—§23 Wave (field) properties of particles. Wave properties of particles Which of the following particles have wave properties
CLASSICAL MODELS OF THE ATOM AND THEIR DEFECTS.
Ideas about what atoms are not indivisible particles and contain as constituents
particles elementary charges, were first stated at the end19th century The term "electron" was proposed in 1881 by the English physicist GeorgeStoney. In 1897, the electron hypothesis received an experimentalconfirmation in studies by Emil Wiechert and Joseph Jan Thomson. From that moment, the creation of various electronic models began.atoms and molecules.Thomson's first model assumed that the positive charge is uniformlydispersed throughout the atom, and into it, like raisins in a bun,embedded electrons.The inconsistency of this model with experimental data became clearafter an experiment in 1906 by Ernest Rutherford, who investigated
the process of scattering of a-particles by atoms. From experience you were made,that the positive charge is concentrated inside the formation, it is essentialsmaller than the size of an atom. This formation was called atomicnucleus, the dimensions of which were 1 o-12 cm, and the dimensions of the atom were 1 o-in cm.
In accordance with the classical concepts of electromagnetisma Coulomb force must act between each electron and the nucleusattraction. The dependence of this force on distance should besame as in law gravity. Therefore, the movement
electrons in an atom should be likebut the motion of the planets solar system. So was born planetary model Rutherford atom.Further exploration of sustainabilityatom gave a stunning result:calculations showed that during1 o-9 s the electron must fall on the nucleus
due to the loss of energy by radiation. Moreover, this model gavecontinuous rather than discrete emission spectra of atoms.
BORON ATOM THEORY.
The next important step in development of the theory of atoms was done by Niels Bohr.
The most important hypothesis put forward by Bohr in 1913, the hypothesis of a discrete structure appeared
energy levels an electron in an atom. This position illustrated on energy
diagrams. Traditionally, energy diagrams, energy is deposited along the vertical
axes. The difference between the motion of a body in a gravitational fieldfrom the motion of an electron in an atomaccording to the Bohr hypothesis isthat the energy of a body can change continuously,and the electron energy at negative valuescan take on a number of discrete values,shown in the figure as blue segmentscolors. These discrete values have been calledenergy levels or, otherwise, energy levels. Of course, the idea of discrete energy levelswas taken from Planck's hypothesis. Energy changeelectron in accordance with Bohr's theory couldoccur only in a jump (from one energy level another). Bohr's theory perfectly explained the line character
atomic spectra. However, to the question about the reason for discreteness
levels, the theory did not actually give an answer.
WAVES OF SUBSTANCE.
The next step in the development of the theory of the microworld was made by Louis de Broglie. In 1924 he suggested thatthe motion of microparticles must be described not as classical mechanical
movement, but as some kind of wave movement. It is from the laws wave motion must be obtained recipes for calculating the differencesother observable quantities. So in science, along with electromagnetic wavesfields appeared waves of matter.The hypothesis about the wave nature of the movement of particles was as bold asas well as Planck's conjecture about the discrete properties of the field. Experiment,directly confirming the hypothesisBroglie, was delivered only in 1927.In this experiment, it was observedelectron diffraction on a crystal,like electromagnetic diffraction waves. The hypothesis about the waves of matter allowedexplain the discrete nature
energy levels. From theory waves, it was known that a wave limited in space always hasdiscrete frequencies. An example is a wave in such a musicalinstrument like a flute. The sound frequency in this case is determinedthe dimensions of the space by which the wave is limited (the dimensions of the flute).It turns out that this is a general property of waves.But in accordance with Planck's hypothesis, the electromagnetic quantum frequencythe waves are proportional to the energy of the quantum. Therefore, the energy of the electronmust take discrete values.De Broglie's idea turned out to be very fruitful, although, as already mentioned,direct experiment confirming the wave properties of an electron, was carried out only in 1927. In 1926, Erwin Schrödinger derived the equation,to which the electron wave must obey, and, having solved thisequation applied to the hydrogen atom, received all the results thatwas capable of giving Bohr's theory. In fact, this was the beginningmodern theory describing processes in the microworld, sincethe wave equation was easily generalized to most different systems- multielectronicatoms, molecules, crystals.The development of the theory led to the understanding that the wave corresponding toparticle, determines the probability of finding a particle at a given pointspace. Thus, the concept of probability entered the physics of the microworld.According to new theory the wave corresponding to the particle completely determinesparticle movement. But general properties waves are such that the wavecannot be localized at any point in space, i.e. meaninglesstalk about the coordinates of the particle at a given time.The consequence of this was the complete exclusion from the physics of the microworld of suchconcepts such as the trajectory of a particle and electron orbits inatom. A beautiful and visual planetary model of the atom, as it turned out,
