed in hydrogen spectrum derive an equation to find the wave number of the line in the hydrogen spectrum.
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The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts.
The energy differences between levels in the Bohr model, and hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula:[4]
{\displaystyle {1 \over \lambda }=RZ^{2}\left({1 \over {n'}^{2}}-{1 \over n^{2}}\right)} {\displaystyle {1 \over \lambda }=RZ^{2}\left({1 \over {n'}^{2}}-{1 \over n^{2}}\right)}
where Z is the atomic number, i.e. the number of protons in the atomic nucleus of this element; n is the upper energy level; n′ is the lower energy level; and R is the Rydberg constant (1.09737×107 m−1).[5] Meaningful values are returned only when n is greater than n′. Note that this equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines are given by Z=1.
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Although hydrogen has only one electron, it contains many energy levels. When its electron jumps from higher energy level to a lower one, it releases a photon. Those photons cause different colours of light of different wavelengths due to the different levels. Those photons appear as lines. For this reason, though hydrogen has only one electron, more than one emission line is observed in its spectrum.
eq is nubar=RH(1÷n^2-1÷n2^2)