If you do not take into account oscillatory ones. Molecular physics and thermodynamics
80. If we do not take into account the vibrational movements in the hydrogen molecule at a temperature of 200 TO, then the kinetic energy in ( J) all molecules in 4 G hydrogen is equal to... Answer:
81. In physiotherapy, ultrasound is used with frequency and intensity. When such ultrasound acts on human soft tissues, the density amplitude of molecular vibrations will be equal to ...
(Read speed ultrasonic waves equal in the human body. Express your answer in angstroms and round to the nearest whole number.) Answer: 2.
82. Two mutually perpendicular oscillations are added. Establish a correspondence between the number of the corresponding trajectory and the laws of point oscillations M along the coordinate axes 
Answer:
1 
2 
3 
4 
83. The figure shows the profile of a transverse traveling wave, which propagates at a speed of . The equation of this wave is the expression... 
Answer:
84. The law of conservation of angular momentum imposes restrictions on the possible transitions of an electron in an atom from one level to another (selection rule). In the energy spectrum of the hydrogen atom (see figure) the transition is forbidden... 
Answer:
85. The energy of an electron in a hydrogen atom is determined by the value of the principal quantum number. If , then equals... Answer: 3.
86. .
The angular momentum of an electron in an atom and its spatial orientation can be conventionally depicted by a vector diagram, in which the length of the vector is proportional to the modulus of the orbital angular momentum of the electron. The figure shows possible orientations of the vector. 
Answer: 3.
87. The stationary Schrödinger equation in the general case has the form 
. Here 
potential energy of a microparticle. The motion of a particle in a three-dimensional infinitely deep potential box is described by the equation... Answer: 
88. The figure schematically shows stationary orbits of an electron in a hydrogen atom according to the Bohr model, and also shows transitions of an electron from one stationary orbit to another, accompanied by the emission of an energy quantum. In the ultraviolet region of the spectrum, these transitions give the Lyman series, in the visible - the Balmer series, in the infrared - the Paschen series. 
The highest quantum frequency in the Paschen series (for the transitions shown in the figure) corresponds to the transition... Answer: 
89. If a proton and a deuteron have passed through the same accelerating potential difference, then the ratio of their de Broglie wavelengths is ... Answer:
90. The figure shows the velocity vector of a moving electron: 
WITH directed... Answer: from us
91. A small electric boiler can be used to boil a glass of water for tea or coffee in the car. Battery voltage 12 IN. If he's over 5 min heats 200 ml water from 10 to 100° WITH, then the current strength (in A
J/kg. TO.)Answer: 21
92. Conducting flat circuit with an area of 100 cm 2 
Tl mV), is equal to... Answer: 0.12
93. Orientational polarization of dielectrics is characterized by... Answer: the influence of thermal motion of molecules on the degree of polarization of the dielectric
94. The figures show graphs of the field strength for various charge distributions: 
R shown in the picture... Answer: 2.
95. Maxwell's equations are the basic laws of classical macroscopic electrodynamics, formulated on the basis of a generalization of the most important laws of electrostatics and electromagnetism. These equations in integral form have the form:
1). 
;
2). 
;
3). 
;
4). 0.
Maxwell's third equation is a generalization Answer: Ostrogradsky–Gauss theorems for an electrostatic field in a medium
96. The dispersion curve in the region of one of the absorption bands has the form shown in the figure. Relationship between phase and group velocities for a section bc looks like... 
Answer:
1. 182 . An ideal heat engine operates according to the Carnot cycle (two isotherms 1-2, 3-4 and two adiabats 2-3, 4-1).
During the process of isothermal expansion 1-2, the entropy of the working fluid ... 2) does not change
2. 183. A change in the internal energy of a gas during an isochoric process is possible... 2) without heat exchange with the external environment
3. 184. When the gun was fired, the projectile flew out of the barrel, located at an angle to the horizon, rotating around its longitudinal axis with an angular velocity. The moment of inertia of the projectile relative to this axis, the time of movement of the projectile in the barrel. A moment of force acts on the gun barrel during a shot... 1)
Electric motor rotor rotating at speed 
, after turning off it stopped after 10s. The angular acceleration of the rotor braking after turning off the electric motor remained constant. The dependence of rotation speed on braking time is shown in the graph. The number of revolutions that the rotor made before stopping is ... 3) 80
5. 186. An ideal gas has minimum internal energy in the state...
2) 1
6. 187. A ball of radius R and mass M rotates with angular velocity . The work required to double its rotation speed is... 4)
7. 189 . After a time interval equal to two half-lives, undecayed radioactive atoms will remain... 2)25%
8. 206 . A heat engine operating according to the Carnot cycle (see figure) performs work equal to...
4)
9. 207. If for polyatomic gas molecules at temperatures the contribution of nuclear vibration energy to the heat capacity of the gas is negligible, then of the ideal gases proposed below (hydrogen, nitrogen, helium, water vapor), one mole has an isochoric heat capacity (universal gas constant) ... 2) water vapor
10. 208.
An ideal gas is transferred from state 1 to state 3 in two ways: along the 1-3 and 1-2-3 paths. The ratio of work done by gas is... 3) 1,5
11. 210. When the pressure increases by 3 times and the volume decreases by 2 times, the internal energy of an ideal gas... 3) will increase by 1.5 times
12. 211.
13. A ball of radius rolls uniformly without slipping along two parallel rulers, the distance between which , and covers 120 cm in 2 s. The angular velocity of rotation of the ball is... 2)
14. 212 . A cord is wound around a drum with a radius, to the end of which a mass of mass is attached. The load descends with acceleration. Moment of inertia of the drum... 3)
15. 216. A rectangular wire frame is located in the same plane with a straight long conductor through which current I flows. The induction current in the frame will be directed clockwise when it ...
