Part A. Choose the correct answer:
A) daylight lamp
B) TV screen
B) Infrared laser
D) Incandescent lamp
A) For heated solids
B) For heated liquids
A) For heated solids
B) For heated liquids
D) For heated atomic gases
Part B. For each
A) continuous spectrum
B) Line spectrum
B) Striped spectrum
D) Absorption spectra
Physics 11 Test "Types of radiation and spectra"
Part A. Choose the correct answer:
A1. Which body emits thermal radiation?
A) daylight lamp
B) TV screen
B) Infrared laser
D) Incandescent lamp
A2. Which bodies are characterized by striped absorption and emission spectra?
A) For heated solids
B) For heated liquids
C) For any of the bodies listed above
D) For heated atomic gases
E) For rarefied molecular gases
A3. Which bodies are characterized by line absorption and emission spectra?
A) For heated solids
B) For heated liquids
C) For rarefied molecular gases
D) For heated atomic gases
E) For any of the bodies listed above
Part B. For each characteristics select the appropriate type of spectrum
- Spectra are obtained by passing light from a continuous spectrum source through a substance whose atoms are in an unexcited state.
- Consists of separate lines of different or the same color, having different arrangements
- Radiate heated solid and liquid substances, gases heated under high pressure.
- Give substances that are in a molecular state
- Emitted by gases, vapors of low density in the atomic state
- Comprises a large number closely spaced lines
- They are the same for different substances, so they cannot be used to determine the composition of a substance
- This is a set of frequencies absorbed by a given substance. The substance absorbs those lines of the spectrum that it emits, being a source of light
- These are spectra containing all wavelengths of a certain range.
- Allows the spectral lines to judge the chemical composition of the light source
A) continuous spectrum
There are three types of radiation spectra - line, striped and continuous. Line spectra are observed when individual atoms or ions emit. They consist of a number of lines characteristic of a given substance, separated by dark gaps. Each line corresponds to a certain wavelength, called monochromatic. Line spectra characterize the phenomena occurring inside the atom.
Striped spectra are emitted by molecules. A band is a series of closely spaced spectral lines. The emission of striped spectra testifies to the complication of the energy states of the molecule compared to the states of an isolated atom, due to the vibrational and rotational movements its constituent nuclei.
Continuous spectra are emitted solid bodies. The continuous nature of these spectra is a consequence of the strong interaction of the particles that make up the solid.
The form of the line spectrum depends on the structure of the corresponding atom chemical element, therefore, strictly defined line spectra are inherent in all chemical elements, differing from each other both in the number of lines and in their wavelengths. The simplest line spectrum gives the hydrogen atom, which has the simplest structure. The search for explanations of the regularities inherent in this spectrum led to the creation of the quantum mechanical theory of the atom.
First of all, it should be noted that the lines in the emission spectrum of any atom, including the hydrogen atom, are not arranged randomly, but can be combined into groups called series. The arrangement of lines in these series is subject to certain patterns. In the visible part of the spectrum of the hydrogen atom, this is the Balmer series, in the ultraviolet - the Lyman series, in the near infrared - the Paschen series, etc. The formula found empirically for the wavelengths of l lines in each of these series has the form:
It is called the generalized Balmer formula. In this formula R = 1.097×10 7 m -1 is the Rydberg constant, n And m whole numbers. For a given n number m takes all integer values, starting with n + 1. If n=1 formula (1) describes the Lyman series, n=2 Balmer series, n=3- Pashen series.
The physical meaning of this formula follows from the theory of the structure of the hydrogen atom and hydrogen-like atoms, created by Bohr on the basis of Planck's quantum hypothesis and Rutherford's classical planetary model of the atom. Bohr postulated the main provisions of the theory developed by him.
The first postulate: there are a number of discrete stationary states in the atom, which correspond to certain values of the energy of the atom: E 1, E 2, E 3,…. In a stationary state, an atom does not emit or absorb energy.
The second postulate: the emission and absorption of energy occurs during the transition from one stationary state to another. In this case, a quantum of energy is emitted or absorbed hn, equal to the energy difference of two stationary states:
hn = E m - E n (2)
Where h is Planck's constant. Expression (2) determines the frequency n of monochromatic radiation emitted or absorbed by an atom during the transition from state m to state n (the Bohr frequency condition).
Discrete stationary states in Bohr's theory were selected using a special orbit quantization rule, which was formulated as follows: out of all possible according to classical mechanics orbits are realized only those on which the angular momentum of the electron is a multiple of the value (third postulate):
In formula (3) m is the electron mass; V n is the speed of the electron n-th stationary orbit; rn is the radius of this orbit; n- integer: 1, 2, 3, ....