Wave-particle duality- the property of any microparticle to detect signs of a particle (corpuscle) and a wave. The corpuscular-wave dualism manifests itself most clearly in elementary particles. An electron, neutron, photon under some conditions behave like material objects (particles) well localized in space, moving with certain energies and momenta along classical trajectories, and under other conditions they behave like waves, which is manifested in their ability to interfere and diffraction. So an electromagnetic wave, scattering on free electrons, behaves like a stream of individual particles - photons, which are quanta of the electromagnetic field (the Compton effect), and the momentum of the photon is given by the formula p \u003d h / λ, where λ is the electromagnetic wave length, and h is Planck's constant . This formula itself is evidence of dualism. In it on the left is the momentum of an individual particle (photon), and on the right is the wavelength of the photon. The dualism of electrons, which we are accustomed to consider as particles, is manifested in the fact that when reflected from the surface of a single crystal, a diffraction pattern is observed, which is a manifestation of the wave properties of electrons. The quantitative relationship between the corpuscular and wave characteristics of an electron is the same as for a photon: р = h/λ (р is the momentum of the electron, and λ is its de Broglie wavelength). Wave-particle duality underlies quantum physics.
A wave (fur) is a process that is always associated with a material medium that occupies a certain volume in space.
64. Waves de Broglie. Electron diffraction Wave properties of microparticles.
The development of ideas about the corpuscular-wave properties of matter received in the hypothesis of the wave nature of the movement of microparticles. Louis de Broglie, from the idea of symmetry in nature for particles of matter and light, attributed to any microparticle some internal periodic process (1924). Combining the formulas E = hν and E = mc 2 , he obtained a relation showing that any particle has its own wavelength : λ B \u003d h / mv \u003d h / p, where p is the momentum of the wave-particle. For example, for an electron having an energy of 10 eV, the de Broglie wavelength is 0.388 nm. Later it was shown that the state of a microparticle in quantum mechanics can be described by a certain complex wave function coordinates Ψ(q), and the square of the modulus of this function |Ψ| 2 defines the probability distribution of coordinate values. This function was first introduced into quantum mechanics by Schrodinger in 1926. Thus, the de Broglie wave does not carry energy, but only reflects the “phase distribution” of some probabilistic periodic process in space. Therefore, the description of the state of the objects of the microworld is probabilistic character, in contrast to the objects of the macrocosm, which are described by the laws of classical mechanics.
To prove de Broglie's idea about the wave nature of microparticles, the German physicist Elsasser suggested using crystals to observe electron diffraction (1925). In the USA, K. Davisson and L. Germer discovered the phenomenon of diffraction during the passage of an electron beam through a nickel crystal plate (1927). Independently of them, the diffraction of electrons when passing through a metal foil was discovered by J.P. Thomson in England and P.S. Tartakovsky in the USSR. So de Broglie's idea of the wave properties of matter found experimental confirmation. Subsequently, diffractive, and therefore wave, properties were discovered in atomic and molecular beams. Corpuscular-wave properties are possessed not only by photons and electrons, but also by all microparticles.
The discovery of the wave properties of microparticles showed that such forms of matter as field (continuous) and matter (discrete), which, from the point of view of classical physics, were considered to be qualitatively different, in certain conditions may exhibit properties inherent in both forms. This speaks of the unity of these forms of matter. A complete description of their properties is possible only on the basis of opposite, but complementary ideas.
Of course, you can call it nonsense,
but I have met such nonsense that in
compared to her, this one seems sensible
dictionary.
L. Carroll
What is the planetary model of the atom and what is its disadvantage? What is the essence of the Bohr model of the atom? What is the hypothesis about the wave properties of particles? What predictions does this hypothesis give about the properties of the microworld?
