Physics. Molecules. Arrangement of molecules in gaseous, liquid and solid distances.
Movement of molecules in gases
In gases, the distance between molecules and atoms is usually significant more sizes molecules, and the attractive forces are very small. Therefore, gases do not have their own shape and constant volume. Gases are easily compressed because repulsive forces over large distances are also small. Gases have the property of expanding indefinitely, filling the entire volume provided to them. Gas molecules move at very high speeds, collide with each other, bounce off each other in different sides. Numerous impacts of molecules on the walls of the vessel create gas pressure.
Movement of molecules in liquids
In liquids, molecules not only oscillate around an equilibrium position, but also make jumps from one equilibrium position to the next. These jumps occur periodically. The time period between such jumps is called the average time of sedentary life (or average relaxation time) and is denoted by the letter ?. In other words, relaxation time is the time of oscillations around one specific equilibrium position. At room temperature this time averages 10-11 s. The time of one oscillation is 10-1210-13 s.
The time of sedentary life decreases with increasing temperature. Distance between liquid molecules smaller sizes molecules, the particles are located close to each other, and the intermolecular attraction is strong. However, the arrangement of liquid molecules is not strictly ordered throughout the volume.
Liquids, like solids, retain their volume, but do not have their own shape. Therefore, they take the shape of the vessel in which they are located. Liquid has the property of fluidity. Thanks to this property, the liquid does not resist changing shape, is slightly compressed, and its physical properties are the same in all directions inside the liquid (isotropy of liquids). The nature of molecular motion in liquids was first established by the Soviet physicist Yakov Ilyich Frenkel (1894 1952).
Movement of molecules in solids
The molecules and atoms of a solid are arranged in a certain order and form a crystal lattice. Such solids are called crystalline. Atoms perform vibrational movements around the equilibrium position, and the attraction between them is very strong. Therefore, solids under normal conditions retain their volume and have their own shape.
This distance can be estimated by knowing the density of the substance and the molar mass. Concentration – the number of particles per unit volume is related to density, molar mass and Avogadro's number by the relationship:
where is the density of the substance.
The reciprocal of concentration is the volume per one particle, and the distance between particles, thus, the distance between particles:
For liquids and solids, density weakly depends on temperature and pressure, therefore it is an almost constant value and approximately equal, i.e. The distance between molecules is of the order of the size of the molecules themselves.
The density of a gas is highly dependent on pressure and temperature. Under normal conditions (pressure, temperature 273 K), the air density is approximately 1 kg/m 3, the molar mass of air is 0.029 kg/mol, then the estimate using formula (5.6) gives the value. Thus, in gases, the distance between molecules is much greater than the size of the molecules themselves.
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Physical foundations of non-relativistic mechanics
Mechanics studies mechanical movement. Mechanical movement is a change in the position of bodies or parts of bodies relative to other bodies or parts of bodies.
Kinematics of a material point. Rigid body kinematics
Methods for specifying the motion of a material point in kinematics. Basic kinematic parameters: trajectory, path, displacement, speed, normal, tangential and full acceleration
Dynamics of a material point and translational motion of a rigid body
Inertia of bodies. Weight. Pulse. Interaction of bodies. Force. Newton's laws. Types of forces in mechanics. Gravitational forces. Ground reaction and weight. Elastic force. Friction force. Deformation of elastic solids. ABOUT
Dynamics of rotational motion
Basic equation of dynamics rotational movement absolutely solid body. Moment of power. Momentum relative to a point and an axis. The moment of inertia of a rigid body relative to the main
Laws of conservation and change of momentum and angular momentum in mechanics
Phone systems
Any set of bodies is called a system of bodies. If bodies included in the system are not affected by other bodies not included
Work and power in mechanics Work and power of force and moment of forces.;
;
;
; ;
Mechanical work
and potential energy
Energy LGO
and potential energy
Movement in any potential well is oscillatory movement (Fig. 2.1.1).