Following Bohr, consider an atomic system consisting of a nucleus with charge Ze and one electron with charge - e.
At Z= 1 such a system corresponds to a hydrogen atom, for other Z - to a hydrogen-like atom, i.e. an atom with atomic number Z from which all but one electron has been removed. To simplify the calculations, we assume that the electron rotates in a circular orbit, and the mass of the nucleus is infinitely large compared to the mass of the electron, and the nucleus is motionless.
Centripetal force, which holds the electron in the n-th stationary orbit, is created by the force of Coulomb attraction to the nucleus.
From here: , (4)
those. when an electron moves along an orbit, its kinetic energy and potential energy are related by the relation 2T=-U (5)
Dividing equation (4) by equation (3), we obtain an expression for the electron velocity per n-th stationary orbit
The total energy (E) of an electron in the n-th stationary orbit is the sum of the kinetic and potential energies and, taking into account formula (5), is equal to:
Substituting the velocity value (6) into this formula, we obtain the following expression for the energies of the stationary states of the atom:
When an electron passes from orbit m to orbit n, an energy quantum is emitted in accordance with formula (3)
Hence the frequency of the spectral line
In spectroscopy, wave numbers are usually used. Then
For hydrogen (Z = 1), formula (7) takes the form:
and coincides with the generalized Balmer formula (1), which was found empirically for the wave numbers of the spectral lines of the hydrogen atom. From formulas (1) and (8) it follows that
This value coincides with the experimentally determined value of the Rydberg constant.
Figure 1 shows the scheme of energy levels and three series of spectral lines of the hydrogen atom.
Transitions from higher levels to the level n = 1 correspond to the radiation of the Lyman ultraviolet series (I), for which from formula (8) we obtain:
Where m = 2, 3, 4, ...
Transitions from higher levels to the level n = 2 correspond to the radiation of the visible Balmer series (II):
Where m = 3, 4, 5, ...
Transitions from higher levels to level n = 3 correspond to the radiation of the Paschen infrared series (III):
Where m = 4, 5, 6, .…
When light is absorbed by an atom, electrons move from lower levels to higher ones. In this case, the atom passes from the ground state to the excited state.
Bohr's theory was characterized by internal logical inconsistency, so it could not become a consistent complete theory of atomic phenomena. At present, the spectra of atoms and molecules are explained within the framework of quantum mechanics.
An approach to describing the state of microparticles in quantum mechanics fundamentally different from the classic. It does not allow one to determine unambiguously the position of the considered particle in space and its trajectory, as is done in classical mechanics, since in the microcosm these concepts lose their meaning, but only predicts with what probability this particle can be found at various points in space. Therefore, quantum mechanics has a statistical character.
The basis of the mathematical apparatus of quantum mechanics is the statement that the description of the state of the system is carried out by a certain function of coordinates and time Y characterizing this state. This function is called the wave function. It is not the wave function itself that has physical meaning, but the square of its modulus, which determines the probability dw of detecting an object (microparticle) in a volume element dV. If the Y-function is normalized, then dw = |Y| 2dV (9)
Let us find out the properties of the wave function. In view of what has been said above about physical sense|Y| 2 wave function, Y should be:
1. final, because the probability cannot be greater than one;
2. unambiguous;
3. continuous, because probability cannot change abruptly.
Thus, to describe the state of a system in quantum mechanics, it is necessary to know the wave function of this system. It is found from the Schrödinger equation, which is the basic equation in nonrelativistic quantum mechanics. This equation is not derived, but postulated on the basis of general considerations. Its validity is proved by the coincidence of the theoretical results obtained from it with experimental facts. In general, the Schrödinger equation has the following form:
Here m is the mass of the particle, U is a function of coordinates and time, equal to the potential taken with the opposite sign force field, i- imaginary unit, - Laplace operator, .
If the force field in which the particle is located is stationary (does not depend on time), then the potential U does not depend on time and acquires the meaning of the potential energy of the considered particle in an external force field. In this case, Y can be represented as a product of two functions, one of which depends only on coordinates, and the other only on time.
Here E is the total energy of the particle, which in the case stationary field does not change over time.
After substituting this expression into equation (10) for the function y(x,y,z) the following equation is obtained:
which is called the Schrödinger equation for stationary states.
Consider the hydrogen atom from the point of view of quantum mechanics. Let us substitute the value of the potential energy of an electron in the field of the nucleus into the stationary Schrödinger equation:
Equation (11) in this case takes the form:
Since the field of the nucleus of the hydrogen atom has spherical symmetry, it is advisable to solve this equation in a spherical coordinate system (r, j, Q). The solution is carried out by the method of separation of variables, representing the wave function as a product of two functions, one of which depends only on r, and the second only on the angular coordinates j , Q.
y(r,Q,j) = R(r)×Y(Q,j)
With this representation, the probability of a particle to have coordinate values in the range from r before r+dr determined by the square |rr| 2.