Lesson-lecture
CLASSICAL MODELS OF THE ATOM AND THEIR DISADVANTAGES. The ideas that atoms are not indivisible particles and contain elementary charges as constituent particles were first expressed in late XIX v. The term "electron" was proposed in 1881 by the English physicist George Stoney. In 1897, the electronic hypothesis received experimental confirmation in the studies of Emil Wiechert and Joseph John Thomson. From that moment, the creation of various electronic models of atoms and molecules began.
Thomson's first model assumed that the positive charge was evenly distributed throughout the atom, and electrons were interspersed in it, like raisins in a bun.
The discrepancy between this model and the experimental data became clear after an experiment in 1906 by Ernest Rutherford, who studied the process of scattering of α-particles by atoms. From the experience it was concluded that the positive charge is concentrated inside the formation, much smaller than the size of the atom. This formation is called atomic nucleus, the dimensions of which were 10 -12 cm, and the dimensions of the atom - 10 -8 cm. In accordance with the classical ideas of electromagnetism, the Coulomb force of attraction must act between each electron and the nucleus. The dependence of this force on distance should be the same as in the law of universal gravitation. Therefore, the movement of electrons in an atom must be similar to the movement of the planets of the solar system. So was born planetary model of the atom Rutherford.
The short lifetime of an atom and the continuous spectrum of radiation, which follow from the planetary model, showed its inconsistency in describing the motion of electrons in an atom.
A further study of the stability of the atom gave a stunning result: calculations showed that in a time of 10 -9 s, the electron must fall on the nucleus due to energy loss for radiation. In addition, such a model gave continuous rather than discrete emission spectra of atoms.
BORON ATOM THEORY. The next important step in the development of the theory of atoms was made by Niels Bohr. The most important hypothesis put forward by Bohr in 1913 was the hypothesis of the discrete structure of the energy levels of an electron in an atom. This position is illustrated in the energy diagrams (Fig. 21). Traditionally, energy diagrams plot energy along the vertical axis.
Rice. 21 Satellite energy in the Earth's gravitational field (а); energy of an electron in an atom (b)
The difference between the motion of a body in a gravitational field (Fig. 21, a) and the motion of an electron in an atom (Fig. 21, b) in accordance with the Bohr hypothesis is that the energy of the body can continuously change, and the energy of an electron with negative values can take the series discrete values shown in the figure as blue segments. These discrete values were called energy levels or, in other words, energy levels.
Of course, the idea of discrete energy levels was taken from Planck's hypothesis. The change in the energy of an electron, in accordance with Bohr's theory, could only occur in a jump (from one energy level to another). During these transitions, a light quantum is emitted (downward transition) or absorbed (upward transition), the frequency of which is determined from the Planck formula hv \u003d E quantum \u003d ΔE of the atom, i.e., the change in the energy of the atom is proportional to the frequency of the emitted or absorbed light quantum.
Bohr's theory perfectly explained the line character of atomic spectra. However, the theory actually did not give an answer to the question about the reason for the discreteness of the levels.
WAVES OF SUBSTANCE. The next step in the development of the theory of the microworld was made by Louis de Broglie. In 1924, he suggested that the motion of microparticles should be described not as classical mechanical movement, but as some kind of wave motion. It is from the laws of wave motion that recipes for calculating various observable quantities must be obtained. So in science along with waves electromagnetic field waves of matter appeared.
The hypothesis about the wave nature of the motion of particles was as bold as Planck's hypothesis about the discrete properties of the field. An experiment directly confirming de Broglie's hypothesis was set up only in 1927. In this experiment, electron diffraction on a crystal was observed, similar to the diffraction of an electromagnetic wave.
Bohr's theory was an important step in understanding the laws of the microworld. It was the first to introduce the provision on discrete values of the energy of an electron in an atom, which corresponded to experience and subsequently became part of quantum theory.
The hypothesis of matter waves made it possible to explain the discrete nature of energy levels. It was known from the theory of waves that a wave limited in space always has discrete frequencies. An example is a wave in such musical instrument like a flute. The sound frequency in this case is determined by the dimensions of the space that the wave is limited to (the dimensions of the flute). It turns out that this is a general property of waves.