Figure 2.1.1. Oscillatory motion in a potential well
Spring pendulum Law of conservation and transformation of oscillation energy of a spring pendulum (Fig. 2.1.2): EPmax = EP + EK = Physical pendulum
Law of conservation and transformation of oscillation energy of a physical pendulum (Fig. 2.1.3): Fig. 2.1.3. Physical pendulum: O - point
Equation of the basic law of the dynamics of rotational motion of an absolutely rigid body: .(2.1.33) Since for a physical pendulum (Fig. 2.1.6), then.
Spring and physical (mathematical) pendulums
β < ω0 – квазипериодический колебательный режим (рис. 2.2.2).
Рис. 2.2.2. График затухающих колебаний
For arbitrary oscillatory systems
differential equation
; ;
In accordance with Newton's second law: , (2.2.17) where (2.2.18) is the external periodic force acting on the spring pendulum.
The process of establishing forced continuous oscillations
The process of establishing forced undamped oscillations can be represented as the process of adding two oscillations: 1. damped oscillations (Fig. 2.2.8);
;
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Fundamentals of Special Relativity
Fundamentals of the special theory of relativity.
Transformations of coordinates and time (1) At t = t’ = 0, the origins of coordinates of both systems coincide: x0
Electric charges. Methods for obtaining charges. Law of conservation of electric charge
In nature there are two types of electric charges, conventionally called positive and negative. Historically positive is called the dawn
Interaction of electric charges. Coulomb's law. Application of Coulomb's law to calculate the interaction forces of extended charged bodies The law of interaction of electric charges was established in 1785 by Charles Coulomb (Coulomb Sh., 1736-1806). The pendant measured the force of interaction between two small charged balls depending on the velocity Electric field. Electric field strength. The principle of superposition of electric fields The interaction of electric charges occurs through special kind
matter generated by charged particles -
electric field
. Electric charges change properties
Basic equations of electrostatics in vacuum. Electric field strength vector flux. Gauss's theorem By definition, the flow of a vector field through the area is the quantity (Fig. 2.1) Fig. 2.1. Toward the definition of vector flux. Application of Gauss's theorem to calculate electric fields
In a number of cases, Gauss's theorem allows us to find the tension
electric field
extended charged bodies, without resorting to the calculation of cumbersome integrals. This usually applies to bodies whose geometer
The work of field forces to move a charge. Electric field potential and potential difference
As follows from Coulomb's law, the force acting on a point charge q in an electric field created by other charges is central. Let us remember that the central
From the relationship that determines the relationship between the intensity and potential of the electric field, the formula for calculating the field potential follows: where the integration is performed
Polarization of dielectrics. Free and bound charges. Main types of polarization of dielectrics
The phenomenon of the appearance of electric charges on the surface of dielectrics in an electric field is called polarization. The resulting charges are polarized
Polarization vector and electrical induction vector
For quantitative characteristics polarization of dielectrics introduce the concept of polarization vector as the total (total) dipole moment of all molecules in a unit volume of the dielectric
Electric field strength in a dielectric
In accordance with the principle of superposition, the electric field in a dielectric is vectorially composed of the external field and the field of polarization charges (Fig. 3.11).
or by absolute value
Boundary conditions for the electric field
When crossing the interface between two dielectrics with different dielectric constants ε1 and ε2 (Fig. 3.12), it is necessary to take into account the boundary forces
Electrical capacity of conductors. Capacitors
A charge q imparted to an isolated conductor creates an electric field around it, the intensity of which is proportional to the magnitude of the charge. The field potential φ, in turn, is related
Calculation of the capacitance of simple capacitors According to the definition, the capacitance of the capacitor is: , where (the integral is taken along the field line between the plates of the capacitor). Hence,
general formula
to calculate e
Energy of a system of stationary point charges
As we already know, the forces with which charged bodies interact are potential. Consequently, a system of charged bodies has potential energy. When the charges are removed
Current characteristics. Current strength and density. Potential drop along a current-carrying conductor
Any ordered movement of charges is called electric current. Charge carriers in conducting media can be electrons, ions, “holes” and even macroscopically
Ohm's law for a homogeneous section of a chain. Conductor resistance
There is a functional relationship between the potential drop - voltage U and the current in the conductor I, called the current-voltage characteristic of a given p
An electrical circuit containing nodes is called a branched circuit. A node is a place in a circuit where three or more conductors meet (Fig. 5.14).