The solution of the Schrödinger equation (12) leads to the following main results.
1. Hydrogen electron has a discrete energy spectrum. The energy eigenvalues are determined by the expression:
Where n- The main thing quantum number, which takes any positive integer value ( n = 1, 2, 3, ...).
2. Orbital angular momentum of an electron L can take only the following discrete series of values:
Where l- orbital (azimuthal) quantum number. It can take any value from the range: l= 0, 1, 2, 3, ..., (n-1) - n values in total. Status since l= 0 is usually called s-state, with l = 1 – R- state, c l= 2 – d-state, with l = 3 – f- state, etc.
3. The orbital angular momentum can be oriented relative to a physically distinguished direction in space (z) only in such a way that its projection onto this direction is a multiple of , therefore
m is called the magnetic quantum number. It can take values:
m=0, ±1, ±2, … , ± l– total (2 l+ 1) values.
Thus, the state of an electron in a hydrogen atom is determined by three quantum numbers - the main n, which determines the energy of the state E n; azimuth l characterizing the angular momentum of the electron L, and magnetic m, defining the orientation L relative to the selected direction in space. The states are described by their own wave functions Y n , l , m which are solutions of the Schrödinger equation (18) .
The Schrödinger equation is non-relativistic. Accounting for relativistic effects (Dirac's equation) leads to the existence of an electron's own angular momentum - spin, determined by the quantum number s equal to 1/2:
The projection of the spin onto the preferred direction z can take 2s + 1= 2 different meanings:
where is the quantum number of the electron spin projection. Taking into account the spin, the state of an electron in an atom is characterized by four quantum numbers: to the quantum numbers n,l,m spin quantum number should be added m s.
Note that the discreteness of physical quantities characteristic of phenomena nuclear world, in quantum mechanics naturally follows from the solution of the Schrödinger (Dirac) equation, while in the Bohr theory it had to be introduced using additional conditions of an essentially nonclassical nature.
In the seventeenth century, denoting the totality of all the meanings of any physical quantity. Energy, mass, optical radiation. It is the latter that is often meant when we talk about the spectrum of light. Specifically, the spectrum of light is a collection of bands of optical radiation of different frequencies, some of which we can see every day in the outside world, while some of them are inaccessible to the naked eye. Depending on the possibility of perception by the human eye, the spectrum of light is divided into visible part and invisible. The latter, in turn, is exposed to infrared and ultraviolet light.
Types of spectra
There are also different types spectra. There are three of them, depending on the spectral density of the radiation intensity. Spectra can be continuous, line and striped. The types of spectra are determined using
continuous spectrum
A continuous spectrum is formed by solids or gases heated to a high temperature. high density. The well-known rainbow of seven colors is a direct example of a continuous spectrum.
line spectrum
It also represents the types of spectra and comes from any substance that is in a gaseous atomic state. It is important to note here that it is in the atomic, not the molecular. Such a spectrum provides an extremely low interaction of atoms with each other. Since there is no interaction, the atoms emit waves of the same wavelength permanently. An example of such a spectrum is the glow of gases heated to a high temperature.
striped spectrum
The striped spectrum visually represents separate bands, clearly delimited by rather dark intervals. Moreover, each of these bands is not radiation of a strictly defined frequency, but consists of a large number of light lines closely spaced to each other. An example of such spectra, as in the case of the line spectrum, is the glow of vapors at high temperatures. However, they are no longer created by atoms, but by molecules that have an extremely close common bond, which causes such a glow.
Absorption spectrum
However, the types of spectra still do not end there. Additionally, another type is distinguished, such as an absorption spectrum. In spectral analysis, the absorption spectrum is dark lines against the background of a continuous spectrum and, in essence, the absorption spectrum is an expression of dependence on the absorption index of a substance, which can be more or less high.
Although there is a wide range of experimental approaches to measuring absorption spectra. The most common experiment is when the generated radiation beam is passed through a cooled (for the absence of particle interaction and, therefore, luminescence) gas, after which the intensity of the radiation passing through it is determined. The transferred energy may well be used to calculate the absorption.
27.02.2014 28264 0Target: show the practical significance of spectral analysis.To encourage students to overcome difficulties in the process of mental activity, to cultivate interest in physics.
During the classes
I.Organizing time
II.Checking homework.
IN What is the essence of the Thomson model?
- Draw and explain the scheme of Rutherford's experiment on the scattering of a-particles. What do we see in this experience?
