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Государственное бюджетное нетиповое образовательное учреждение «Санкт-Петербургский городской Дворец творчества юных» Аничков лицей
Государственное бюджетное общеобразовательное учреждение
гимназия № 116 Приморского района Санкт-Петербурга
Региональный конкурс исследовательских работ школьников «КРЫЛЬЯ НАУКИ»
TEMA ИССЛЕДОВАТЕЛЬСКОЙ РАБОТЫ:
«ПРИМЕНЕНИЕ ЭФФЕКТА ДОПЛЕРА ДЛЯ ИЗМЕРЕНИЯ ТЕМПЕРАТУРЫ ФОТОСФЕРЫ ЗВЕЗДЫ»
Ученица 8 «Б» класса
Учитель физики Быков Н. А.
2018- 2019 УЧ. ГОД
TOC \o "1-3" \h \z \u INTRODUCTION PAGEREF _Toc4541523 \h 3CHAPTER I. THE DOPPLER EFFECT PAGEREF _Toc4541524 \h 5CHAPTER II. ABSORPTION AND EMISSION OF LIGHT BY ATOMS PAGEREF _Toc4541525 \h 72.1 Bohr model and its properties PAGEREF _Toc4541526 \h 72.2 Atomic emission and absorption spectra PAGEREF _Toc4541527 \h 72.3 Thermal radiation PAGEREF _Toc4541528 \h 8CHAPTER III. DOPPLER BROADENING PAGEREF _Toc4541529 \h 10CONCLUSION PAGEREF _Toc4541530 \h 11REFERENCES PAGEREF _Toc4541531 \h 12
INTRODUCTIONThe starry sky is not only delight and eternal mystery, but also a source of fundamental knowledge about the world in which we exist. Numerous people consider studying various galaxies, black holes, moons, planets, comets and asteroids to be extremely fascinating. However, the author is especially interested in researching stars: their formation and evolution, structure, characteristics, classification, distribution, radiation.
Since it was first described in 1842, the Doppler Effect has found various applications. For example, sirens, radar, satellite communication and
The astronomers did not ignore this effect either: the Doppler shift of the spectra of stars and other celestial bodies determines their speed of movement relative to the Earth. For example, it led to the discovery of the expansion of the Universe.
The object of this work is the application of the Doppler Effect for studying stars.
However, the author is particularly interested in the not very well known application of the Doppler Effect in astronomy, namely that with its help one can measure the temperature of a star.
The subject of this research is the relation between the temperature of the photosphere and the broadening of the spectrum lines caused by the Doppler Effect.
The purpose of this research is to study the principles of measuring the temperature of a star`s photosphere using the Doppler broadening of the spectrum lines. To achieve the goal, the following tasks are identified:
1) to explore the essence of the Doppler Effect,
2) to study the general principles of emission and absorption of light by atoms,
3) to describe the dependence of the broadening of spectrum lines on the temperature.
The practical value of the research performed is reflected in the fact that its results can find application in popular science lectures, be a part of an astronomy lesson with an in-depth study of the relevant sections of the course, as additional materials for self-study
Structure of the work: the work consists of an introduction, three chapters dedicated to the features of the Doppler Effect, absorption and emission of light by atoms; including the properties of the Bohr model, absorption and emission spectra and thermal radiation; Doppler broadening and conclusion.
CHAPTER I. THE DOPPLER EFFECTA change in frequency or wavelength in relation to the observer`s movement relative to the wave source was described by Christian Doppler in 1842 and subsequently was named after him.
The common example of the Doppler Effect is the change of pitch of a sound produced by a car driving past the observer (e.g. a horn signal or engine noise). While the vehicle is approaching the observer, the frequency of the received sound is higher than of the emitted one and it is lower while it is receding.
The Doppler Effect occurs not only for sound waves, but also for electromagnetic ones. Let the distance to the source be ct (c is the speed of light, t is time it takes for the light the reach the receiver) and 𝜈0 - the source radiation frequency. During time t, the source emits 𝜈0t waves. In the absence of movement 𝜈0t waves fit on the segment ct but if the source moves (for example, it moves away with the velocity 𝑣r), then 𝜈0t waves will be laid on the segment of length ct + 𝑣rt.
We proceed to the wavelengths. In the absence of movement the wavelength λ0, called the source’s own wavelength is λ0=ctν0t. However, if the source moves away, then λ=ct+vrtν0t. Thus, the increase in wavelength is:
∆λ=λ -λ0=ct+vrtν0t-ctν0t=vrν0=λ0vrcThen the velocity of the source moving away is:
vr=∆λλ0cThis method is used to determine the velocity of approach or recess of various objects: from stars and galaxies to cars exceeding the speed limit. This method plays a significant role in astronomy and astrophysics, where there is often no other way to find out how fast distant objects move. According to the resulting equation, we can determine the radial velocity of the source (star) relative to the Earth if we know source`s own wavelength λ0 and the received wavelength λ. The ways to determine the wavelength of the light emitted by a distant star will be considered in the following chapter.
