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 ...
(Assume the speed of ultrasonic waves in the human body to be equal. 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 of various types of movement of atoms in the 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 strength 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... intrinsic mechanical torque of an 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. The complete system of Maxwell’s equations for the electromagnetic 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 the speed and acceleration of a 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. 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.
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. At room temperature, the ratio of molar heat capacities at constant pressure and constant volume is 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. A plane light wave with wavelength is incident on a diffraction grating along the normal to its surface. If the grating constant is , then the total number of main maxima observed in the focal plane of the collecting lens is ... 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. A skater rotates around a vertical axis with a 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 the spaceship there is an emblem in the form of a 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. When heat enters a non-isolated thermodynamic system 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. The amplitude of 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 an 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 ... 
α particle
If a positron, proton, neutron and alpha particle have the same de Broglie wavelength, then the one with the highest speed is...
positron
If a positron, proton, neutron and alpha particle have the same speed, then the shortest de Broglie wavelength has...
α particle
If a positron, proton, neutron and alpha particle have the same speed, then the longest de Broglie wavelength has...
positron
In the experiment of Davisson and Germer, the diffraction of electrons passed through an accelerating voltage on a nickel single crystal was studied. If the accelerating voltage is reduced by a factor of 2, then the de Broglie wavelength of the electron...
will increase by times
In the experiment of Davisson and Germer, the diffraction of electrons passed through an accelerating voltage on a nickel single crystal was studied. If the accelerating voltage is doubled, then the de Broglie wavelength of the electron...
will decrease by 2 times
In the experiment of Davisson and Germer, the diffraction of electrons passed through an accelerating voltage on a nickel single crystal was studied. If the accelerating voltage is reduced by a factor of 4, then the de Broglie wavelength of the electron...
will increase 2 times
In the experiment of Davisson and Germer, the diffraction of electrons passed through an accelerating voltage on a nickel single crystal was studied. If the accelerating voltage is increased by a factor of 4, then the de Broglie wavelength of the electron...
will decrease by 2 times
The electron is localized in space within Δx = 1.0 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the electron mass is 9.1⋅10-31 kg, the uncertainty of the speed Δvx is no less...
The electron is localized in space within Δx = 2.0 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the electron mass is 9.1⋅10-31 kg, the uncertainty of the speed Δvx is no less...
The electron is localized in space within Δx = 0.5 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the electron mass is 9.1⋅10-31 kg, the uncertainty of the speed Δvx is no less...
The electron is localized in space within Δx = 0.2 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the electron mass is 9.1⋅10-31 kg, the uncertainty of the speed Δvx is no less...
The electron is localized in space within Δx = 0.1 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the electron mass is 9.1⋅10-31 kg, the uncertainty of the speed Δvx is no less...
1.15⋅103 m/s
The proton is localized in space within Δx = 1.0 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the proton mass is 1.67⋅10-27 kg, the uncertainty of the velocity Δvx is no less...
6.3⋅10-2 m/s
The proton is localized in space within Δx = 0.1 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the proton mass is 1.67⋅10-27 kg, the uncertainty of the velocity Δvx is no less...
The proton is localized in space within Δx = 0.5 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the proton mass is 1.67⋅10-27 kg, the uncertainty of the velocity Δvx is no less...
The position of the carbon atom in the diamond crystal lattice was determined with an error of Δx = 0.05 nm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the mass of a carbon atom is 2⋅10-26 kg, the uncertainty in the speed Δvx of its thermal motion is no less...
The position of the carbon atom in the diamond crystal lattice was determined with an error of Δx = 0.10 nm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the mass of a carbon atom is 2⋅10-26 kg, the uncertainty in the speed Δvx of its thermal motion is no less...
The position of the carbon atom in the diamond crystal lattice was determined with an error of Δx = 0.02 nm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, and the mass of a carbon atom is 2⋅10-26 kg, the uncertainty in the speed Δvx of its thermal motion is no less...
The position of a dust particle weighing 10-9 kg can be determined with an uncertainty of Δx = 0.1 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, the uncertainty of the speed Δvx will be no less...