- Explain the reason for the scattering of a-particles by atoms of matter?
- What is the essence of the planetary model of the atom?
III. Learning new material
The word "spectrum" was introduced into physics by Newton, who used it in his scientific works. Translated from classical Latin, the word "spectrum" means "spirit", "casting", which quite accurately reflects the essence of the phenomenon - the appearance of a festive rainbow when colorless sunlight passes through a transparent prism.
All sources do not give light of a strictly defined wavelength. The frequency distribution of the radiation is characterized by the spectral density of the radiation intensity.
Spectra types
Emission spectra
The set of frequencies (or wavelengths) that are contained in the radiation of any substance is called the emission spectrum. They are of three types.
Solidis a spectrum containing all wavelengths of a certain range from red to at k= 7.6 10 7 and up to purple
y f\u003d 4-10 11 m. A continuous spectrum is emitted by heated solid and liquid substances, gases heated under high pressure.
Ruled -this is the spectrum emitted by gases, vapors of low density in the atomic state. It consists of separate lines of different or the same color, having different locations. Each atom emits a set of electromagnetic waves of certain frequencies. Therefore, each chemical element has its own spectrum.
striped -is the spectrum that is emitted by the gas in the molecular state.
Line and stripe spectra can be obtained by heating a substance or by passing an electric current.
Absorption spectra
Absorption spectra are obtained by passing light from a continuous spectrum source through a substance whose atoms are in an unexcited state.
Absorption spectrum - is the totality of frequencies absorbed by a given substance. According to Kirchhoff's law, a substance absorbs those lines of the spectrum that it emits, being a source of light.
The discovery of spectral analysis aroused keen interest even among the public, far from science, which at that time did not happen very often. As always in such cases, idle amateurs found many other scientists who allegedly did everything long before Kirchhoff and Bunsen. Unlike many of their predecessors, Kirchhoff and Bunsen immediately realized the significance of their discovery.
For the first time, they clearly understood to themselves (and convinced others of this) that spectral lines are a characteristic of the atoms of matter.
After the discovery of Kirchhoff and Bunsen on August 18, 1868, the French astronomer Pierre-Jules-Cesar Jansen (1824-1907) observed a yellow line of unknown nature in the spectrum of the solar corona during a solar eclipse in India. Two months later, the English physicist Joseph Norman Lockyer (1836-1920) learned to observe the corona of the Sun without waiting for solar eclipses and at the same time discovered the same yellow line in its spectrum. He called the unknown element that emitted it helium, that is, the solar element.
Both scientists wrote letters to the French Academy of Sciences about their discovery, both letters arrived at the same time and were read out at a meeting of the Academy on October 26, 1868. This coincidence amazed the academicians, and they decided to knock out a commemorative gold medal- on the one hand, the profile of Jansen and Lockyer, on the other, the god Apollo on a chariot and the inscription: "Analysis of solar prominences."
On Earth, helium was discovered in 1895 by William Ramsay in thorium minerals.
Studies of the emission and absorption spectra make it possible to establish the qualitative composition of a substance. The quantitative content of an element in a compound is determined by measuring the brightness of the spectral lines.
The method of determining the qualitative and quantitative composition of a substance by its spectrum is called spectral analysis. Knowing the wavelengths emitted by various vapors, it is possible to establish the presence of certain elements of matter. This method is very sensitive. It is possible to detect an element whose mass does not exceed 10~10 g. Spectral analysis has played a great role in science. With its help, the composition of stars was studied.
Due to its relative simplicity and versatility, spectral analysis is the main method for monitoring the composition of a substance in metallurgy and mechanical engineering. With the help of spectral analysis, the chemical composition of ores and minerals is determined. Spectral analysis can be carried out using both absorption and emission spectra. The composition of complex mixtures is analyzed by the molecular spectrum.
IV. Consolidation of the studied material
- Line emission spectra give excited atoms that do not interact with each other. Which bodies have a line emission spectrum? (Highly rarefied gases and unsaturated vapors.)
- What is the spectrum of white-hot metals, molten metal? (Solid.)
- What spectrum can be observed with a spectroscope from an incandescent spiral of an electric lamp? (Solid.)
- In which state of aggregation in the laboratories of spectral analysis examine any substance to determine its elemental composition? (In gaseous.)
- Why, in the absorption spectrum of the same chemical element, dark lines are exactly located in the places of colored lines of the line emission spectrum? (The atoms of each chemical element absorb only those rays of the spectrum that they themselves emit.)
- What is determined by the absorption lines solar spectrum? (Chemical composition of the Sun's atmosphere.)
V. Summing up the lesson
Homework
§ 54. questions for self-control from the textbook