3) translational movement in the negative direction of the OX axis
16. 218. A frame with a current with a magnetic dipole moment, the direction of which is indicated in the figure, is in a uniform magnetic field:
The moment of forces acting on the magnetic dipole is directed... 2) perpendicular to the plane of the drawing to us
17. 219. The average kinetic energy of gas molecules at temperature depends on their configuration and structure, which is associated with the possibility various types movement of atoms in a molecule and the molecule itself. Provided that there is translational and rotational motion of the molecule as a whole, the average kinetic energy of a water vapor molecule () is equal to ... 3)
18. 220. The eigenfunctions of an electron in a hydrogen atom contain three integer parameters: n, l and m. The parameter n is called the principal quantum number, the parameters l and m are called the orbital (azimuthal) and magnetic quantum numbers, respectively. Magnetic quantum number m determines... 1) projection of the orbital angular momentum of the electron to a certain direction
19. 221.
Stationary Schrödinger equation 
describes the motion of a free particle if the potential energy has the form... 2)
20. 222. The figure shows graphs reflecting the nature of the dependence of polarization P of the dielectric on the voltage of the external electric field E.
Non-polar dielectrics correspond to the curve ... 1) 4
21. 224. A horizontally flying bullet pierces a block lying on a smooth horizontal surface. In the “bullet-bar” system... 1) momentum is conserved, mechanical energy is not conserved
22. A hoop rolls down a slide 2.5 m high without slipping. The speed of the hoop (in m/s) at the base of the slide, provided that friction can be neglected, is ... 4) 5
23. 227. T The momentum of the body changed under the influence of a short-term impact and became equal, as shown in the figure:
At the moment of impact, the force acted in the direction... Answer:2
24. 228. The accelerator imparted speed to the radioactive nucleus (c is the speed of light in vacuum). At the moment of departure from the accelerator, the nucleus ejected a β-particle in the direction of its motion, the speed of which was relative to the accelerator. The speed of a beta particle relative to the nucleus is... 1) 0.5 s
25. 231. The average kinetic energy of gas molecules at temperature depends on their configuration and structure, which is associated with the possibility of various types of movement of atoms in the molecule and the molecule itself. Provided that there is translational, rotational motion of the molecule as a whole and vibrational motion of the atoms in the molecule, the ratio of the average kinetic energy of vibrational motion to the total kinetic energy of the nitrogen molecule () is equal to ... 3) 2/7
26. 232. The spin quantum number s determines... own mechanical moment electron in an atom
27. 233. If a hydrogen molecule, positron, proton and -particle have the same de Broglie wavelength, then the highest speed has ... 4) positron
28. A particle is located in a rectangular one-dimensional potential box with impenetrable walls 0.2 nm wide. If the energy of a particle at the second energy level is 37.8 eV, then at the fourth energy level it is equal to _____ eV. 2) 151,2
29. The stationary Schrödinger equation in the general case has the form 
. Here 
potential energy of a microparticle. An electron in a one-dimensional potential box with infinitely high walls corresponds to the equation... 1) 
30. Complete system of Maxwell's equations for electro magnetic field in integral form has the form:
,
,
The following system of equations:
valid for... 4) electromagnetic field in the absence of free charges
31. The figure shows sections of two straight long parallel conductors with oppositely directed currents, and . The magnetic field induction is zero in the area ...
4)d
32. A conducting jumper of length (see figure) moves along parallel metal conductors located in a uniform magnetic field with constant acceleration. If the resistance of the jumper and guides can be neglected, then the dependence of the induction current on time can be represented by a graph ...
33. The figures show the time dependence of speed and acceleration material point oscillating according to a harmonic law.
The cyclic frequency of oscillations of a point is ______ Answer: 2
34. Two harmonic oscillations of the same direction with the same frequencies and amplitudes, equal to and , are added. Establish a correspondence between the phase difference of the added oscillations and the amplitude of the resulting oscillation.
35. Answer options:
36. If the frequency of an elastic wave is increased by 2 times without changing its speed, then the intensity of the wave will increase by ___ times. Answer: 8
37. The equation of a plane wave propagating along the OX axis has the form 
. The wavelength (in m) is... 4) 3,14
38. A photon with an energy of 100 keV was deflected by an angle of 90° as a result of Compton scattering by an electron. The energy of a scattered photon is _____. Express your answer in keV and round to the nearest whole number. Please note that the rest energy of the electron is 511 keV Answer:84
39. The angle of refraction of a beam in a liquid is equal to If it is known that the reflected beam is completely polarized, then the refractive index of the liquid is equal to ... 3) 1,73
40. If the axis of rotation of a thin-walled circular cylinder is transferred from the center of mass to the generatrix (Fig.), then the moment of inertia relative to the new axis is _____ times.
1) will increase by 2
41. A disk rolls uniformly on a horizontal surface at speed without slipping. The velocity vector of point A, lying on the rim of the disk, is oriented in the direction ...
3) 2
42. A small puck starts moving without an initial speed along a smooth ice slide from point A. Air resistance is negligible. The dependence of the potential energy of the puck on the x coordinate is shown on the graph:
The kinetic energy of the puck at point C is ______ than at point B. 4) 2 times more
43. Two small massive balls are attached to the ends of a weightless rod of length l. The rod can rotate in a horizontal plane around a vertical axis passing through the middle of the rod. The rod was spun to angular velocity. Under the influence of friction, the rod stopped, and 4 J of heat were released.
44. If the rod is spun to angular velocity , then when the rod stops, an amount of heat (in J) will be released equal to ... Answer : 1
45. Light waves in a vacuum are... 3) transverse
46. The figures show the time dependence of the coordinates and speed of a material point oscillating according to a harmonic law:
47. The cyclic frequency of oscillations of a point (in) is equal to... Answer: 2
48. The energy flux density transferred by a wave in an elastic medium with density , increased 16 times at a constant speed and frequency of the wave. At the same time, the amplitude of the wave increased by _____ times. Answer: 4
49. The magnitude of the saturation photocurrent during the external photoelectric effect depends... 4) on the intensity of the incident light
50. The figure shows a diagram of the energy levels of the hydrogen atom, and also conventionally depicts the transitions of an electron from one level to another, accompanied by the emission of an energy quantum. In the ultraviolet region of the spectrum, these transitions give rise to the Lyman series, in the visible region – the Balmer series, in the infrared region – the Paschen series, etc.