Resistance connection
The connection of resistances can be series, parallel and mixed.
1) Serial connection.
In a series connection, the current flowing through all
By moving electric charges along a closed circuit, the current source does work. A distinction is made between useful and complete operation of a current source. Interaction of conductors with current. Ampere's law It is known that
permanent magnet
exerts an effect on a current-carrying conductor (for example, a current-carrying frame); the opposite phenomenon is also known - a current-carrying conductor exerts an effect on a permanent magnet (for example
Biot-Savart-Laplace law. The principle of superposition of magnetic fields
Moving electric charges (currents) change the properties of the space surrounding them - they create a magnetic field in it. This field manifests itself in the fact that the wires placed in it
Circuit with current in a magnetic field. Magnetic moment of current
In many cases we have to deal with closed currents, the dimensions of which are small compared to the distance from them to the observation point. We will call such currents elementary
Magnetic field on the axis of a circular coil with current
According to the Biot-Savart-Laplace law, the induction of the magnetic field created by a current element dl at a distance r from it is, where α is the angle between the current element and the radius
Moment of forces acting on a circuit with current in a magnetic field
Let us place a flat rectangular circuit (frame) with current in a uniform magnetic field with induction (Fig. 9.2).
Energy of a circuit with current in a magnetic field
A current-carrying circuit placed in a magnetic field has a reserve of energy. Indeed, in order to rotate a current-carrying circuit through a certain angle in the direction opposite to the direction of its rotation in the magnetic field
Circuit with current in a non-uniform magnetic field
If the circuit with current is in a non-uniform magnetic field (Fig. 9.4), then, in addition to the torque, it is also acted upon by a force due to the presence of a magnetic field gradient. Projection of this
Work done when moving a current-carrying circuit in a magnetic field
The flow of a vector through any surface S is called the integral: , where is the projection of the vector onto the normal to the surface S at a given point (Fig. 10.1).
Fig. 10.1. TO
Magnetic field circulation theorem. Magnetic voltage
The circulation of the magnetic field along a closed contour l is called the integral: , where is the projection of the vector onto the direction of the tangent to the contour line at a given point.
Relevant
Magnetic field of solenoid and toroid
Let us apply the results obtained to find the magnetic field strength on the axis of a straight long solenoid and toroid.
1) Magnetic field on the axis of a straight long solenoid.
Magnetic field in matter. Ampere's hypothesis on molecular currents. Magnetization vector
Various substances are, to varying degrees, capable of magnetization: that is, under the influence of the magnetic field in which they are placed, they acquire a magnetic moment. Some substances
Description of the magnetic field in magnets. Magnetic field strength and induction. Magnetic susceptibility and magnetic permeability of a substance A magnetized substance creates a magnetic field, which is superimposed on the external field (field in a vacuum). Both fields in sum give the resulting magnetic field with induction, and according to Boundary conditions for the magnetic field
When crossing the interface between two magnets with different
magnetic permeabilities
μ1 and μ2 magnetic field lines experience n
Magnetic moments of atoms and molecules
The atoms of all substances consist of a positively charged nucleus and negatively charged electrons moving around it. Each electron moving in orbit forms a circular current of force - h
The nature of diamagnetism. Larmore's theorem
If an atom is placed in an external magnetic field with induction (Fig. 12.1), then the electron moving in orbit will be affected by a rotational moment of forces, tending to establish the magnetic moment of the electron
Paramagnetism. Curie's law. Langevin theory
If the magnetic moment of atoms is different from zero, then the substance turns out to be paramagnetic. An external magnetic field tends to establish the magnetic moments of atoms along the
We already know that an Ampere force acts on a current-carrying conductor placed in a magnetic field. But the current in a conductor is the directional movement of charges. This suggests the conclusion that the force de
Motion of a charged particle in a uniform constant electric field
IN in this case and the Lorentz force has only an electrical component. The equation of particle motion in this case is: .
Let's consider two situations: a)
Motion of a charged particle in a uniform constant magnetic field
In this case, the Lorentz force has only a magnetic component. The equation of particle motion, written in the Cartesian coordinate system, in this case is: .
Practical applications of the Lorentz force. Hall effect
One of the well-known manifestations of the Lorentz force is the effect discovered by Hall (Hall E., 1855-1938) in 1880.
