- The origin of spectral lines in the hydrogen atom can be explained on the basis of Bohr’s theory. The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. This orbit is called the ground state.
- The electron gains energy from the surrounding and jumps into a higher orbit with principal quantum number n = 2, 3, 4, 5, ….. These higher orbits are called excited states. When electrons start revolving in excited state the atom becomes unstable. To acquire stability the electron jumps from the higher orbit to lower orbit by the emission of energy of value hν. Where ν is the frequency of radiation energy or radiation photon. This radiation is emitted in form of spectral lines.

#### Expression for the Wavelength of line in the Hydrogen Spectrum:

- Let E
_{n}and E_{p}be the energies of an electron in the n^{th}and p^{th}orbits respectively (n > p) So when an electron takes a jump from the n^{th}orbit to the p^{th}orbit energy will be radiated in the form of a photon or quantum such that -
E

_{n}– E_{p}= hν ………… (1)where ν is the frequency of radiation, h = Planck’s constant

- This formula is called Bohr’s formula of spectral lines.
- The wavelength λ obtained is characteristic wavelength due to jumping of the electron from n
^{th}orbit to p^{th}orbit. We get different series of spectral lines due to the transition of the electron from different outer orbits to fixed inner orbit.

#### Energy Level Diagram for Hydrogen Atom:

- Energy level diagrams indicate us the different series of lines observed in a spectrum of hydrogen atom. The horizontal lines of diagram indicates different energy levels. The vertical lines indicate the transition of electron from higher energy level to lower energy level.
- It is very important that as indicated in the diagram each transition corresponds to definite characteristic wavelength. Thus different transitions give different series of lines. Different Series obtained are a) Lyman series, b) Balmer series, c) Paschen series, d) Brackett series, e) Pfund series and f) Henry series

#### Different Series in Hydrogen Spectrum:

#### Lyman Series :

- If transition of electron takes place from any higher orbit (principal quantum number = 2, 3, 4,…….) to the first orbit (principal quantum number = 1). We get Lyman series of hydrogen atom.
- It is obtained in ultra violet region.

This formula gives wavelength of lines in Lyman series of hydrogen spectrum

- Different lines of Lyman series are
- α line of Lyman series p = 1 and n = 2
- α line of Lyman series p = 1 and n = 3
- γ line of Lyman series p = 1 and n = 4
- longest line of Lyman series p = 1 and n = 2
- shortest line of Lyman series p = 1 and n = ∞

#### Balmer Series :

- If transition of electron takes place from any higher orbit (principal quantum number = 3,4, 5, …….) to the second orbit (principal quantum number = 2). We get Balmer series of hydrogen atom.
- It is obtained in visible region.

This formula gives wavelength of lines in Balmer series of hydrogen spectrum

- Different lines of Balmer series area l
- α line of Balmer series p = 2 and n = 3
- β line of Balmer series p = 2 and n = 4
- γ line of Balmer series p = 2 and n = 5
- longest line of Balmer series p = 2 and n = 3
- shortest line of Balmer series p = 2 and n = ∞

#### Paschen Series :

- If transition of electron takes place from any higher orbit (principal quantum number = 4, 5, 6, …….) to the third orbit (principal quantum number = 3). We get Paschen series of hydrogen atom.
- It is obtained in infra-red region.

This formula gives wavelength of lines in Paschen series of hydrogen spectrum.

#### Brackett Series:

- If transition of electron takes place from any higher orbit (principal quantum number = 5, 6, 7, …….) to the fourth orbit (principal quantum number = 4). We get Brackett series of hydrogen atom.
- It is obtained in far infra-red region.

This formula gives wavelength of lines in Brackett series of hydrogen spectrum

#### Pfund Series :

- If transition of electron takes place from any higher orbit (principal quantum number = 6,7, 8, …….) to the fifth orbit (principal quantum number = 5). We get pfund series of hydrogen atom.
- It is obtained in far infra-red region.

This formula gives wavelength of lines in pfund series of hydrogen spectrum

** Notes: **Shortest wavelength is called series limit

#### Continuous or Characteristic X-rays:

- Characteristic x-rays are emitted from heavy elements when their electrons make transitions between the lower atomic energy levels.. The characteristic x-ray emission which is shown as two sharp peaks in the illustration at left occur when vacancies are produced in the n=1 or K-shell of the atom and electrons drop down from above to fill the gap.

- The x-rays produced by transitions from the n=2 to n=1 levels are called K-alpha x-rays, and those for the n=3 to n = 1 transition are called K-beta x-rays. For particular material wavelength has definite value. Hence these x rays are called continuous or characteristic X-rays . The values of energy are different for different material.
- The frequencies of the characteristic x-rays can be predicted from the Bohr model. Moseley measured the frequencies of the characteristic x-rays from a large fraction of the elements of the periodic table and produced a plot of them which is now called a “Moseley plot”.
- Characteristic x-rays are used for the investigation of crystal structure by x-ray diffraction. Crystal lattice dimensions may be determined with the use of Bragg’s law in a Bragg spectrometer.

Sir please tell me the number of shells in paschen series (1)for maximum frequency and (2)for minimum frequency

For the longest wavelength of Paschen series p = 3 and n = 4. As frequency is inversely proportional to the wavelength. the frequency will be minimum ( p = 3 and n = 4).

Foe the shortest wavelength of Paschen series p = 3 and n = ∞. As frequency is inversely proportional to the wavelength. the frequency will be maximum ( p = 3 and n = ∞).

Thank you very very much Hemant More sir.

You are always welcome. We are working to help as many students as we can. I would like to receive suggestions and corrections from your side. If you like the article share it in your group using social media. Let us make quality education free. Be the part of our movement.

Of course, this have to be shared, I have been searching for this and you explained it more clearly than the previous post, pls An issue in hybridization from the beginning to the end, it you can work on that, I will be happy and more students can also know it, because I know students in chemistry have an issue with that, i will surely share.

Thank You.

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calculate the wavelength in angstrom units, of the second line in the paschen series.(R^H=109678cm^-1)