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Hydrogen Spectrum

Absorption and Emission Hydrogen Spectrum

Hydrogen spectrum (absorption or emission), in optics, an impotent type of tool for the determination of the atomic structure of chemical elements or atoms in quantum chemistry or physics. Bohr theory explained the existence of various electromagnetic spectrum lines (visible, ultraviolet, and infrared) for the hydrogen atom for the spectroscopic study. Therefore, the calculation of the atomic emission or absorption spectrum is feasible in quantum chemistry or physics because each hydrogen energy level has definite energies in which the electron particle can stay. When the value of the principal quantum number increases the energy values for orbits become closer to each other. The absorption energy corresponding to the electronic transition spectrum from n = ∞ to n = 1 gives the ionization energy of the hydrogen atom.

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 following emission spectrum or hydrogen spectrum diagram with a definite frequency of radiation.

Atomic emission spectrum of hydrogen

Frequency of Emission Hydrogen Spectrum

In 1901 plank proposed a formula for the electromagnetic spectrum in which he connected photon energy and frequency of the emitted light for the chemical elements in the periodic table. Therefore, ΔE = hν or, ν = ΔE/h, where ν = frequency of emitted light and h = plank constant. 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 theory provides the energy of an electron at a particular energy level. Therefore, the energy of an electron, En = – 2π2me4/n2h2 and 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 is related to energy by plank equation, ν = ΔE/h. With the help of this formula, we can calculate the frequency, wavelength, and wavenumber of the line observed in the hydrogen spectrum.

Rydberg Constant Value for Hydrogen

The spectrum equation of hydrogen uses to measure the values of the Rydberg constant for the hydrogen in learning chemistry or quantum physics. Therefore, 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) in the spectrum indicates the number of waves passing a given point per second and is expresses as cycles per second in chemistry or physics. But wavenumber in hydrogen spectrum data defined 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 the Rydberg constant for hydrogen spectrum equal to 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 the hydrogen emission spectrum.

Types of Spectral lines in Hydrogen

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 of hydrogen.

Some of the atoms absorbed such energy to shift their electron to the 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 to give different types of the hydrogen absorption spectrum diagram. 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. Therefore, the different drop back meaning different lines of the hydrogen spectrum.

Spectrum Series or Region of Hydrogen

According to the name of the discoverer, the transition to the ground state to excited states constitute the Lyman, Balmer, Pashen, Brackett, Pfund, and Hampe series of spectrum lines for the hydrogen atom. This emission hydrogen spectrum lies from the ultraviolet region to the far IR region obtained by putting the values of n1 and n2 in the Rydberg equation, hence the longest or shortest wavelength or frequency of different spectral lines represent in 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 explanation of the emission and absorption spectrum data for one electronic system like hydrogen atom or helium and lithium ion by Bohr theory or model has some limitations. The atoms with more than one electron were not successfully explained by the Bohr model. The theory did not provide any explanation of the atomic emission spectrum for the union of atoms to produce the molecule.