1.05⋅10-18 m/s
The position of a dust particle weighing 10-9 kg can be determined with an uncertainty of Δx = 0.2 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, the uncertainty of the speed Δvx will be no less...
5.3⋅10-19 m/s
The position of a dust particle weighing 10-9 kg can be determined with an uncertainty of Δx = 0.5 µm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, the uncertainty of the speed Δvx will be no less...
2.1⋅10-19 m/s
The position of a dust particle weighing 10-9 kg can be determined with an uncertainty of Δx = 1.0 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, the uncertainty of the speed Δvx will be no less...
1.05⋅10-19 m/s
The position of a dust particle weighing 10-9 kg can be determined with an uncertainty of Δx = 2.0 μm. Considering that Planck's constant = 1.05⋅10-34 J⋅s, the uncertainty of the speed Δvx will be no less...
5.3⋅10-20 m/s
The lifetime of an atom in an excited state is 10 ns. Considering that Planck's constant = 6.6⋅10-16 eV⋅s, the width of the energy level is no less...
The lifetime of an atom in an excited state is 5 ns. Considering that Planck's constant = 6.6⋅10-16 eV⋅s, the width of the energy level is no less...
The lifetime of an atom in an excited state is 20 ns. Considering that Planck's constant = 6.6⋅10-16 eV⋅s, the width of the energy level is no less...
The high monochromaticity of laser radiation is due to the relatively long lifetime of electrons in a metastable state, on the order of 1 ms. Considering that Planck's constant = 6.6⋅10-16 eV⋅s, the width of the metastable level will be no less...
6.6⋅10-13 eV
< x < l). Вероятность обнаружить электрон на участке 0 < x < l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 0 < x < l/2 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 0 < x < 3l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/4 < x < l/2 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/4 < x < 3l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/4 < x < l равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/2 < x < 3l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/2 < x < l равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/6 < x < l/3 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/6 < x < l/2 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/6 < x < 2l/3 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/6 < x < 5l/6 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/3 < x < l/2 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/3 < x < 2l/3 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/3 < x < 5l/6 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/2 < x < 2l/3 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/2 < x < 5l/6 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < 3l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < l/2 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < 5l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < 3l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/8 < x < 7l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке l/4 < x < 7l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 3l/8 < x < 3l/4 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 3l/8 < x < 5l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 3l/8 < x < 7l/8 равна...
The figure shows the distribution of the Ψ-function of an electron in a one-dimensional potential box (0< x < l). Вероятность обнаружить электрон на участке 3l/8 < x < l равна...xxx
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 2 m/s3, B = 2 m/s2, C = 2 m/s). The path traveled by the body in the first 3 seconds of movement is...
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 3 m/s3, B = 3 m/s2, C = 3 m/s). The path traveled by the body in the first 2 seconds of movement is...
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 6 m/s3, B = 6 m/s2, C = 6 m/s). The path traveled by the body in the first 2 seconds of movement is...
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 4 m/s3, B = 4 m/s2, C = 4 m/s). The path traveled by the body in the first 3 seconds of movement is...
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 1 m/s3, B = 2 m/s2, C = 3 m/s). The path traveled by the body in the first 3 seconds of movement is...
The speed of the body changes with time according to the law: v(t) = At2 + Bt + C (A = 3 m/s3, B = 2 m/s2, C = 1 m/s). The path traveled by the body in the first 3 seconds of movement is...
The path traveled by the body depends on time according to the law: s(t) = At3 + Bt2 + Ct (A = 2 m/s3, B = 2 m/s2, C = 2 m/s). Acceleration at time t = 3 s is...
The path traveled by the body depends on time according to the law: s(t) = At3 + Bt2 + Ct (A = 3 m/s3, B = 3 m/s2, C = 3 m/s). Acceleration at time t = 2 s is...