_ _ _ _ _ _ The phenomenon of electromagnetic induction. Faraday's law and Lenz's rule. Induction emf. Electronic mechanism for the occurrence of induction current in metals Phenomenon
electromagnetic induction
was opened in 1831. Michael Faraday (Faraday M., 1791-1867), who established that in any closed conductive circuit, when the sweat changes
The phenomenon of self-induction. Conductor inductance
Whenever the current in a conductor changes, its own magnetic field also changes. Along with it, the flux of magnetic induction that penetrates the surface covered by the conductor contour also changes.
Transient processes in electrical circuits containing inductance. Extra currents of closing and breaking
With any change in current strength in any circuit, a self-inductive emf appears in it, which causes the appearance of additional currents in this circuit, called extra currents
Magnetic field energy. Energy Density
In the experiment, the diagram of which is shown in Fig. 14.7, after the switch is opened, a decreasing current flows through the galvanometer for some time. The work of this current is equal to the work of external forces, the role of which is played by the ED Comparison of the basic theorems of electrostatics and magnetostatics So far we have studied static electrical and magnetic fields, that is, such fields that are created
stationary charges
and direct currents.
Vortex electric field. Maxwell's first equation
Maxwell's main idea is the idea of the interconvertibility of electric and magnetic fields. Maxwell suggested that not only alternating magnetic fields are sources
Differential form of Maxwell's equations
1. Applying Stokes' theorem, we transform the left side of Maxwell's first equation to the form: .
Then the equation itself can be rewritten as, whence
Closed system of Maxwell's equations. Material equations
To close the system of Maxwell’s equations, it is also necessary to indicate the connection between the vectors, and, that is, to specify the properties of the material medium in which the electron is considered
Consequences from Maxwell's equations. Electromagnetic waves. Speed of light
Let's consider some of the main consequences that follow from Maxwell's equations given in Table 2. First of all, we note that these equations are linear. It follows that
Electric oscillatory circuit. Thomson's formula
Electromagnetic oscillations can occur in a circuit containing inductance L and capacitance C (Fig. 16.1). Such a circuit is called an oscillatory circuit. Excite to
Free damped oscillations. Quality factor of the oscillatory circuit
Every real oscillatory circuit has resistance (Fig. 16.3). The energy of electrical vibrations in such a circuit is gradually spent on heating the resistance, turning into Joule heat
Forced electrical oscillations. Vector diagram method
If a source of variable EMF is included in the circuit of an electrical circuit containing capacitance, inductance and resistance (Fig. 16.5), then in it, along with its own damped oscillations,
Resonance phenomena in an oscillatory circuit. Voltage resonance and current resonance As follows from the above formulas, at a frequency of the EMF variable ω equal to, the amplitude value of the current in oscillatory circuit
, accepts
Wave equation. Types and characteristics of waves The process of propagation of vibrations in space is called a wave process or simply a wave. Waves of different nature
(sound, elastic,
Electromagnetic waves
From Maxwell's equations it follows that if an alternating electric or magnetic field is excited with the help of charges, a sequence of mutual transformations will arise in the surrounding space
Energy and momentum of an electromagnetic wave. Poynting vector The propagation of an electromagnetic wave is accompanied by a transfer of energy and momentum electromagnetic field
Elastic waves in solids. Analogy with electromagnetic waves
Laws of propagation elastic waves in solids follow from the general equations of motion of a homogeneous elastically deformed medium: , where ρ
Standing waves
When two counterpropagating waves with the same amplitude are superimposed, standing waves arise. The appearance of standing waves occurs, for example, when waves are reflected from an obstacle. P
Doppler effect
When the source and/or receiver of sound waves move relative to the medium in which the sound propagates, the frequency ν perceived by the receiver may turn out to be about
Molecular physics and thermodynamics
Introduction. Subject and tasks of molecular physics. Molecular physics studies the state and behavior of macroscopic objects when external influences
(n
Quantity of substance
A macroscopic system must contain a number of particles comparable to Avogadro's number in order to be considered within the framework of statistical physics.