The ratio of the minimum line frequency in the Balmer series to the maximum line frequency in the Lyman series of the spectrum of the hydrogen atom is ... 3)5/36
51. The ratio of the de Broglie wavelengths of a neutron and an alpha particle having the same speeds is ... 4) 2
52. The stationary Schrödinger equation has the form 
. This equation describes... 2) linear harmonic oscillator
53. The figure schematically shows the Carnot cycle in coordinates:
54. 
55. An increase in entropy takes place in the area ... 1) 1–2
56. Dependence of ideal gas pressure in an external uniform gravity field on height for two different temperatures are presented in the figure.
57. For the graphs of these functions, the statements that... 3) the dependence of the pressure of an ideal gas on height is determined not only by the temperature of the gas, but also by the mass of the molecules 4) temperature below temperature
1.
The stationary Schrödinger equation has the form 
.
This equation describes...an electron in a hydrogen-like atom
The figure schematically shows the Carnot cycle in coordinates: 
An increase in entropy occurs in areas 1–2
2. On ( P,V)-diagram shows 2 cyclic processes. 
The ratio of work completed in these cycles is equal to...Answer: 2.
3. Dependences of the pressure of an ideal gas in an external uniform field of gravity on height for two different temperatures are presented in the figure. 
For graphs of these functions unfaithful are statements that ... the temperature is below the temperature
the dependence of the pressure of an ideal gas on height is determined not only by the temperature of the gas, but also by the mass of the molecules
4. When room temperature ratio of molar heat capacities at constant pressure and constant volume is equal to 5/3 for ... helium
5. The figure shows the trajectories of charged particles flying at the same speed into a uniform magnetic field perpendicular to the plane of the figure. At the same time, for charges and specific charges of particles, the statement is true... 
, , 
6. Unfaithful for ferromagnets is the statement...
The magnetic permeability of a ferromagnet is a constant value that characterizes its magnetic properties.
7. Maxwell's equations are the basic laws of classical macroscopic electrodynamics, formulated on the basis of a generalization of the most important laws of electrostatics and electromagnetism. These equations in integral form have the form:
1). 
;
2). 
;
3). 
;
4). 0.
Maxwell's fourth equation is a generalization...
Ostrogradsky–Gauss theorem for magnetic field
8. A bird sits on a power line wire whose resistance is 2.5 10 -5 Ohm for every meter of length. If a wire carries a current of 2 kA, and the distance between the bird’s paws is 5 cm, then the bird is energized...
9. Current strength in a conducting circular circuit with inductance 100 mH changes over time
according to the law (in SI units): 
Absolute value of self-induction emf at time 2 With equal to ____ ; in this case the induction current is directed...
0,12 IN; counterclock-wise
10. An electrostatic field is created by a system of point charges. 
The field strength vector at point A is oriented in the direction ...
11. The angular momentum of an electron in an atom and its spatial orientation can be conventionally depicted by a vector diagram, in which the length of the vector is proportional to the modulus of the orbital angular momentum of the electron. The figure shows possible orientations of the vector. 
Minimum value of the principal quantum number n for the specified state is 3
12. The stationary Schrödinger equation in the general case has the form 
. Here 
potential energy of a microparticle. The motion of a particle in a three-dimensional infinitely deep potential box is described by the equation 
13. The figure schematically shows the stationary orbits of an electron in a hydrogen atom according to the Bohr model, and also shows transitions of an electron from one stationary orbit to another, accompanied by the emission of an energy quantum. In the ultraviolet region of the spectrum, these transitions give the Lyman series, in the visible - the Balmer series, in the infrared - the Paschen series. 
The highest quantum frequency in the Paschen series (for the transitions shown in the figure) corresponds to the transition 
14. If a proton and a deuteron have passed through the same accelerating potential difference, then the ratio of their de Broglie wavelengths is
15. The figure shows the velocity vector of a moving electron: 
Vector of magnetic induction field created by an electron when moving, at a point WITH sent... from us
16. A small electric boiler can be used to boil a glass of water for tea or coffee in the car. Battery voltage 12 IN. If he's over 5 min heats 200 ml water from 10 to 100° WITH, then the current strength (in A) consumed from the battery is equal to...
(The heat capacity of water is 4200 J/kg. TO.) 21
17. Conducting flat circuit with an area of 100 cm 2 located in a magnetic field perpendicular to the lines of magnetic induction. If magnetic induction changes according to the law 
Tl, then the induced emf arising in the circuit at the moment of time (in mV), equal to 0.1
18. The orientational polarization of dielectrics is characterized by the influence of the thermal motion of molecules on the degree of polarization of the dielectric
19. The figures show graphs of the field strength for various charge distributions: 
Dependence graph for a charged metal sphere of radius R shown in the figure...Answer: 2.
20. Maxwell's equations are the basic laws of classical macroscopic electrodynamics, formulated on the basis of a generalization of the most important laws of electrostatics and electromagnetism. These equations in integral form have the form:
1). 
;
2). 
;
3). 
;
4). 0.
Maxwell's third equation is a generalization of the Ostrogradsky–Gauss theorem for the electrostatic field in a medium
21. The dispersion curve in the region of one of the absorption bands has the form shown in the figure. Relationship between phase and group velocities for a section bc looks like... 
22. sunlight falls on a mirror surface along the normal to it. If the solar radiation intensity is 1.37 kW/m 2, then the light pressure on the surface is _____. (Express your answer in µPa and round to the nearest whole number). Answer: 9.