The path traveled by the body depends on time according to the law: s(t) = At3 + Bt2 + Ct (A = 2 m/s3, B = 2 m/s2, C = 2 m/s). Average speed for the first 3 seconds of movement...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 2 rad/s3, B = 2 rad/s2, C = 2 rad/s) . Tangential acceleration at time t = 3 s is...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 3 rad/s3, B = 3 rad/s2, C = 3 rad/s) . Tangential acceleration at time t = 2 s is...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 6 rad/s3, B = 6 rad/s2, C = 6 rad/s) . Tangential acceleration at time t = 2 s is...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 4 rad/s3, B = 4 rad/s2, C = 4 rad/s) . Tangential acceleration at time t = 3 s is...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 1 rad/s3, B = 2 rad/s2, C = 3 rad/s) . Tangential acceleration at time t = 3 s is...
The body moves in a circle with radius R = 2 m. Angular velocity depends on time according to the law: ω(t) = At2 + Bt + C (A = 3 rad/s3, B = 2 rad/s2, C = 1 rad/s) . Tangential acceleration at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 2 rad/s3, B = 1 rad/s). The speed of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 3 rad/s3, B = 4 rad/s). The speed of the body at time t = 2 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 1 rad/s3, B = 8 rad/s). The speed of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 4 rad/s3, B = 2 rad/s). The speed of the body at time t = 2 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 1 rad/s3, B = 3 rad/s). The speed of the body at time t = 2 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 1 rad/s3, B = 3 rad/s). The speed of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 2 rad/s3, B = 6 rad/s). The angular velocity of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 3 rad/s3, B = 4 rad/s). The angular velocity of the body at time t = 2 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 6 rad/s3, B = 8 rad/s). The angular velocity of the body at time t = 2 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 4 rad/s3, B = 2 rad/s). The angular velocity of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 1 rad/s3, B = 3 rad/s). The angular velocity of the body at time t = 3 s is...
The body moves in a circle with radius R = 2 m. The angular position of the body depends on time according to the law: φ(t) = At3 + Bt (A = 3 rad/s3, B = 9 rad/s). The angular velocity of the body at time t = 3 s is...
A body of mass m = 8 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 140 N. The total acceleration at this point...
A body of mass m = 7 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 200 N. The total acceleration at this point...
A body of mass m = 7 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 270 N. The total acceleration at this point...
A body of mass m = 10 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 490 N. The total acceleration at this point...
A body of mass m = 12 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 710 N. The total acceleration at this point...
A body of mass m = 13 kg, thrown at an angle to the horizontal, at the top point of the trajectory is subject to a drag force of 900 N. The total acceleration at this point...
A body of mass m = 6 kg, thrown at an angle to the horizontal, has a total acceleration a = 13 m/s2 at the top point of the trajectory. The resistance force of the medium at this point...
A body of mass m = 12 kg, thrown at an angle to the horizontal, has a total acceleration a = 13 m/s2 at the top point of the trajectory. The resistance force of the medium at this point...
The carousel accelerates from rest in 30 s to an angular velocity of 2 rad/s. It is assumed that the carousel is a homogeneous disk with a radius of 50 cm and a mass of 240 kg. The required moment of force for this is...
The carousel accelerates from rest in 25 s to an angular velocity of 2 rad/s. It is assumed that the carousel is a homogeneous disk with a radius of 50 cm and a mass of 300 kg. The required moment of force for this is...
The carousel accelerates from rest in 21 s to an angular velocity of 3 rad/s. It is assumed that the carousel is a homogeneous disk with a radius of 50 cm and a mass of 224 kg. The required moment of force for this is...
The carousel accelerates from rest in 35 s to an angular velocity of 4 rad/s. It is assumed that the carousel is a homogeneous disk with a radius of 50 cm and a mass of 350 kg. The required moment of force for this is...
Last week, joyful and long-awaited news came from the University of California, Riverside. Physics professor Allen P. Mills, Jr. and his assistant David Cassidy reported in the journal on September 13 Nature that they managed to create very short-lived quasi-molecules consisting of a pair of electrons and a pair of positrons. And not just create it, but also reliably prove it. Thus, they successfully completed a bold research project that they began several years ago. In any case, I would like to hope that their application will remain valid.
