Atomic Physics - Spectral Hydrogen Atom

Spectral Hydrogen Atom

Long before Bohr gave his theory of hydrogen atom, various scientists had observed experimentally, the spectral series of hydrogen atom. Bohr offered a theoretical explanation of these spectral series as follows:

1. Lyman series: Bohr postulated Lyman series is obtained when an electron jumps to the first orbit (n₁ = 1) from any outer orbit (n₂ = 2, 3, 4……).

Wave numbers of spectral lines Lyman series were calculated by

v? = R [1/12 – 1/k²], where k = 2, 3, 4…

These values of v? lie in the ultra violet region of the spectrum and agree well with the values of v?observed experimentally by Lyman.

2. Balmer series: according to Bohr, Balmer series is obtained when an electron jumps to the second orbit(n₁ =2) from any outer orbit (n₂ = 3, 4, 5…..).

Wave numbers of these spectral lines were calculated as

v?= R [1/2² – 1/k²], where k = 3, 4, 5…..

This set of spectral lines lie in the visible part of the spectrum.

3. Paschen series: according to Bohr, Paschen series is obtained when an electron jumps to the third orbit(n₁ =3) from any outer orbit (n₂ = 4, 5, 6…) Bohr calculated the wave numbers of spectral lines of Paschen series from the relation:

v?= R [1/3² – 1/k²], where k = 4, 5, 6……

These values of v? lie in the infra red region of the spectrum and agree well with values of v? observed experimentally by Paschen.

Bohr also predicted two new series in the infra red region of the spectrum, which were observed later by Brackett and Pfund.

4. Bracket series: according to Bohr, Brackett series is obtained when an electron jumps to the 4th orbit(n₁ = 4) from any outer orbit (n₂ = 5, 6, 7……)

5. Pfund series: according to Bohr, is obtained when an electron jumps to the 5th orbit (n₁ =5) from any outer orbit (n2 = 6, 7, 8…….)

The origins of various spectral series of hydrogen atom are represented by table under which gives the longest and the shortest wavelengths of some of the spectral series of hydrogen atom.

Wave length limits of some spectral series of hydrogen

Spectral series	Lower state	Upper state	λ max Å	Lower state	Upper state	λ max Å
Lyman	1	2	1216	1	∞	912
Balmer	2	3	6563	2	∞	3646
Paschen	3	4	18751	3	∞	8220

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