23. The phenomenon of external photoelectric effect is observed. In this case, as the wavelength of the incident light decreases, the magnitude of the retarding potential difference increases
24. On diffraction grating a flat plane falls normal to its surface light wave with wavelength If the lattice constant is , then total number the main maxima observed in the focal plane of the collecting lens are equal to ...Answer: 9.
25. A particle moves in a two-dimensional field, and its potential energy is given by the function. The work of field forces to move a particle (in J) from point C (1, 1, 1) to point B (2, 2, 2) is equal to ...
(The function and coordinates of the points are given in SI units.) Answer: 6.
26. The skater rotates around a vertical axis with certain frequency. If he presses his hands to his chest, thereby reducing his moment of inertia relative to the axis of rotation by 2 times, then the speed of the skater’s rotation and his kinetic energy of rotation will increase by 2 times
27. On board spaceship emblem in the form geometric figure:
If the ship moves in the direction indicated by the arrow in the figure at a speed comparable to the speed of light, then in a stationary frame of reference the emblem will take the shape shown in the figure
28. Three bodies are considered: a disk, a thin-walled pipe and a ring; and the masses m and radii R their bases are the same. 
For the moments of inertia of the bodies under consideration relative to the indicated axes, the following relation is correct: 
29. The disk rotates uniformly around a vertical axis in the direction indicated by the white arrow in the figure. At some point in time, a tangential force was applied to the disk rim. 
In this case, vector 4 correctly depicts the direction of the angular acceleration of the disk
30. The figure shows a graph of body speed versus time t. 
If body weight is 2 kg, then the force (in N), acting on the body, is equal to...Answer: 1.
31. Establish a correspondence between the types of fundamental interactions and radii (in m) their actions.
1.Gravitational
2.Weak
3. Strong
32. -decay is a nuclear transformation that occurs according to the scheme 
33. The charge in electron charge units is +1; the mass in electron mass units is 1836.2; spin in units is 1/2. These are the main characteristics of the proton
34. The law of conservation of lepton charge prohibits the process described by the equation 
35. In accordance with the law of uniform distribution of energy over degrees of freedom, the average kinetic energy of an ideal gas molecule at temperature T equal to: . Here , where , and are the number of degrees of freedom of translational, rotational and vibrational movements of the molecule, respectively. For hydrogen() number i equals 7
36. A diagram of the cyclic process of an ideal monatomic gas is shown in the figure. The ratio of the work during heating to the work of gas for the entire cycle in modulus is equal to ...
37. The figure shows graphs of the distribution functions of ideal gas molecules in an external uniform field of gravity versus height for two different gases, where are the masses of gas molecules (Boltzmann distribution). 
For these functions it is true that...
mass greater than mass
the concentration of gas molecules with a lower mass at the “zero level” is less
38. Upon admission to a non-isolated thermodynamic system heat during a reversible process for the increment of entropy the following relation will be correct:
39. The traveling wave equation has the form: , where is expressed in millimeters, – in seconds, – in meters. The ratio of the amplitude value of the velocity of particles of the medium to the velocity of wave propagation is 0.028
40. Amplitude damped oscillations decreased by a factor of ( – the base of the natural logarithm) for . The attenuation coefficient (in) is equal to...Answer: 20.
41. Two harmonic oscillations of the same direction with the same frequencies and equal amplitudes are added. Establish a correspondence between the amplitude of the resulting oscillation and the phase difference of the added oscillations.
1. 2. 3. Answer: 2 3 1 0
42. The figure shows the orientation of the electric () and magnetic () field strength vectors in electromagnetic wave. The energy flux density vector of the electromagnetic field is oriented in the direction... 
43. Two conductors are charged to potential 34 IN and –16 IN. Charge 100 nCl need to be transferred from the second conductor to the first. In this case, it is necessary to perform work (in µJ), equal to...Answer: 5.
44. The figure shows bodies of the same mass and size rotating around a vertical axis with the same frequency. Kinetic energy of the first body J. If kg, cm, then the angular momentum (in mJ s) of the second body is equal to ... 
If 5155 J of heat were transferred to one mole of a diatomic gas and the gas performed work equal to 1000 J, then its temperature increased by ………….. K. (the bond between the atoms in the molecule is rigid)
The change in internal energy of the gas occurred only due to work
gas compression in……………………………..process.
adiabatic
Longitudinal waves are
sound waves in the air
Resistance R, inductor L = 100 H and capacitor C = 1 μF are connected in series and connected to an alternating voltage source that varies according to the law
The loss of alternating current energy per period on a capacitor in an electrical circuit is equal to...................................(VT)
If the efficiency of the Carnot cycle is 60%, then the temperature of the heater is ………………………… times greater than the temperature of the refrigerator.
Entropy of an isolated thermodynamic system…………..
cannot decrease.
The figure schematically shows the Carnot cycle in coordinates. An increase in entropy takes place in the area ……………………………….
The unit of measurement for the quantity of a substance is………….
Isochores of an ideal gas in P-T coordinates represent..........................................
Isobars of an ideal gas in V-T coordinates represent….
INDICATE AN INCORRECT STATEMENT
The greater the inductance of the coil, the faster the capacitor discharges
If the magnetic flux through a closed loop uniformly increases from 0.5 Wb to 16 Wb in 0.001 s, then the dependence of the magnetic flux on time t has the form
1.55*10V4T+0.5V
The oscillatory circuit consists of an inductor L = 10 H, a capacitor C = 10 μF and a resistance R = 5 Ohm. The quality factor of the circuit is ……………………………
One mole of an ideal monatomic gas received 2507 J of heat during a certain process. At the same time, its temperature decreased by 200 K. The work done by the gas is equal to …………………………J.
An ideal monatomic gas in an isobaric process is supplied with an amount of heat Q. In this case, .........% of the supplied amount of heat is spent to increase the internal energy of the gas
If we do not take into account the vibrational movements in the carbon dioxide molecule, then the average kinetic energy of the molecule is equal to ……………
INDICATE AN INCORRECT STATEMENT
The greater the inductance in the oscillating circuit, the greater the cyclic frequency.