As is known, theoretical physicists are often ahead of experimentalists. This case is no exception, since the creations of Cassidy and Mills were predicted back in 1946. This story in itself is quite interesting, so I will describe it in detail.
It started in the Balkans. In 1934, Croatian physicist Stjepan Mohorovicic (son of the great seismologist who discovered the interface between the Earth's crust and mantle named after him) predicted the existence of a bound state of electron and positron. He relied on the theory of the hydrogen atom developed by Niels Bohr, only instead of a proton he used a positron. Mohorovicic published his findings in a very prestigious German journal Astronomische Nachrichten. I think that the choice of publication was explained by the fact that at that time the positron had a completely celestial status: in 1931, Paul Dirac predicted the existence of a positively charged antielectron, and a year later Carl Anderson discovered it in showers of cosmic particles (and at the same time christened it). And a year later, Irene and Frederic Joliot-Curie already observed antielectrons of purely terrestrial origin, arising from the birth of electron-positron pairs from gamma quanta emitted by a radioactive source.
Mohorovicic's work was not lucky. Astronomers were not particularly interested in it, and physicists, it seems, did not notice it. The name he proposed for the electron-positron pseudoatom, electrum, also did not catch on. The now common term "positronium" was invented by Washington physicist Arthur Edward Ruark, who came up with the same idea in 1945. And a year later, Princeton professor John Archibald Wheeler, from a more general position, considered the possibility of not only paired, but also more complex bound states of electrons and positrons, which he called polyelectrons. Soon these theories began to be confirmed in experiment, and, naturally, it all started with positronium. It was first observed in 1951 by the Austrian physicist Martin Deutsch, who moved to the United States and was then a professor at the Massachusetts Institute of Technology.
Now the properties of positronium atoms are well studied. In experiments, they are formed during collisions of slow positrons with atoms. Some of these collisions result in a positron capturing one of the outer electrons of the atomic shell. A positronium atom is twice the size of a hydrogen atom.
As is known, a hydrogen atom can exist in two ground states, determined by the mutual orientation of the spins of the proton and electron. When the spins are parallel, we have orthohydrogen; when the spins are antiparallel, we have parahydrogen (by the way, the cosmic radio emission of hydrogen is explained precisely by transitions between these states). Positronium atoms are also born in ortho- and paraversions. Orthopositronium annihilates into an odd number of electromagnetic radiation quanta with a total energy of 1022 keV, most often into three gamma quanta. Parapositronium, on the contrary, always gives rise to a pair of gamma rays.
This difference in decay methods (which is determined by the law of conservation of charge parity) leads to the fact that the lifetimes of the two forms of positronium are very different. Orthopositronium exists in a vacuum for 142 nanoseconds, parapositronium for 125 picoseconds. In material media, positronium atoms live even less than in emptiness. In general, these are very unstable systems. However, they, like ordinary atoms, can also exist in the form of ions. In 1981, Allen Mills, who was then working at Bell Labs, obtained a negative positronium ion, composed of a pair of electrons and one positron.
The analogy between positronium and hydrogen extends further. Hydrogen atoms tend to combine into diatomic molecules. It is natural to assume that positronium atoms are also capable of this. Wheeler was the first to guess about this, which he wrote about in the already mentioned article on polyelectrons (moreover, he even predicted the existence of molecules of three positronium atoms). Physicists have repeatedly tried to experimentally create the diatomic systems predicted by Wheeler, but for a long time nothing came of it. Only in 2005, employees of the University of California at Riverside with colleagues from Japan and two other American research centers announced (Pdf, 560 Kb) that they were able to produce diatomic molecular positronium - dipositronium (in chemical nomenclature denoted Ps 2). It was a fairly large group (8 members), but the same Cassidy and Mills played a key role in it. However, the experimental results of that time allowed for different interpretations, so the scientific world was waiting for more convincing evidence.