Avogadro calls the number Gas kinetic parameters
Average length
free path - the average distance traveled by a gas molecule between two successive collisions is determined by the formula: . (4.1.7) In this form
Ideal gas pressure
The pressure of a gas on the wall of a container is the result of collisions of gas molecules with it. Each molecule upon collision transfers a certain impulse to the wall, therefore, it acts on the wall with n
Discrete random variable. Concept of probability
Let's look at the concept of probability using a simple example. Let there be white and black balls mixed in a box, which are no different from each other except for color. For simplicity we will Distribution of molecules by speed
Experience shows that the velocities of gas molecules that are in an equilibrium state can have the most
different meanings – both very large and close to zero. The speed of molecules can Basic equation of molecular kinetic theory
The average kinetic energy of translational motion of molecules is equal to: . (4.2.15) Thus,
absolute temperature
proportional to the average kinetic energy
Number of degrees of freedom of a molecule Formula (31) determines only the energy of translational motion of the molecule. Molecules of a monatomic gas have this average kinetic energy. For polyatomic molecules, it is necessary to take into account the contribution to Internal energy of an ideal gas
Barometric formula. Boltzmann distribution
Atmospheric pressure at height h is determined by the weight of the overlying gas layers. If the air temperature T and the acceleration of gravity g do not change with altitude, then the air pressure P at altitude
The first law of thermodynamics. Thermodynamic system. External and internal parameters. Thermodynamic process
The word "thermodynamics" comes from the Greek words thermos - heat, and dynamics - force. Thermodynamics emerged as the science of driving forces arising during thermal processes, about the law
Equilibrium state. Equilibrium processes
If all system parameters have certain values that remain unchanged external conditions constant for an arbitrarily long time, then such a state of the system is called equilibrium, or
Mendeleev - Clapeyron equation
In a state of thermodynamic equilibrium, all parameters of a macroscopic system remain unchanged for as long as desired under constant external conditions. The experiment shows that for any
Internal energy of a thermodynamic system
In addition to thermodynamic parameters P,V and T the thermodynamic system is characterized by a certain state function U, which is called internal energy.
If the designation
The concept of heat capacity
According to the first law of thermodynamics, the amount of heat dQ imparted to the system goes to change its internal energy dU and the work dA that the system does on external
Lecture text
Compiled by: GumarovaSonia Faritovna The book is published in the author's edition Sub. to print 00.00.00. format 60x84 1/16.
Solids are those substances that are capable of forming bodies and have volume. They differ from liquids and gases in their shape. Solids retain their body shape due to the fact that their particles are not able to move freely. They differ in their density, plasticity, electrical conductivity and color. They also have other properties. For example, most of these substances melt during heating, acquiring a liquid state of aggregation. Some of them, when heated, immediately turn into gas (sublimate). But there are also those that decompose into other substances.
Solid crystalline substances prevail over amorphous ones in their numbers.
In the solid state, almost all substances have crystal structure. They differ in their lattices at their nodes containing various particles and chemical elements. It is in accordance with them that they received their names. Each type has characteristic properties:
Solids and substances are practically the same thing. These terms refer to one of 4 states of aggregation. Solids have stable shape and character thermal movement atoms. Moreover, the latter perform small oscillations near the equilibrium positions. The branch of science that studies the composition and internal structure is called solid state physics. There are other important areas of knowledge dealing with such substances. Changing shape under external influences and movement is called the mechanics of a deformable body.
Due to the different properties of solids, they have found application in various technical devices created by man. Most often, their use was based on properties such as hardness, volume, mass, elasticity, plasticity, and fragility. Modern science makes it possible to use other qualities of solids that can only be detected in laboratory conditions.
Crystals are solids with particles arranged in a certain order. Each has its own structure. Its atoms form a three-dimensional periodic arrangement called a crystal lattice. Solids have different structure symmetries. The crystalline state of a solid is considered stable because it has a minimum amount of potential energy.
The vast majority of solids consist of a huge number of randomly oriented individual grains (crystallites). Such substances are called polycrystalline. These include technical alloys and metals, as well as many rocks. Single natural or synthetic crystals are called monocrystalline.