CHAPTER II. ABSORPTION AND EMISSION OF LIGHT BY ATOMS2.1 Bohr model and its propertiesBohr model of the atom describes the atomic structure. Although Bohr model has been supplanted by other models, its general principles are still valid.
The system of an atom, consisting of nucleus and electrons, has some stationary states. In these states, the atom does not emit or absorb light. Each of these states has its own energy level. The atom absorbs energy while moving from a low energy level to higher levels, and emits it when moving in the opposite direction. The emitted or absorbed energy is equal to the energy difference of the stationary states between which the transition takes place:
En and Em are the energies of the stationary states and
h is Planck's constant
Then the radiation frequency is:
νnm=En-Emh2.2 Atomic emission and absorption spectraWe now turn to the emission and absorption spectra of light. Like the unique fingerprints of people, the atoms of one chemical element emit a characteristic spectrum of light, peculiar only to them.
The individuality of the spectra is due to the fact that they contain only those frequencies at which the atoms of a given element emit or absorb. And the energies of the stationary states of the atoms of each chemical element are different. Therefore, the electron can move between certain states, radiating or absorbing certain amounts of energy.
Spectral analysis is based on the uniqueness of the spectra of various chemical elements. It is a method of determining the chemical composition of a substance by its ability to emit and absorb light.
Using spectral analysis, scientists research the chemical composition of various stars which led to the discovery of such chemical elements as rubidium, caesium and helium.
But the main contribution to the spectra of stars makes hydrogen. Its stationary levels, and hence the frequencies of emission and absorption, are well known and recognizable. Comparing them with the observed spectra, one can quite accurately calculate the radial velocity of the source.
2.3 Thermal radiationUnlike the emission spectrum of rarefied gases, the emission spectrum of solids, liquids, and dense gases is continuous. This means that they emit at all possible frequencies. The fact is that the formation of an emission line-spectrum, described above, during the transitions of atoms between stationary states is valid only for a free atom.
However, if the atom constantly interacts with other atoms, the position of its energy levels will depend on this interaction. This phenomenon is called energy level splitting. The number of resulting levels will be huge because of the extremely large number of interacting atoms. As a result, all possible transitions between all possible levels give so many lines in the spectrum that they all merge into one continuous band.
To sum up, thermal radiation, generated by thermal motion particles in the star, is partially absorbed by photosphere, mainly consisting of hydrogen, in accordance with its absorption spectrum. The rest of the emitted frequencies reach the receiver to be examined and researched. The ways to infer the temperature from the received frequencies will be described in the next chapter.
CHAPTER III. DOPPLER BROADENINGDoppler broadening of the spectral lines is due to the chaotic thermal motion of atoms or molecules. It is most characteristic of rarefied luminous gases, such as the photosphere, the radiating layer, of stars. Thus, the width of the spectral emission lines of hydrogen in stars depends on the temperature of the gas itself.
When the particle moves towards the receiver, radiation of higher frequency is emitted. Likewise, when the particle moves away, the frequency is lower. It is worth noting that only the radial velocity of atoms is important here, which is usually determined by the shift of lines in the spectrum.
Higher temperature of the star's photosphere, consisting mainly of hydrogen, causes a greater difference in the velocity of chaotic thermal motion of atoms. Thus, a greater number of frequencies is emitted by the star as a whole. Therefore, the spectral lines become wider.
Methods of statistical physics showed that the width of the spectral line should be proportional to the square root of temperature.
There are other reasons for widening lines:
Convective Doppler Effect
Rotation of the star
The movement of the star in space
All in all, the width of spectral lines depends on the temperature of the emitting body.
CONCLUSIONThe goal set in studying the principles of measuring the temperature of a star`s photosphere using the Doppler broadening of the spectrum lines is achieved by solving problems, one of which is studying of the properties of the Doppler Effect.
The gist of the Doppler Effect is that frequency or wavelength change in relation to the radial velocity of the observer moving relative to the wave source. The frequency of the received sound is higher than of the emitted one during the observer`s approach and it is lower during the recess.
Having studied the general principles of emission and absorption of light by atoms, it should be mentioned that thermal radiation of the star is being absorbed by the photosphere according to its absorption spectrum. Only the remaining spectral lines reach the receiver and can be analysed.
After studying Doppler broadening, the author described that the width of the spectrum lines correspond to the temperature of the emitting body.
Therefore, one can determine the temperature of the star`s photosphere by comparing the width of the spectral lines at a certain temperature to the received one.
REFERENCESБорн М. Атомная физика, 2-е изд., М.:Мир,1967.- 493с. стр. 105-107
И.В.Савельев Курс общей физики, том I. Механика, колебания и волны, молекулярная физика. Издательство «Наука», Главная редакция физико-математической литературы, М.,1970 г. стр. 287-289
Emission and absorption spectra of hydrogen
Redshift of spectral lines in the absorption spectrum of hydrogen