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Hydrogen Spectrum

Absorption and Emission Hydrogen Spectrum

Hydrogen emission spectrum is an impotent tool for the determination of the atomic structure of chemical elements. Bohr’s theory explained the existence of various lines in the hydrogen spectrum. But the emission energy of hydrogen always produces a series of line spectra. Therefore, the measurements of the atomic emission spectrum are feasible in quantum chemistry. Because each hydrogen energy level has definite energies in which the electron particle can stay. As the value of the principal quantum number increases the energy values for orbits become closer to each other. Hence when the energy corresponding to the electronic transition from n = ∞ to n = 1 gives the ionization energy of the hydrogen atom.

Atomic emission spectrum of hydrogen

Therefore, on the addition of thermal energy or electrical energy, the electron moved to the higher energy level or higher energy orbital of an atom. When this excited electron returns to the ground state it forms the emission spectrum with a definite frequency of radiation.

Frequency of Atomic Spectra

In 1901 plank proposed a hypothesis in which he connected photon energy and frequency of the emitted light for the chemical elements in the periodic table.

ΔE = hν
or, ν = ΔE/h
where ν = frequency of emitted light
h = plank constant

Emission Spectrum of Hydrogen

The energy corresponding to a particular line in the emission and absorption spectra or spectrum of hydrogen is the energy difference between the ground level and the exited level. Bohr’s theory provides the energy of an electron at a particular energy level. Therefore, the energy of an electron, En = – 2π2me4/n2h2
but ΔE = E2 – E1.

    \[ \boxed{\Delta E=\frac{2\pi ^{2}me^{4}}{h^{2}}\left ( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right )} \]

But the frequency of emitted light from the electromagnetic spectrum related to energy by plank equation, ν = ΔE/h. With the help of these equations, we can calculate the frequency, wavelength, and wavenumber of the line observed in the hydrogen spectrum.

Rydberg Constant Value for Hydrogen

Spectrum equation of hydrogen uses to measure the values of the Rydberg constant for the hydrogen in learning chemistry or quantum chemistry.

Rydberg constant (R) = 2π2me4/h3
= 3.2898 × 1015 cycles sec-1
Again, ν = c/λ and ν = c × wavenumber
where wavenumber = ν/c
and c = velocity of light

Therefore, the frequency (ν) indicates the number of waves passing a given point per second and is expresses as cycles per second in basic chemistry. But wavenumber stands for the number of waves connected in CGS or SI unit length that is per centimeter (cm-1) or per meter (m-1). The experimental value of Rydberg constant = 109737 cm-1 or 10973700 m-1 slightly varies from atom to atom depending upon the nuclear mass.

Emission Spectra of Hydrogen Atom

Putting n = 1, n = 2, n = 3, etc in the Rydberg equation we get the energies of the different stationary states for the hydrogen electron. Therefore, the released energy calculated from the Rydberg equation exhibited several series of lines in the electronic transition of hydrogen.

Spectral lines in Hydrogen Atom

Hydrogen is given several spectral lines because any given sample of hydrogen contains an almost infinite number of atoms. Under normal conditions, the electron of each hydrogen atom remains in the ground state near the nucleus, which is n = 1 (K – Shell). When a specific heat or electrical energy is supplied to hydrogen gas, it absorbed different amounts of energy to give absorption spectra or spectrum.

Some of the atoms absorbed such energy to shift their electron to third energy level, while some others may absorb a large amount of energy to shift their electron to the fourth, fifth, sixth, and seventh energy levels. But the electrons of hydrogen in the excited state are relatively unstable and hence drop back to the ground state by the emission of energy in the form of the spectrum. Thus for different drop back given different lines of the hydrogen spectrum.

Line Spectrum of Hydrogen Atom

Transition to the ground state to excited states constitute the Lyman, Balmer, Pashen, Brackett, Pfund and Hampe series of spectral lines. This emission spectrum lies from the ultraviolet region to the far IR region. When we putting the values of n1 and n2 in the Rydberg equation, we obtained the frequency of different spectral lines represent on the below table.

Series of lines n1 n2 Spectral region Wavelength
Lyman Series 1 > 1 UV < 4000
Balmer Series 2 > 2 Visible 4000 to 7000
Paschen Series 3 > 3 Near IR > 7000
Brackett Series 4 > 4 Far IR > 7000
Pfund Series 5 > 5 Far IR > 7000

The emission spectrum data obtained from Bohr’s theory explain the atomic spectral data but the theory has some limitations. The theory of atoms with more than one electron was not successful. The theory did not provide any explanation of the atomic emission spectrum for the union of atoms to produce the molecule.