The maximum efficiency value that a heat engine with a heater temperature of 3270 C and a refrigerator temperature of 270 C can have is …………%.
The figure shows the Carnot cycle in coordinates (T,S), where S is entropy. Adiabatic expansion occurs in the area ………………………..
The process depicted in the figure in coordinates (T,S), where S is entropy, is…………………
adiabatic expansion.
The equation of a plane wave propagating along the OX axis has the form. The wavelength (in m) is...
Voltage on the inductor versus current strength in phase....................................
Leads by PI/2
Resistor with resistance R = 25 Ohm, coil with inductance L = 30 mH and capacitor with capacitance
C = 12 µF are connected in series and connected to an alternating voltage source varying according to the law U = 127 cos 3140t. The effective value of the current in the circuit is ……………A
The Clapeyron-Mendeleev equation looks like this…….
INDICATE AN INCORRECT STATEMENT
The self-induction current is always directed towards the current whose change generates the self-induction current
The equation of a plane sinusoidal wave propagating along the OX axis has the form. The amplitude of acceleration of oscillations of particles of the medium is equal to....................................
T6.26-1 Indicate the incorrect statement
Vector E (alternating electric field strength) is always antiparallel to vector dE/dT
Maxwell's equation, which describes the absence of magnetic charges in nature, has the form........................
If we do not take into account the vibrational movements in a hydrogen molecule at a temperature of 100 K, then the kinetic energy of all molecules in 0.004 kg of hydrogen is equal to……………………….J
Two moles of a hydrogen molecule impart 580 J of heat at constant pressure. If the bond between atoms in a molecule is rigid, then the gas temperature has increased by ……………….K
The figure shows the Carnot cycle in coordinates (T, S), where S is entropy. Isothermal expansion occurs in the area …………………
In the process of reversible adiabatic cooling of a constant mass of an ideal gas, its entropy is ……………
does not change.
If a particle with a charge moves in a uniform magnetic field with induction B in a circle of radius R, then the modulus of the particle’s momentum is equal to
1. van der Waals chemical bond characteristic of electrically neutral atoms that do not have an electric dipole moment.
The force of attraction is called dispersion force.
For polar systems with a constant dipole moment, the orientational mechanism of the van der Waals chemical bond predominates.
Molecules with high polarization are characterized by an induced electric moment when the molecules approach each other sufficiently close quarters. In the general case, all three types of van der Waals chemical bond mechanism can occur, which is weaker than all other types of chemical bond by two to three orders of magnitude.
The total interaction energy of molecules with a van der Waals chemical bond is equal to the sum of the energies of dispersion, orientation and induced interactions.
2. Ionic (heteropolar) chemical bond occurs when one atom is able to transfer one or more electrons to another atom.
As a result, positively and negatively charged ions appear, between which a dynamic equilibrium is established. This bond is typical for halogens and alkali metals. The dependence W p (r) for molecules with ionic bonds is shown in Fig. 8.1. The distance r 0 corresponds to the minimum potential energy.
3. Covalent (homeopolar) chemical bond or atomic bond occurs when atoms with similar properties interact.
During interaction, states appear with an increased density of the electron cloud and the appearance of exchange energy.
IN quantum theory It is shown that the exchange energy is a consequence of the identity of closely spaced particles.
Characteristic feature atomic bond is its saturation, i.e. each atom is capable of forming a limited number of bonds.
4. In a metal chemical bond All atoms of the crystal participate, and the shared electrons move freely within the entire crystal lattice.
Hydrogen molecule
The hydrogen molecule is bound by the forces leading to this bond, which are exchangeable, i.e., a quantum approach is required for consideration.
Using perturbation theory, Heitler and F. London in 1927 solved an approximate version.
IN quantum mechanics the problem of the hydrogen molecule is reduced to solving the Schrödinger equation for a stationary state.
Using the adiabatic approximation, i.e., we consider the wave function as a function only of the coordinates of electrons, and not of atomic nuclei.
The complete wave function depends not only on the spatial coordinates of the electrons, but also on their spins and is antisymmetric.
If we take into account only the electron wave function, the problem can be solved by taking into account 2 cases:
1. The spin wave function is antisymmetric, and the spatial wave function is symmetric and the total spin of two electrons is zero (singlet state).
2. The spin wave function is symmetric, and the spatial wave function is antisymmetric and the total spin of two electrons is equal to unity and can be oriented by three different ways(triplet state).
In a symmetric state, when the spin wave function is antisymmetric and in the zero approximation a symmetric spatial wave function with separable variables is obtained.
In the triplet state, when the spin wave function is symmetric, an antisymmetric spatial wave function is obtained.
Due to the identity of the electrons, an exchange interaction arises, which manifests itself in calculations due to the use of symmetric and antisymmetric spatial wave functions.
When atoms in a singlet spin state (spins are antiparallel) approach each other, the interaction energy first decreases and then quickly increases. In the triplet spin state (the spins are parallel), the energy minimum does not occur.
The equilibrium position of the atom exists only in the singlet spin state, when the energy reaches a minimum. Only in this state is the formation of a hydrogen atom possible.
Molecular spectra
Molecular spectra arise as a result of quantum transitions between the energy levels of W * and W ** molecules according to the relation
hn = W * - W ** , (1)
where hn is the energy of an emitted or absorbed quantum of frequency n.
Molecular spectra are more complex than atomic spectra, which is determined by the internal motion in the molecules.
Since, in addition to the movement of electrons relative to two or more nuclei in a molecule, oscillatory movement of nuclei (together with the internal electrons surrounding them) around equilibrium positions and rotational molecular movements.
Three types of energy levels correspond to the electronic, vibrational and rotational movements of molecules:
W e , W count and W time,
and three types of molecular spectra.