And now they seem to have been received. Cassidy and Mills again used a positron trap that their colleagues at the University of California at San Diego, led by Clifford M. Surko, had invented several years earlier. Having accumulated about twenty million positrons in it, the experimenters fired them into a small section of a quartz film 230 nanometers thick, containing many tiny holes. Each pulse was very short, the positrons hitting the target in less than a nanosecond. Penetrating inside these pores, positrons met electrons and sometimes, in alliance with them, gave rise to positronium atoms. The efficiency of this process was very low; the number of positronium atoms did not exceed one hundred thousand. Some of the atoms of the more durable orthopositronium managed to migrate to the surface of the film and there combined into dipositronium molecules.
Cassidy and Mills did not choose quartz as a target by chance. When dipositronium is formed, energy is released. It must be taken somewhere, otherwise the positronium atoms will almost certainly repel each other and again disperse in different directions. The surface of the quartz film absorbed this energy and thereby stabilized the atomic pairing. The pores penetrating it greatly increased its area, creating more space for the birth of dipositronium molecules.
Naturally, no one saw these molecules themselves. However, upon annihilation, they produced characteristic gamma radiation, which was recorded. The intensity of this radiation decreased with increasing film temperature. This was to be expected, since more dipositronium molecules should have been preserved on the cold surface. Therefore, Cassidy and Mills believe that they now have completely reliable evidence of his birth in their hands.
These experiments can also yield quite practical results. Cassidy and Mills calculated that in their experiment the density of positronium atoms was 10 15 per cm 3. Calculations show that when this density increases by three orders of magnitude, these atoms at a temperature of 15 kelvins will merge into a single quantum system - a Bose-Einstein condensate. With a subsequent increase in density by another thousand times, it will be possible to launch a cascade reaction of positronium annihilation in it, which will lead to the birth of coherent gamma rays. As a result, an emitter can be created that so far exists only on the pages of science fiction novels - a gamma laser.
Positronium
Positronium is a coupled quantum mechanical system consisting of an electron and a positron. Positronium is designated by the chemical symbol Ps. The possibility of positronium formation was discussed back in the mid-40s. Cross section for positronium production in e + e - collisions at a relatively low velocity v, calculated D. Ivanenko And A. Sokolov(DAN USSR 58, 1320 (1947)),
α = 1/137 is the fine structure constant, r 0 = e 2 /m e c 2 is the classical radius of the electron. Ratio of positronium production cross sections σ Ps and annihilation σ a
At v ≈ α·c, which corresponds to the relative kinetic energy of colliding particles 13.5 eV, the positronium production cross section is 50 times larger than the annihilation cross section. Therefore, in most cases, a bound state, positronium, will be formed before annihilation.
It has been shown theoretically that there should be two types of positronium atoms, differing in lifetime.
The positronium atom was synthesized for the first time M. Deychem in 1951
A positronium atom consists of a particle of ordinary matter - an electron - and a particle of antimatter - a positron.
The characteristics of various states of positronium can be obtained from the characteristics of the hydrogen atom, based on the fact that the proton is replaced by a positron, which leads to a reduction in the reduced mass of the electron μ in positronium by half compared to the reduced mass of the electron in the hydrogen atom m e
The energies of states with principal quantum number n in a positronium atom are determined by the relation
Ry = 13.602 eV – Rydberg constant.
Accordingly, the energies of transitions in positronium are approximately two times less than the energies of the corresponding transitions in the hydrogen atom, and the emitted wavelengths λ are twice as long.
The radius of the Bohr orbit of the positronium atom R(Ps) is twice the radius of the Bohr orbit of the hydrogen atom R(H)
The ionization potential of positronium is 6.77 eV, which is half the ionization potential of the hydrogen atom. Since the electron and positron spins are equal to s = 1/2, in the ground bound state two values of the positronium spin S(Ps) are possible.
- S(Ps) = 0. The spins of the electron and positron are directed in opposite directions - the total spin is S(Ps) = 0. This state is called parapositronium.
- S(Ps) = 1. The electron and positron spins are directed in the same direction - the total spin
S(Ps)= 1. This state is called orthopositronium.