Most often, such solids are formed from the state of the liquid phase, represented by a melt or solution. Sometimes they are obtained from the gaseous state. This process is called crystallization. Thanks to scientific and technological progress, the cultivation (synthesis) procedure various substances received an industrial scale. Most crystals have natural shape in the form Their sizes vary greatly. Thus, natural quartz (rock crystal) can weigh up to hundreds of kilograms, and diamonds - up to several grams.
In amorphous solids, atoms are in constant vibration around randomly located points. They retain a certain short-range order, but lack long-range order. This is due to the fact that their molecules are located at a distance that can be compared with their size. The most common example of such a solid in our life is the glassy state. often considered as a liquid with infinitely high viscosity. The time of their crystallization is sometimes so long that it does not appear at all.
It is the above properties of these substances that make them unique. Amorphous solids are considered unstable because they can become crystalline over time.
The molecules and atoms that make up a solid are packed at high density. They practically retain their relative position relative to other particles and are held together due to intermolecular interaction. The distance between the molecules of a solid in different directions is called the crystal lattice parameter. The structure of a substance and its symmetry determine many properties, such as the electronic band, cleavage and optics. When acting on a solid substance, it is sufficient great strength these qualities may be impaired to one degree or another. In this case, the solid body is subject to residual deformation.
Atoms of solids undergo vibrational movements, which determine their possession of thermal energy. Since they are negligible, they can only be observed under laboratory conditions. of a solid substance greatly affects its properties.
The features, properties of these substances, their qualities and the movement of particles are studied in various subfields of solid state physics.
The following methods are used for research: radio spectroscopy, structural analysis using X-rays and other methods. This is how the mechanical, physical and thermal properties of solids are studied. Hardness, load resistance, tensile strength, phase transformations are studied by materials science. It has a lot in common with solid state physics. There is another important modern science. The study of existing substances and the synthesis of new ones are carried out by solid state chemistry.
The nature of the movement of the outer electrons of the atoms of a solid substance determines many of its properties, for example, electrical ones. There are 5 classes of such bodies. They are established depending on the type of bond between atoms:
What do we know today? Scientists have long studied the properties of the solid state of matter. When it is exposed to temperatures, it also changes. The transition of such a body into liquid is called melting. The transformation of a solid into a gaseous state is called sublimation. As the temperature decreases, the solid crystallizes. Some substances under the influence of cold pass into the amorphous phase. Scientists call this process glass transition.
When the internal structure of solids changes. It acquires the greatest order as the temperature decreases. At atmospheric pressure and temperature T > 0 K, any substances existing in nature solidify. Only helium, which requires a pressure of 24 atm to crystallize, is an exception to this rule.
The solid state of a substance gives it various physical properties. They characterize the specific behavior of bodies under the influence of certain fields and forces. These properties are divided into groups. There are 3 methods of influence, corresponding to 3 types of energy (mechanical, thermal, electromagnetic). Accordingly, there are 3 groups physical properties solids:
Solids are also classified according to their so-called zone structure. So, among them there are:
The movements of molecules in solids determine their electromagnetic properties.
Solids are also classified according to their magnetic properties. There are three groups:
What are they? The density of solids largely determines their hardness. Behind last years Scientists have discovered several materials that claim to be the “most durable body.” The hardest substance is fullerite (a crystal with fullerene molecules), which is approximately 1.5 times harder than diamond. Unfortunately, it is currently only available in extremely small quantities.
Today, the hardest substance that may be used in industry in the future is lonsdaleite (hexagonal diamond). It is 58% harder than diamond. Lonsdaleite - allotropic modification carbon. Its crystal lattice is very similar to that of diamond. A cell of lonsdaleite contains 4 atoms, and a diamond - 8. Of the widely used crystals today, diamond remains the hardest.
What is the average distance between molecules of saturated water vapor at a temperature of 100°C?
Problem No. 4.1.65 from the “Collection of problems for preparing for entrance exams in physics at USPTU”
\(t=100^\circ\) C, \(l-?\)
Let's consider water vapor in some arbitrary quantity equal to \(\nu\) mole. To determine the volume \(V\) occupied by a given amount of water vapor, you need to use the Clapeyron-Mendeleev equation:
In this formula, \(R\) is the universal gas constant equal to 8.31 J/(mol K). The saturated water vapor pressure \(p\) at a temperature of 100° C is 100 kPa, this is a known fact and every student should know it.