But in accordance with Planck's hypothesis, the frequencies of the quantum of an electromagnetic wave are proportional to the energy of the quantum. Consequently, the electron energy must also take discrete values.
The idea of de Broglie turned out to be very fruitful, although, as already mentioned, a direct experiment confirming the wave properties of an electron was carried out only in 1927. hydrogen atom, got all the results that Bohr's theory was capable of giving. In fact, this was the beginning of a modern theory describing processes in the microworld, since the wave equation was easily generalized for a variety of systems - many-electron atoms, molecules, crystals.
The development of the theory led to the understanding that the wave corresponding to the particle determines the probability of finding the particle at a given point in space. So the concept of probability entered the physics of the microcosm
According to the new theory, the wave corresponding to the particle completely determines the motion of the particle. But the general properties of waves are such that a wave cannot be localized at any point in space, i.e., it is meaningless to talk about the coordinates of a particle at a given moment in time. The consequence of this was the complete exclusion from the physics of the microcosm of such concepts as the trajectory of a particle and electron orbits in an atom. A beautiful and visual planetary model of the atom, as it turned out, does not correspond to the real movement of electrons.
All processes in the microcosm have a probabilistic character. Only the probability of a particular process occurring can be determined by calculations.
In conclusion, let's return to the epigraph. Hypotheses about matter waves and field quanta seemed like nonsense to many physicists who were brought up on the traditions of classical physics. The fact is that these hypotheses are deprived of the usual visualization that we have when making observations in the macrocosm. However, the subsequent development of the science of the microworld led to such ideas that ... (see the epigraph to the paragraph).
- What experimental facts did Thomson's model of the atom contradict?
- What remains of Bohr's model of the atom in modern theory and what has been discarded?
- What ideas contributed to de Broglie's hypothesis about the waves of matter?
Wave properties of microparticles.
The development of ideas about the corpuscular-wave properties of matter received in the hypothesis of the wave nature of the movement of microparticles. Louis de Broglie, from the idea of symmetry in nature for particles of matter and light, attributed to any microparticle some internal periodic process (1924). Combining the formulas E \u003d hν and E \u003d mc 2, he obtained a ratio showing that any particle has its own wavelength: λ B \u003d h / mv \u003d h / p, where p is the momentum of the wave-particle. For example, for an electron having an energy of 10 eV, the de Broglie wavelength is 0.388 nm. Later it was shown that the state of a microparticle in quantum mechanics can be described by a certain complex wave function of the coordinates Ψ(q), and the square of the modulus of this function |Ψ| 2 defines the probability distribution of coordinate values. This function was first introduced into quantum mechanics by Schrodinger in 1926. Thus, the de Broglie wave does not carry energy, but only reflects the “phase distribution” of some probabilistic periodic process in space. Consequently, the description of the state of microcosm objects is probabilistic, unlike macrocosm objects, which are described by the laws of classical mechanics. To prove de Broglie's idea about the wave nature of microparticles, the German physicist Elsasser suggested using crystals to observe electron diffraction (1925). In the USA, K. Davisson and L. Germer discovered the phenomenon of diffraction during the passage of an electron beam through a nickel crystal plate (1927). Independently of them, the diffraction of electrons when passing through a metal foil was discovered by J.P. Thomson in England and P.S. Tartakovsky in the USSR. So the idea of de Broglie about the wave properties of matter found experimental confirmation. Subsequently, diffractive, and therefore wave, properties were discovered in atomic and molecular beams. Corpuscular-wave properties are possessed not only by photons and electrons, but also by all microparticles. The discovery of wave properties in microparticles showed that such forms of matter as field (continuous) and matter (discrete), which, from the point of view of classical physics, were considered qualitatively different, under certain conditions, they can exhibit properties inherent in both forms. This speaks of the unity of these forms of matter. A complete description of their properties is possible only on the basis of opposite, but complementary ideas.Electron diffraction.