According to quantum mechanics, the energies of all types of molecular movements can only take on certain values (except for the energy of translational motion).
The energy of a molecule W, the change in which determines the molecular spectrum, can be represented as a sum of quantum energy values:
W = W e + W count + W time, (2)
and in order of magnitude:
W e: W count: W time = 1: .
Hence,
W e >> W count >> W time
DW = DW * - DW ** = DW e + DW count + DW time (3)
The electron energy W e is on the order of several electron volts:
W count » 10 - 2 - 10 - 1 eV, W time » 10 - 5 - 10 - 3 eV.
The system of energy levels of molecules is characterized by a set of electronic energy levels widely spaced from each other.
The vibrational levels are located much closer to each other, and the rotational energy levels are located even closer to each other.
Typical molecular spectra-collections of narrow stripes (consisting of large number individual lines) of varying widths in the UV, visible and IR regions of the spectrum, clear at one end and blurry at the other.
Energy levels A And b correspond to the equilibrium configurations of 2 molecules (Fig. 2).
Each electronic state corresponds to a certain energy value W e - smallest value, ground electronic state (ground electronic level molecular energy).
The set of electronic states of a molecule is determined by the properties of its electron shell.
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Vibrational Energy Levels
Vibrational Energy Levels can be found by quantizing the oscillatory motion, which is approximately considered harmonic.
A diatomic molecule (one vibrational degree of freedom corresponding to a change in the internuclear distance r) can be considered as a harmonic oscillator, the quantization of which gives equally spaced energy levels:
, (4)
where n is the fundamental frequency of harmonic vibrations of the molecule;
v count = 0, 1, 2, ... - vibrational quantum number.
Rotational energy levels
Rotational energy levels can be found by quantizing the rotational motion of the molecule, considering it as a rigid body with a certain moment of inertia I.
In the case of a diatomic or linear triatomic molecule, its rotational energy
where I is the moment of inertia of the molecule relative to an axis perpendicular to the axis of the molecule; L - angular momentum.
According to quantization rules
, (6)
where J = 0, 1, 2, 3, ... is the rotational quantum number.
For rotational energy we obtain
, (7)
The rotational constant determines the scale of the distance between energy levels.
The diversity of molecular spectra is due to the difference in types of transitions between the energy levels of molecules.
MINISTRY OF EDUCATION AND SCIENCE OF THE REPUBLIC OF TATARSTAN
ALMETYEVSK STATE OIL INSTITUTE
Department of Physics
on the topic of: "Debye's Law of Cubes"
Completed by a student of group 18-13B Gontar I.V. Teacher: Mukhetdinova Z.Z.
Almetyevsk 2010
1. Energy crystal lattice …………………………… 3
2. Einstein’s model…………………………………………….. 6
3. Debye model ………………………………………….. 7
4. Debye’s law of cubes……………………………………………… 8
5. Debye’s achievements…………………………………………… 9
6. References……………………………………………………….. 12
Energy of the crystal lattice
Peculiarity solid- the presence of long-range and short-range orders. In an ideal crystal, particles occupy certain positions and there is no need to take N into account! in statistical calculations.
The energy of the crystal lattice of a monatomic crystal consists of two main contributions: E = U o + E count. Atoms in the lattice vibrate. For polyatomic particles forming a crystal, it is necessary to take into account the internal degrees of freedom: vibrations and rotations. If we do not take into account the anharmonicity of atomic vibrations, which gives the dependence of U o on temperature (changes in the equilibrium positions of atoms), U o can be equated to the potential energy of the crystal and does not depend on T. At T = 0, the energy of the crystal lattice, i.e. the energy for removing crystal particles to an infinite distance will be equal to E cr = - E o = - (U o + E o,col).
Here E o,kol is the energy of zero-point oscillations. Typically this value is on the order of 10 kJ/mol and much less than U o.
Consider Ecr = - Uo. (Method of largest term). Ecr in ionic and molecular crystals up to 1000 kJ/mol, in molecular and crystals with hydrogen bonds: up to 20 kJ/mol (CP 4 - 10, H 2 O - 50). The quantities are determined from experience or calculated on the basis of some model: ionic interaction according to the Coulomb, van der Waals forces according to the Sutherland potential.
Let us consider an ionic NaCl crystal having a face-centered cubic lattice: in the lattice each ion has 6 neighbors of the opposite sign at a distance R, in the next second layer there are 12 neighbors of the same sign at a distance of 2 1/2 R, 3rd layer: 8 ions at a distance of 3 1/2 R, 4th layer: 6 ions at a distance of 2R, etc. 
+ sign for repulsion of like, - attraction of different ions. e - charge. Let us introduce the value of the reduced distance p ij = r ij / R, where r ij is the distance between the ions, R is the lattice parameter.
The energy of interaction of the ion with all its neighbors where
Madelung's constant = 6/1 - 12/2 1/2 + 8/3 1/2 - 6/2 + .... Here - for ions of the same charge sign, + for different ones. For NaCl a = 1.747558... A n = S 1/ p ij n in the first term. Distance R o (half the edge of a cube in in this case) corresponds to the minimum potential energy at T = 0 and can be determined from crystallographic data and knowing the repulsive potential. It's obvious that 
and then
From here we find A n and energy 
or 
.
n is the repulsive potential parameter and is usually ³ 10, i.e. The main contribution is made by the Coulomb interaction (we assume that R is not noticeably independent of T), and repulsion makes less than 10%.
For NaCl, the Coulomb interaction is 862, repulsion is 96 kJ/mol (n = 9). For molecular crystals, the potential can be calculated as 6-12 and the energy will be equal to 
z 1 is the number of atoms in the 1st coordination sphere, R 1 is the radius of the first coordination sphere, b is the potential parameter.