To determine the number of water vapor molecules \(N\), we use the following formula:
Here \(N_A\) is Avogadro’s number, equal to 6.023·10 23 1/mol.
Then for each molecule there is a cube of volume \(V_0\), obviously determined by the formula:
\[(V_0) = \frac(V)(N)\]
\[(V_0) = \frac((\nu RT))((p\nu (N_A))) = \frac((RT))((p(N_A)))\]
Now look at the diagram for the problem. Each molecule is conditionally located in its own cube, the distance between two molecules can vary from 0 to \(2d\), where \(d\) is the length of the cube edge. The average distance \(l\) will be equal to the length of the edge of the cube \(d\):
The edge length \(d\) can be found like this:
As a result, we get the following formula:
Let's convert the temperature to the Kelvin scale and calculate the answer:
If you do not understand the solution and you have any questions or you have found an error, then feel free to leave a comment below.
Let us consider how the projection of the resulting force of interaction between them on the straight line connecting the centers of the molecules changes depending on the distance between the molecules. If molecules are located at distances several times greater than their sizes, then the interaction forces between them have practically no effect. The forces of interaction between molecules are short-range.
At distances exceeding 2-3 molecular diameters, the repulsive force is practically zero. Only the force of attraction is noticeable. As the distance decreases, the force of attraction increases and at the same time the force of repulsion begins to affect. This force increases very quickly when the electron shells of the molecules begin to overlap.
Figure 2.10 graphically shows the projection dependence F r the forces of interaction of molecules on the distance between their centers. On distance r 0, approximately equal to the amount molecular radii, F r = 0 , since the force of attraction is equal in magnitude to the force of repulsion. At r > r 0 there is an attractive force between the molecules. The projection of the force acting on the right molecule is negative. At r < r 0 there is a repulsive force with a positive projection value F r .
The dependence of the interaction forces between molecules on the distance between them explains the appearance of elastic force during compression and stretching of bodies. If you try to bring the molecules closer to a distance less than r0, then a force begins to act that prevents the approach. On the contrary, when molecules move away from each other, an attractive force acts, returning the molecules to their original positions after the cessation of external influence.
With a small displacement of molecules from equilibrium positions, the forces of attraction or repulsion increase linearly with increasing displacement. In a small area, the curve can be considered a straight segment (the thickened section of the curve in Fig. 2.10). That is why, at small deformations, Hooke’s law turns out to be valid, according to which the elastic force is proportional to the deformation. At large molecular displacements, Hooke's law is no longer valid.
Since the distances between all molecules change when a body is deformed, the neighboring layers of molecules account for an insignificant part of the total deformation. Therefore, Hooke's law is satisfied at deformations millions of times greater than the size of the molecules.
The device of an atomic force microscope (AFM) is based on the action of repulsive forces between atoms and molecules at short distances. This microscope, unlike a tunnel microscope, allows you to obtain images of surfaces that do not conduct electrical current. Instead of a tungsten tip, AFM uses a small fragment of diamond, sharpened to atomic size. This fragment is fixed on a thin metal holder. As the tip approaches the surface under study, the electron clouds of diamond and surface atoms begin to overlap and repulsive forces arise. These forces deflect the tip of the diamond tip. The deviation is recorded using a laser beam reflected from a mirror mounted on a holder. The reflected beam drives a piezoelectric manipulator, similar to the manipulator of a tunnel microscope. The feedback mechanism ensures that the height of the diamond needle above the surface is such that the bend of the holder plate remains unchanged.
In Figure 2.11 you see an AFM image of the polymer chains of the amino acid alanine. Each tubercle represents one amino acid molecule.
At present, atomic microscopes have been constructed, the design of which is based on the action of molecular forces of attraction at distances several times greater than the size of an atom. These forces are approximately 1000 times less than the repulsive forces in AFM. Therefore, a more complex sensing system is used to record the forces.
Atoms and molecules are made up of electrically charged particles. Due to the action of electrical forces over short distances, molecules are attracted, but begin to repel when the electron shells of the atoms overlap.