A diffraction grating is used to obtain the spectrum of light waves and determine their length. It is a collection a large number narrow slits separated by opaque gaps, for example, a glass plate with scratches (strokes) applied to it. As with two slits (see lab. work 2), when a plane monochromatic wave passes through such a grating, each slit will become a source of secondary coherent waves, as a result of which an interference pattern will appear as a result of their addition. The condition for the occurrence of interference maxima on a screen located at a distance L from the diffraction grating is determined by the path difference between the waves from adjacent slots. If at the observation point the path difference is equal to an integer number of waves, then they will be amplified and the maximum of the interference pattern will be observed. The distance between the maxima for light of a certain wavelength λ is determined by the formula: h 0 = λL/d. The value d is called the grating period and is equal to the sum of the widths of the transparent and opaque gaps. To observe electron diffraction, metal crystals are used as a natural diffraction grating. The period d of such a natural diffraction grating corresponds to the characteristic distance between the atoms of the crystal. The installation scheme for observing electron diffraction is shown in Figure 1. Passing through the potential difference U between the cathode and anode, the electrons acquire kinetic energy Ekin. = Ue, where e is the electron charge. From the formula of kinetic energy E kin. = (m e v 2)/2 you can find the speed of the electron: . Knowing the electron mass m e, one can determine its momentum and, accordingly, the de Broglie wavelength.
According to the same scheme, an electron microscope was created in the 30s, giving a magnification of 10 6 times. Instead of light waves, it uses the wave properties of a beam of electrons accelerated to high energies in a deep vacuum. Significantly smaller objects were studied than with a light microscope, and in terms of resolution, the improvement was thousands of times. Under favorable conditions, it is possible to photograph even individual large atoms, as close as possible to the details of an object with a size of about 10 -10 m. Without it, it was hardly possible to control microcircuit defects, obtain pure substances, develop microelectronics, molecular biology etc.
Laboratory work No. 7. The order of the work.
Open a working window.
A). By moving the slider on the right side of the working window, set an arbitrary value of the accelerating voltage U ( until you move the slider, the buttons will be inactive!!!) and write down this value. Click the button Start. Observe on the screen of the working window how the interference pattern appears during the diffraction of electrons on a metal foil. Note that electrons entering various points the screen is random, but the probability of electrons getting into certain areas of the screen is zero, while in others it is non-zero. That is why the interference pattern appears. Wait until the concentric circles of the interference pattern clearly appear on the screen and press the button Test. Attention! Until the interference pattern becomes clear enough, the Test button will be inactive. It will become active after the mouse cursor, when hovering over this button, changes its view from an arrow to a hand!!! A graphic representation of the probability of electron distribution along the x axis will appear on the screen, corresponding to the interference pattern. Drag the measuring ruler to the graph area. Use the right mouse button to zoom in on the graph and determine the distance between the two extreme interference maxima with an accuracy of tenths of a millimeter. Write down this value. By dividing this value by 4 you get the distance h 0 between the maxima of the interference pattern. Write it down. Use the right mouse button to return the image to its original state. Using the formulas in the theoretical part, determine the de Broglie wavelength. Substitute this value in the test window and click the button Check Right!!! B). Using the formulas in the theoretical part, find the electron velocity from the accelerating voltage and write it down. Substitute this value in the test window and click the button Check. If the calculations are correct, an inscription will appear Right!!! Calculate the momentum of an electron and use de Broglie's formula to find the wavelength. Compare the value obtained with that found from the interference pattern. V). Change the voltage and pressing the button Test repeat points A and B. Show your test results to your teacher. Based on the results of the measurements, make a table:| Electron speed v | Electron momentum p | ||||
Laboratory work No. 7. Report form.
The heading states:
NAME OF THE LABORATORY WORK
Exercise. Electron diffraction.
A). Found distance h 0 . Wavelength calculation λ.
B). Calculations of electron speed, momentum and wavelength.
V). Repeat items A and B.Table with results:
| h 0 (distance between maxima) | Electron speed v | Electron momentum p | |||
G). Analysis of results. Answers on questions.
D). Determination of the de Broglie wavelength for a car. Answers on questions. Conclusions.
1. What is the essence of Louis de Broglie's hypothesis?
2. What experiments confirmed this hypothesis?
3. What is the specificity of the description of the state of the objects of the microcosm, in contrast to the description of the objects of the macrocosm?