For nonionic crystals, the vibrational component of energy must be taken into account. There are no translational or rotational movements at absolute zero. The vibrational component of energy remains. There are 6 vibrations 3N, but translational and rotational vibrations apply to the crystal as a whole. Roughly it can be considered 3N, because N (large, the number of particles in the crystal). Then all 3N degrees of freedom of a crystal of N particles are vibrational. In principle, it is easy to calculate the sum over states and thermodynamic functions. But you need to know the frequency spectrum of crystal vibrations. The point is that the displacement of a particle causes the displacement of others and the oscillators are connected. The total sum over the states of oscillatory motion will be determined:
.
Because this is a crystal, then on N! no need to divide. The average energy is equal to the derivative of lnZ with respect to T at constant V, multiplied by kT 2. Hence the lattice energy is equal to the sum of the contributions of potential and vibrational energy, 
and entropy S = E/ T + k ln(Z).
Two main models are used for calculations.
Einstein's model
All frequencies are considered the same: a collection of one-dimensional harmonic oscillators. The sum over the states of a three-dimensional oscillator consists of 3 identical terms q = [ 2sh(hn/ 2kT)] -3. For N particles there will be 3N factors. Those. energy 
At high T, expanding the exponential into a series, the limit sh(hn/ 2kT) = hn/ 2kT and 
Entropy of vibrational motion 
Heat capacity of crystals: 
The OP has a mistake. Hence, at large T >> q E = hn/ k, the limit is C v ® 3Nk: Dulong-Ptied law for monatomic crystals. AND 
(The exponent quickly approaches 0).
In the classical approximation, Ecol without zero oscillations is equal to 3NkT and the contribution of oscillations to the heat capacity is 3Nk = 3R. Calculation according to Einstein: the lower curve, which deviates more noticeably from the experimental data.
Einstein's model gives the equation of state of a solid: (according to Melvin-Hughes)
u o = - q sublimation, m, n are experimental parameters, so for xenon m = 6, n = 11, a o is the interatomic distance at T = 0. That is pV/ RT = f(n, a o , n, m).
But near T = 0, Einstein’s assumption of equal frequencies does not work. Oscillators can differ in interaction strength and frequency. Experiments at low temperatures show a cubic dependence on temperature.
Debye model
Debye proposed a model for the existence of a continuous spectrum of frequencies (strictly for low frequencies, for thermal vibrations - phonons) up to a certain maximum. The frequency distribution function of harmonic oscillators has the form , where c l, c t- speed of propagation of longitudinal and transverse vibration waves. At frequencies above the maximum g = 0.
The areas under the two curves must be the same. In reality, there is a certain spectrum of frequencies; the crystal is nonisotropic (this is usually neglected and the speeds of wave propagation in the directions are assumed to be the same). It may be that the maximum Debye frequency is higher than actually existing ones, which follows from the condition of equality of areas. The value of the maximum frequency is determined by the condition that the total number of oscillations is equal to 3N (we neglect the discreteness of energy) and 
, с is the speed of the wave. We assume that the speeds c l and c t are equal. Debye characteristic temperature Q D = hn m/k.
Let's introduce x = hn/ kT. The average energy of oscillations is then at maximum
The second term under the integral will give E zero-point vibrations E o = (9/8)NkQ D and then the vibrational energy of the crystal: 
Since U o and E o do not depend on T, the contribution to the heat capacity will be made by the 2nd term in the expression for energy.
Let us introduce the Debye function 
At high T we obtain the obvious D(x) ® 1. Differentiating with respect to x, we obtain 
.
At high T the limit is C V = 3Nk, and at low T: 
.
At small T, the upper limit of integration tends to infinity, E - E o = 3Rp 4 T 4 /5Q D 3 and we obtain a formula for determining C v at T® 0: where
Got Debye's cube law.
Debye's law of cubes.
The characteristic Debye temperature depends on the density of the crystal and the speed of propagation of vibrations (sound) in the crystal. A strictly Debye integral must be solved on a computer.
Debye characteristic temperature (Phys. encyclopedia)
Na 150 Cu 315 Zn 234 Al 394 Ni 375 Ge 360 Si 625
A.U 157 342 316 423 427 378 647
Li 400 K 100 Be 1000 Mg 318 Ca 230 B 1250 Ga 240
As 285 Bi 120 Ar 85 In 129 Tl 96 W 310 Fe 420
Ag 215 Au 170 Cd 120 Hg 100 Gd 152 Pr 74 Pt 230
La 132 Cr 460 Mo 380 Sn(white) 170, (gray) 260 C(diamond) 1860
To estimate the characteristic Debye temperature, you can use Lindemann’s empirical formula: Q D =134.5[Tmel/ (AV 2/3)] 1/2, here A - atomic mass metal For the Einstein temperature it is similar, but the first factor is 100.
Debye's achievements
Debye is the author of fundamental works on the quantum theory of solids. In 1912, he introduced the concept of a crystal lattice as an isotropic elastic medium capable of oscillating in a finite frequency range (Debye's solid state model). Based on the spectrum of these vibrations, he showed that at low temperatures the lattice heat capacity is proportional to the cube of the absolute temperature (Debye's heat capacity law). Within the framework of his solid state model, he introduced the concept of characteristic temperature at which quantum effects become significant for each substance (Debye temperature). In 1913, one of Debye's most famous works was published, devoted to the theory of dielectric losses in polar liquids. Around the same time, his work on the theory of X-ray diffraction was published. The beginning of Debye's experimental activities is associated with the study of diffraction. Together with his assistant P. Scherrer, he obtained an x-ray diffraction pattern of finely ground LiF powder. The photographs clearly showed rings resulting from the intersection of X-rays, diffracted from randomly oriented crystals along the forming cones, with photographic film. The Debye–Scherrer method, or powder method, has long been used as the main one in X-ray diffraction analysis. In 1916, Debye, together with A. Sommerfeld, applied quantization conditions to explain the Zeeman effect and introduced the magnetic quantum number. In 1923 he explained the Compton effect. In 1923, Debye, in collaboration with his assistant E. Hückel, published two large articles on the theory of electrolyte solutions. The ideas presented in them served as the basis for the theory of strong electrolytes, called the Debye-Hückel theory. Since 1927 Debye's interests have focused on issues chemical physics
Debye's main research interest during his time at Cornell University was polymer physics. He developed a method for determining the molecular weight of polymers and their shape in solution based on light scattering measurements. One of his last major works (1959) was devoted to an issue that is extremely relevant today - the study of critical phenomena. Among Debye's awards are the medals of H. Lorentz, M. Faraday, B. Rumford, B. Franklin, J. Gibbs (1949), M. Planck (1950), and others. Debye died in Ithaca (USA) on November 2, 1966.