Due to the difference in spin values in the ground state, the energy of orthopositronium 3S 1 on
8.4·10 -4 eV is greater than the energy of the ground state 1S 0 .
In the interaction of an unpolarized electron and a positron, the probability of the formation of a state with spin S(Ps) = 1 is three times greater than the probability of the formation of a state with spin S(Ps) = 0, which is explained by the greater statistical weight g = 2S + 1 of the state S = 1 by compared to the state S = 0.
The lifetime of positronium depends on the relative orientation of the spins of the electron and positron. The average lifetime of parapositronium at rest in a vacuum relative to annihilation is 125 ps, and orthopositronium is 143 ns. Such a large difference in lifetime is due to the fact that, as a result of annihilation, parapositronium can decay into two γ quanta, while orthopositronium decays into three γ quanta (Fig. 7.1).
Rice. 7.1. Decay diagrams for parapositronium S(Ps) = 0 and orthopositronium S(Ps) = 1.
It is also possible to annihilate parapositronium into a larger even number of photons, and orthopositronium into a larger odd number of photons.
The spontaneous transition of positronium from the ortho state to the para state is prohibited, despite the small (8.4·10 -4 eV) energy difference between these states. However, this transition can be induced when positronium collides with gas molecules that have one unpaired electron. In this case, a resonant exchange of electrons can occur between the positronium and the gas molecule.
Positronium molecule
In 1976 D. Wheeler showed that positronium can form two- and three-atomic molecules similar to the hydrogen molecule. The study of the properties of positronium became possible thanks to the creation of intense positron sources.
The first positron sources had an intensity of the order of tens of positrons per second. More intense sources of positrons were obtained as a result of the β + decay of radioactive isotopes formed during irradiation in nuclear reactors or in proton and deuteron accelerators. As a result, it was possible to increase the intensity of positron beams to 10 7 positron/s. The next stage in increasing the intensity of positron beams was the creation of positron storage devices. The isotope 22 Na was used as the initial source of positrons.
The most intense positron beams can be obtained through the interaction of intense laser radiation with matter. The interaction of a short intense laser beam with the target material leads to the formation of electrons, which, when accelerated in the intense laser field, generate bremsstrahlung γ-radiation with the subsequent formation of electrons and positrons. The resulting electrons and positrons can then be separated quite simply using electromagnetic separators.
The positronium atom has some analogy with the hydrogen atom.
- In positronium, as well as in the hydrogen atom, parallel and antiparallel orientations of the spins of the positron and electron lead to two states: parapositron - a state with the total spin of the electron and positron S = 0 and orthopositronium - a state with the total spin of the electron and positron S = 1.
- In the case of hydrogen, it is possible to create a negative hydrogen ion from one proton and two electrons. Similarly, in the case of positronium, it is possible to create a negative positronium ion, consisting of one positron and two electrons.
- Hydrogen atoms combine into diatomic molecules 1 H + 1 H → 2 1 H. Therefore, it was of interest to obtain a molecule of diatomic positronium. Positronium molecules were first obtained in 2007.
Preliminary calculations showed that the binding energy of such a molecule is ≈0.4 eV. Therefore, in order for a positronium molecule to form as a result of a collision of two positronium atoms, a third body is needed that would take away the excess energy and thereby stabilize the resulting positronium molecule - preventing its rapid collapse. A specially treated porous quartz surface (pore size ≈ 40 Å) was chosen as such a third body. It was shown that positronium atoms are effectively formed in a microporous surface when irradiated with an intense positron beam. About 20 million positrons were accumulated in a specially designed positron accumulator, which were then fired into a quartz plate within one nanosecond. Positronium atoms were formed in micropores. Positronium atoms were formed both in the long-lived o-Ps orthopositronium state and in the short-lived p-Ps parapositronium state. At a positron beam density of ~10 9 cm–2, two processes occur in porous cells. - Exchange of spins between interacting states of orthopositronium and parapositronium
o-Ps + oPs ↔ pPs + pPs + 2E 1,
where E 1 is the energy difference between the 3S 1 states. - Formation of the parapositronium molecule Ps 2 from two o-Ps states
X + o-Ps + oPs ↔ X + Ps 2 + E 2,
where X represents the medium in which the formation of a positronium molecule occurs, E 2 = 0.4 eV is the energy that is released during the formation of a positronium molecule Ps 2 (Fig. 7.2).