4. Why did the discovery of wave properties of microparticles, along with the manifestation of corpuscular properties of electromagnetic waves (light), make it possible to talk about the corpuscular-wave dualism of matter? Explain the essence of these representations.
5. How does the de Broglie wavelength depend on the mass and speed of the microparticle?
6. Why don't macro objects show wave properties?
Lab #8 DESCRIPTION
Diffraction of photons. Uncertainty relation.
Working window
The view of the working window is shown in Fig. 1.1. The working window shows the photon diffraction model. The test buttons are located in the lower right part of the window. The calculated parameters are entered into the window under the test buttons. In the upper position of the switch, this is the uncertainty of the photon momentum, and in the lower position, the product of the momentum uncertainty and the x-coordinate uncertainty. In the windows below, the number of correct answers and the number of attempts are recorded. By moving the sliders, you can change the photon wavelength and the size of the slit.
Figure 1.1.
To measure the distance from the maximum of the diffraction pattern to the minimum, the slider located to the right of the model window is used. The measurements are carried out for several values of the gap sizes. The test system records the number of correctly given answers and total number attempts.
Laboratory work number 8. Theory
Uncertainty relation.
PURPOSE OF THE WORK: Using the example of photon diffraction, to give students an idea of the uncertainty relation. Using the model of photon diffraction by a slit, it is clear to demonstrate that the more accurately the x coordinate of a photon is determined, the less accurately the value of its momentum projection p x is determined.
Uncertainty relation
In 1927, W. Heisenberg discovered the so-called uncertainty relations, according to which the uncertainties of coordinates and momenta are interconnected by the relation:
, where 
, h Planck's constant. The peculiarity of the description of the microcosm is that the product of the uncertainty (accuracy of determination) of the position Δx and the uncertainty (accuracy of determination) of the momentum Δp x must always be equal to or greater than a constant equal to –. It follows from this that a decrease in one of these quantities should lead to an increase in the other. It is well known that any measurement is associated with certain errors, and by improving measuring instruments, it is possible to reduce errors, i.e., increase the accuracy of measurement. But Heisenberg showed that there are conjugate (additional) characteristics of a microparticle, the exact simultaneous measurement of which is fundamentally impossible. Those. uncertainty is a property of the state itself, it is not related to the accuracy of the device. For other conjugate quantities - energy E and time t the ratio looks like: . This means that for the characteristic evolution time of the system Δ t, the error in determining its energy cannot be less than . From this relation follows the possibility of the emergence of the so-called virtual particles from nothing for a period of time less than 
and having energy Δ E. In this case, the law of conservation of energy will not be violated. Therefore, according to modern ideas vacuum is not a void in which there are no fields and particles, but a physical entity in which virtual particles constantly appear and disappear. One of the basic principles of quantum mechanics is uncertainty principle discovered by Heisenberg. Obtaining information about some quantities that describe the micro-object inevitably leads to a decrease in information about other quantities that are additional to the first ones. Instruments that record quantities related by uncertainty relations are of different types, they are complementary to each other. Measurement in quantum mechanics means any process of interaction between classical and quantum objects that occurs apart from and independently of any observer. If in classical physics the measurement did not perturb the object itself, then in quantum mechanics each measurement destroys the object, destroying its wave function. For a new measurement, the object must be prepared again. In this regard, N. Bohr put forward Pcomplementarity principle, the essence of which is that for complete description objects of the microworld, it is necessary to use two opposite, but complementary representations. Photon diffraction as an illustration of the uncertainty relation
From the point of view of quantum theory, light can be considered as a stream of light quanta - photons. When a monochromatic plane wave of light is diffracted by a narrow slit, each photon passing through the slit hits a certain point on the screen (Fig. 1.). It is impossible to predict exactly where the photon will hit. However, in aggregate, getting into different points screen, photons give a diffraction pattern. When a photon passes through a slit, we can say that its x coordinate was determined with an error Δx, which is equal to the size of the slit. If the front of a plane monochromatic wave is parallel to the plane of the screen with a slit, then each photon has a momentum directed along the z axis perpendicular to the screen. Knowing the wavelength, this momentum can be accurately determined: p = h/λ.