Debye - an outstanding representative of Dutch science - received Nobel Prize in Chemistry in 1936. With exceptional versatility, he made major contributions not only to chemistry but also to physics. These achievements brought Debye great fame; he was awarded honorary degrees of Doctor of Science by more than 20 universities around the world (Brussels, Oxford, Brooklyn, Boston and others). He was awarded many medals and prizes, including Faraday and Lorentz. Plank. Since 1924, Debye has been a corresponding member. Academy of Sciences of the USSR.
Law cube iv Debye”, similar to each other. ... space). Weekdays laws savings (and also law saving electrical charge) є ...
Basic concepts laws chemistry. Lecture notes
Abstract >> Chemistry... laws chemistry 1.3.1 Law Saving Masi 1.3.2 Law warehouse status 1.3.3 Law multiples 1.3.4 Law equivalents 1.3.5 Law volume of delivery 1.3.6 Law... honor of the Dutch physicist P. Debye: 1 D = ... multicentering cube(bcc), face centering cube(GCC...
Development of the financial mechanism for the gas complex of Ukraine
Thesis >> Financial Sciences1000 cube. meters of gas on the skin 100 kilometers of distance. Zhidno Law... obligation to write off sums of doubtful deb itor's obscurity; 5) Creditors' debt ... 0 0 other financial investments 045 0 0 Dovgostrokova deb Itorska oborgovanist 050 0 0 Developed...
Indirect contributions and their contributions to the financial and government activities of enterprises
Thesis >> Financial SciencesType of adaptation to the issues referred to in article 5 Law, the delivery slip will have the entry “Without... 25”. deb itors' and creditors' debts - ... 3.0 euros per 1 cube. cm 2.4 euros per 1 cube. see Other cars from...
If we do not take into account the vibrational movements in the carbon dioxide molecule, then the average kinetic energy of the molecule is ...
Solution: The average kinetic energy of a molecule is equal to: , where is Boltzmann’s constant, is the thermodynamic temperature; – the sum of the number of translational, rotational and twice the number of vibrational degrees of freedom of the molecule: . For a carbon dioxide molecule, the number of degrees of freedom of translational motion, rotational - , vibrational - , therefore, the average kinetic energy of the molecule is equal to: .
TASK N 2 Topic: The first law of thermodynamics. Work with isoprocesses
The figure shows a diagram of the cyclic process of an ideal monatomic gas: 
During a cycle, the gas receives an amount of heat (in) equal to ...
Solution: The cycle consists of isochoric heating (4–1), isobaric expansion (1–2), isochoric cooling (2–3) and isobaric compression (3–4). During the first two stages of the cycle, the gas receives heat. According to the first law of thermodynamics, the amount of heat received by a gas is 
, where is the change in internal energy and is the work done by the gas. Then . Thus, the amount of heat received by the gas per cycle is equal to
TASK N 3 Topic: Second law of thermodynamics. Entropy
During an irreversible process, when heat enters a non-isolated thermodynamic system for an increase in entropy, the following relation will be correct...
Solution: The ratio in a reversible process is the total differential of the system state function, called the entropy of the system: 
. In isolated systems, entropy cannot decrease during any processes occurring in it: . The equal sign refers to reversible processes, and the greater than sign refers to irreversible processes. If heat enters a non-insulated system and an irreversible process occurs, then entropy increases due not only to the heat received, but also to the irreversibility of the process: .
Task n 4 Topic: Maxwell and Boltzmann distributions
The figure shows a graph of the velocity distribution function of ideal gas molecules (Maxwell distribution), where 
– the proportion of molecules whose velocities lie in the velocity range from to per unit of this interval: 
For this function the following statements are true...
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the position of the maximum of the curve depends not only on temperature, but also on the nature of the gas (its molar mass) |
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as the number of molecules increases, the area under the curve does not change |
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with increasing gas temperature, the value of the maximum of the function increases |
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for a gas with a higher molar mass (at the same temperature), the maximum of the function is located in the region of higher velocities |
Solution: From the definition of the Maxwell distribution function it follows that the expression 
determines the fraction of molecules whose velocities lie in the velocity range from to (on the graph this is the area of the shaded strip). Then the area under the curve is 
and does not change with changes in temperature and number of gas molecules. From the formula for the most probable speed 
(at which the function is maximum) it follows that it is directly proportional and inversely proportional to , where and is the temperature and molar mass gas accordingly.
TASK N 5 Topic: Electrostatic field in a vacuum
The figures show graphs of the field strength for various charge distributions: 
Dependency graph for a ball of radius R, uniformly charged throughout the volume, is shown in the figure ...
TASK N 6 Topic: Laws of direct current
The figure shows the dependence of the current density j, flowing in conductors 1 and 2, from the electric field strength E:
The ratio of resistivity r 1 /r 2 of these conductors is equal to ...
TASK N 7 Topic: Magnetostatics
A frame with a current with a magnetic dipole moment, the direction of which is indicated in the figure, is in a uniform magnetic field: 
The moment of forces acting on the magnetic dipole is directed...
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perpendicular to the drawing plane to us |
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perpendicular to the drawing plane from us |
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in the direction of the magnetic induction vector |
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opposite to the magnetic induction vector |