Class 11 Chemistry Hydrogen Spectrum

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Hydrogen Spectrum :
If an electric discharge is passed through hydrogen gas is taken in a discharge tube under low pressure, and the emitted radiation is analysed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and IR regions. This series of lines is known as line or atomic spectrum of hydrogen. The lines in the visible region can be directly seen on the photographic film.
Each line of the spectrum corresponds to a light of definite wavelength. The entire spectrum consists of six series of lines each series, known after their discovery as the Lyman, Balmer, Paschen, Brackett, Pfund and Humphrey series. The wavelength of all these series can be expressed by a single formula which is attributed to Rydberg.

[Note: All lines in the visible region are of Balmer series but reverse is not true i.e. all Balmer lines will not fall in visible region]

As discussed earlier, the above pattern of lines in the atomic spectrum is characteristic of hydrogen. Explanation for hydrogen spectrum by Bohr’s theory

According to the Bohr’s theory electron neither emits nor absorbs energy as long as it stays in a particular orbit.
However, when an atom is subjected to electric discharge or high temperature, and electron in the atom may jump from the normal energy level, i.e., ground state to some higher energy level i.e. the excited state. Since the lifetime of the electron in the excited state is short, it returns to the ground state in one or more jumps.
During each jump, energy is emitted in the form of a photon of light of definite wavelength or frequency. The frequency of the photon of light thus emitted depends upon the energy difference of the two energy levels concerned and is given by

The frequencies of the spectral lines calculated with the help of above equation are found to be in good agreement with the experimental values. Thus, Bohr’s theory elegantly explains the line spectrum of hydrogen and hydrogen species.

Bohr had calculated Rydberg constant from the above equation.

Further application of Bohr’s work was made, to other one electron species (Hydrogenic ion) such as He+and Li2+ . In each case of this kind, Bohr’s prediction of the spectrum was correct.

Now after obtaining the explanation of Rydberg’s equation from Bohr’s theory, can you derive what could be the equation for other uni-electronic species? What would be the value of Rydberg’s constant for He+1 Li+2 ,?
Illustration: Find out the longest wavelength of absorption line for hydrogen gas containing atoms i the ground state.

Illustration: The series limit for the Paschen series of hydrogen spectrum occurs at 8205.8A. Calculate.

(a) the ionization energy of hydrogen atom
(b) Wavelength of the photon that would remove the electron in the ground state of the hydrogen atom.
Solution : (A) Energy corresponding to 8205.8A°

E1H= 13.608 eV

lonisation energy of hydrogen atom = 13.6 eV

Illustration: Calculate frequency of the spectral line when an electron from Bohr orbit jumps to the second Bohr orbit in a hydrogen atom

Illustration: Calculate the energy of an electron in Bohr orbit.

Illustration: Calculate the energy in kj per mole of electronic charge accelerated by a potential of 1 volt.

Solution : Energy in joules = charge in coulombs potential difference in volt

Illustration: What is highest frequency photon that can be emitted from hydrogen atom? What is the wavelength of this photon?

Solution: Highest frequency photon is emitted when electron comes from infinity to energy level.

Illustration: Calculate the longest wavelength transition in the Paschen series of He+.







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