Rice. 7.2. The interaction of positronium atoms in a vacuum prevents the formation of a positronium molecule. The interaction of positronium atoms on the surface of porous silicon promotes the formation of a positronium molecule.
Most of the positrons implanted into the quartz substrate immediately annihilated with the substrate electrons without producing positronium. However, the annihilation time diagram made it possible to observe the annihilation of the resulting atoms in the S = 1 state within 150 ns after the moment of positron implantation into the quartz substrate. Positrons captured by the porous surface interact with free silicon electrons, resulting in the formation of positronium atoms. The annihilation of positrons was recorded by a Cherenkov counter with a PbF 2 scintillator.
Evidence of the formation of positronium was the temperature dependence of the signal intensity of annihilation γ-quanta with an energy of 511 keV. At a lower temperature, more molecules of positronium Ps 2 are formed, because Positronium atoms have lower energy and collide with the surface less often. An increase in the fast component of the signal was observed at low temperatures, which indicated the formation of Ps 2 molecules.
Before the positronium atoms annihilated, about 100 thousand molecules of positronium Ps 2 were formed. Once a positronium molecule in the orthopositronium state is formed, the positron can capture an electron with the opposite spin, resulting in faster annihilation of the positronium. Positronium molecules are distinguished by the fact that they are a mixture of four particles of the same mass and annihilate faster than atoms, because In a positronium molecule it is easier for a positron to meet an electron than in an atom.
So far, the number of positronium molecules formed is small. The density of the resulting positronium molecules in the first experiments was 10 15 cm–3. However, it is planned to increase the intensity of the positron beam to a level at which studies of the spectra of molecular positronium will become possible. Already the first experiments with molecular positronium showed that the energy of the first excited state of a free positronium atom and a positronium atom located in a silicon micropore are different. This opens up the fundamental possibility of measuring the sizes of various surface defects. In future experiments, it is planned to study the properties of the Bose condensate from positronium molecules and to create a source of gamma radiation - an electron-positron gamma laser.
Muonium
Muonium is a bound quantum system consisting of a positively charged muon μ + and an electron e -. Muonium differs from the hydrogen atom by replacing the proton with a positively charged muon μ +. Muonium is formed when muons μ + are decelerated in matter. A muon can attach one of the electrons of the electron shell of an atom of the medium, forming a bound state μ + e - . The lifetime of muonium is determined by the average lifetime of a muon τ(μ) = 2.2·10 -6 s. The energy levels of the muonic atom E n can be calculated based on the non-relativistic Schrödinger equation
where Ry = 13.6 eV is the Rydberg constant, n = 1,2,3, ... is the principal quantum number.
The radius of the Bohr orbit of muonium is R = 0.532 Å. The ionization potential of the muonium atom is Eionis = 13.54 eV. Muonium is the simplest system, consisting of a lepton e - and antilepton μ +, connected by electromagnetic interaction. Therefore, precision measurement of the fine structure of the muonium spectrum is one of the precise methods for testing quantum electrodynamics. Since the electron and muon are fermions with spin s = 1/2 their total spin value is
= 1 + 2 can take the value = 0, i.e. Fermion spins can be either antiparallel or parallel. In 75% of cases, muonium atoms are formed in the = state with parallel spins of the muon and electron, and in 25% of cases the total spin of muonium is zero. The energies of these states differ by ~2·10 -5 eV and quantum transitions with the emission of photons with a frequency of ν = 4463 MHz are possible between them. The energy splitting of states = 0 is due to the interaction between the magnetic moments of the electron e - and the muon μ +. In an external magnetic field, the = level is split into three states that differ in the values of the projection Fz = +1,0,-1 vector onto the external magnetic field.
One of the effective ways of producing a muon μ + is the formation of μ + as a result of the decay of positively charged pions