The spectrum of hydrogen atom has four spectral lines in the visible range, one of which is in the indigo region, which is emitted when the hydrogen atom with quantum number n=4 transitions to energy level n=2. The energy level of hydrogen atom is shown in the figure. If Planck constant h = 6.63×10-34j s is known, the photon energy of this spectral line is 2.55 eV, and the photon frequency of this spectral line is 2.55 ev.

Hydrogen atomic spectrum is the simplest atomic spectrum. It was first obtained by A. estelen from a hydrogen discharge tube, and then W. hagens and H. Vogel also discovered the hydrogen atomic spectrum when shooting the star spectrum. Up to 1885, 14 spectral lines of hydrogen atom spectrum have been found in visible light and near ultraviolet light spectrum, and the intensity and interval of spectral lines decrease along the short wave direction. There are four visible light regions, which are represented by Hα, Hβ, Hγ and Hδ respectively, and their rough wavelengths are 656.28nm (nm), 486. 13nm, 434.05nm and 4 10. 17nm respectively.

The spectrum of hydrogen atom is the spectrum formed by electrons in hydrogen atom emitting or absorbing photons of different frequencies at different energy level transitions. The spectrum of hydrogen atom is a discontinuous line spectrum.

A brief history of discovery

1885, J. Balmer, a Swiss math teacher, discovered the spectral Balmer system of hydrogen atom in visible light band, and gave an empirical formula.

1908, german physicist F. Paschen discovered the Paschen system of hydrogen atom spectrum, which is located in infrared band.

19 14 years, physicist T. Lyman discovered that the Lyman system of hydrogen atom spectrum is located in ultraviolet band.

1922, physicist F. Blara discovered the Blara system of hydrogen atom spectrum, which is located in the near infrared band.

1924, physicist A. Fender discovered that the Fender system of hydrogen atom spectrum is located in far infrared light band.

1953, physicist C. Humphrey discovered the Humphrey system of hydrogen atom spectrum, which is located in far infrared light band.

Spectral line series

Hydrogen atom is composed of a proton and an electron, which is the simplest atom, so its spectrum has always been a theory to understand the structure of matter.

Main basis. By studying its spectrum, we can make the electrons in the hydrogen atom jump to the high energy level and then jump back to the low energy level by applying energy, and at the same time release photons with the transition amount equal to the energy difference between the two energy levels, and then analyze their photon energy and intensity with grating, prism or interferometer, and we can get the bright line of its emission spectrum. When the hydrogen atom is irradiated by a light source with a certain energy and intensity, photons with the same energy level difference will be absorbed by the hydrogen atom and the dark line of its absorption spectrum will be obtained. In addition, it is not easy to analyze the spectrum of hydrogen atoms from outer space, because hydrogen exists in the form of diatomic molecules in nature. Spectral lines can be divided into Lyman system, Balmer system, Paschen system, brala system, discoverer system and Humphrey system according to their energy bands.

Spectral line formula

1885, the Swiss physicist J. Balmer first used the empirical formula of the above spectrum:

Linear spectrogram of infrared region, visible region and ultraviolet region

λ=Bn2/(n2-22)(n=3，4，5，)

Where b is a constant. This set of spectral lines is called Balmer line system. When n→∞ and λ→B are the limits of this line system, the wavelength difference between two adjacent spectral lines tends to zero. In 1890, J. Rydberg simplified Balmer's formula as:

1/λ= RH( 1/22- 1/N2)(n = 3，4，5，)

Where RH is called Rydberg constant of hydrogen atom, and its value is (1.096775854+0.000000083) ×10-1. After ...

Hydrogen Spectrometer and Visible Spectrum of Hydrogen Atom

Later, other spectral lines of hydrogen atoms were discovered, which can be expressed by similar formulas. The reciprocal of the wavelength is called the wave number, and the unit is m- 1. The wave number of each spectral line system of hydrogen atom spectrum can be expressed by the general formula:

σ=RH( 1/m2- 1/n2)

For a known line system, m is a certain value, and n is a series of integers greater than m. This formula is called the generalized Balmer formula. The six spectral lines in the spectrum of hydrogen atoms are named as follows:

Lyman system m = 1, n = 2, 3, 4, ...

Balmer system m = 2, n = 3, 4, 5, ...

Paschen system m = 3, n = 4, 5, 6, ...

In the near infrared region, M = 4, N = 5, 6, 7. ...

Fender system m = 5, n = 6, 7, 8, ...

Humphrey system m = 6, n = 7, 8, 9, ...

In the generalized Balmer formula, if T(m)=RH/m2 and T(n)=RH/n2 are spectral terms, the formula can be written as σ = T (m)-T (n). The law that the wave number of any spectral line of hydrogen atom can be expressed as the difference between two spectral terms is called combination principle, also known as Ritz combination principle.

For hydrogen-like atoms (such as He+, Li2+, etc.). ) In the case that there is only one electron outside the nucleus, the generalized Balmer formula is still applicable, but the electric quantity and mass of the nucleus are different from those of the hydrogen nucleus, so the Rydberg constant r should be changed accordingly.

When observing the spectral lines of hydrogen atoms with a high-resolution spectrometer, it is found that they are composed of several similar spectral lines, which is called the fine structure of the spectral lines of hydrogen atoms. It comes from the detailed splitting of hydrogen atomic energy level, which is mainly caused by relativistic effect and the additional energy generated by the interaction between electron spin and orbit. It can be explained by Dirac's relativistic wave equation. Therefore, the energy level formula of hydrogen atom is:

e = hcR/N2-hcRα2/n3-[ 1/(j+ 1/2)-(3/4)n]

Where h is Planck constant; C is the speed of light in vacuum; R is Rydberg constant; N is principal quantum number; J is the total angular momentum quantum number; α is called the fine structure constant, and its value is very small, so the second term is much smaller than the first term. If the second term is ignored, the above formula is the hydrogen atomic energy level formula of Bohr's hydrogen atom theory; If the second term is retained, each energy level with principal quantum number n shows its fine structure according to the different total angular momentum quantum number J. But this formula does not contain the orbital angular momentum quantum number L, but J = L 1/2, which shows that according to the theory of quantum mechanics, hydrogen atoms are two different L's, while N and J of the same energy level have the same energy, which is degenerate for L, and the fine structure is also the same as the atomic number. In the early days, some fine structures of Hα lines of hydrogen were observed by high-resolution spectrometer. After analysis, it was found that they were slightly different from quantum mechanics theory.

1947 W. Lamb and R. Reithofer discovered that the hydrogen's 2S 1/2 is higher than 2P 1/2 1, 057.8MHz by atomic beam magnetic * * vibration method, which is the famous Lamb shift. In order to explain this phenomenon, the theory of quantum electrodynamics was developed. The study of hydrogen spectrum has promoted the development of quantum mechanics, and now it has become one of the most important experimental methods to promote and verify the development of quantum electrodynamics. By the year 2000, the accuracy of measuring some spectral frequencies of hydrogen has reached the order of 10- 13, and the accuracy of Rydberg constant derived from it has also reached the order of 10- 12.