However, after passing through the slit, the direction of the pulse changes, as a result of which a diffraction pattern is observed. The momentum modulus remains constant, since the wavelength does not change during the diffraction of light. Deviation from the original direction occurs due to the appearance of the component Δp x along the x axis (Fig. 1.). It is impossible to determine the value of this component for each competitive photon, but its maximum value in absolute value determines the width of the 2S diffraction pattern. The maximum value of Δp x is a measure of the uncertainty of the photon momentum that occurs when determining its coordinates with an error of Δx. As can be seen from the figure, the maximum value of Δp x is: Δp x = psinθ, 
. If L>> s , then we can write: sinθ =s/ L and Δp x = p(s/ L).
Laboratory work No. 8. The order of the work.
Check out theoretical part work.
Open a working window.A). By moving the sliders on the right side of the working window, set arbitrary values of the wavelength λ and the slit size Δx. Write down these values. Click the button Test. Using the right mouse button, zoom in on the diffraction pattern. Using the slider to the right of the diffraction pattern image, determine the maximum distance s that photons are deflected along the x-axis, and write it down. Use the right mouse button to return the image to its original state. Using the formulas in the theoretical part, determine Δp x . Substitute this value in the test window and click the button Check. If the calculations are correct, an inscription will appear Right!!!B). Using the found values, find the product Δp x Δx. Substitute this value in the test window and click the button Check. If the calculations are correct, an inscription will appear Right!!!.V). Change the slot size and by pressing the button Test repeat points A and B. Show your test results to your teacher. Make a table according to the results of measurements:| Δx (slit width) | Photon momentum p | Δp x (calculated) | ||||
Laboratory work No. 8. Report form.
General requirements for registration.
The work is carried out on sheets of A4 paper, or on double notebook sheets.
The heading states:
Surname and initials of the student, group number
NAME OF THE LABORATORY WORK
Each task of laboratory work is made out as its section and should have a heading. In the report for each task, answers to all questions should be given and, if indicated, conclusions are drawn and the necessary drawings are given. results test items must be shown to the teacher. In tasks that include measurements and calculations, the measurement data and the data of the calculations performed should be given.
Exercise. Uncertainty relation.
A). Wavelength λ and slit size Δx. Measured maximum distance s. Calculations of the photon momentum and Δp x .
B). Calculations of the product Δp x Δx.
V). Repeat items A and B.Table with results:
| Δx (slit width) | Photon momentum p | Δp x (calculated) | ||||
G). Analysis of results. Conclusions. Answers on questions.
D). Answers on questions.
Control questions to check the assimilation of the topic of laboratory work:
1. Explain why it follows from the uncertainty relation that it is impossible to simultaneously accurately determine the conjugate quantities?
2. Energy Spectra radiation is associated with the transition of electrons from higher energy levels to lower ones. This transition takes place over a certain period of time. Is it possible to absolutely accurately determine the energy of radiation?
3. State the essence of the uncertainty principle.
4. What is the role of the device in the microworld?
5. From the uncertainty relation, explain why, in photon diffraction, a decrease in the size of the slit leads to an increase in the width of the diffraction pattern?
6. State the essence of Bohr's complementarity principle.
7. What is vacuum according to modern concepts?
Lab #9 DESCRIPTION
Thermal motion (1)
Working window
The view of the working window is shown in Fig. 6.1. The left part of the working window shows a model of the thermal motion of particles in a volume, which is divided into two parts by a partition. With the mouse, the partition can be moved to the left (by pressing the left mouse button on its upper part) or removed (by clicking on its lower part).
R 
Figure 6.1.
In the right part of the working window are given: temperature (in the right and left parts of the simulated volume), instantaneous particle velocities, and the number of collisions of particles with walls during the observation process. button Start the movement of particles is started, while the initial velocities and the location of the particles are set randomly. In the box next to the button Start the number of particles is set. Button Stop stops the movement. By pressing the button Continue the movement is resumed, and the windows for recording the number of collisions with the walls are cleared. With button Heat it is possible to increase the temperature in the right part of the simulated volume. Button Off turns off the heating. The switch to the right of the control buttons can set several different operating modes.
To open the working window, click on its image.
Laboratory work number 9. Theory
