Electronic conductivity of metals - Knowledge hypermarket. Electrical conductivity of various substances

In order to talk about electrical conductivity, you need to remember the nature of the electric current as such. Thus, when a substance is placed inside electric field charges move. This movement provokes the action of just an electric field. It is the flow of electrons that is the electric current. The strength of the current, as we know from school lessons in physics, it is measured in Amperes and is denoted by the Latin letter I. 1 A is an electric current at which a charge of 1 Coulomb passes in a time equal to one second.

There are several types of electric current, namely:

• direct current, which does not change in relation to the indicator and the trajectory of movement at any time;
• alternating current, which changes its indicator and trajectory in time (produced by generators and transformers);
• the pulsating current undergoes changes in magnitude, but does not change its direction.

The electrical conductivity index is directly related to the content of freely moving charges in the material, which have no connection with the crystal network, molecules or atoms.

Thus, according to the degree of current conductivity, materials are divided into the following types:

• conductors;
• dielectrics;
• semiconductors.

The high capacity for electrical conductivity is interpreted in electronic theory. So, electrons run among atoms throughout the conductor due to their weak valence bond with the nuclei. That is, freely moving charged particles inside the metal close the voids among the atoms and are characterized by the randomness of movement. If in electric field a metal conductor is placed, the electrons will take order in their movement, moving to a pole with a positive charge. This is what creates the electric current. The speed of propagation of an electric field in space is similar to the speed of light. It is with this speed that the electric current moves inside the conductor. It is worth noting that this is not the speed of movement of the electrons themselves (their speed is very small and equals a maximum of several mm / s), but the speed of propagation of electricity throughout the substance.

With the free movement of charges inside the conductor, they meet various microparticles on their way, with which a collision occurs and some energy is given to them. Conductors are known to experience heat. This is just due to the fact that overcoming the resistance, the energy of the electrons is distributed as a heat release.

Such "accidents" of charges create an obstacle to the movement of electrons, which is called resistance in physics. A small resistance slightly heats the conductor, and at a high resistance, high temperatures are reached. Last appearance used in heating devices as well as traditional incandescent lamps. Resistance is measured in ohms. Designated with the Latin letter R.

Electrical conductivity- a phenomenon that reflects the ability of a metal or electrolyte to conduct an electric current. This value is the reciprocal of electrical resistance.
The electrical conductivity is measured by Siemens (Cm), and is denoted by the letter G.

Since atoms create an obstacle to the passage of current, the resistance index of substances is different. For designation, the concept of resistivity (Ohm-m) was introduced, which just gives information about the conduction abilities of substances.

Modern conductive materials are in the form of thin ribbons, wires with a specific cross-sectional area and a certain length. Electrical conductivity and resistivity is measured in following units: Sm-m/mm.sq. and Ohm-mm.sq.m respectively.

Thus, electrical resistivity and electrical conductivity are characteristics of the conductive capacity of a material, the cross-sectional area of ​​\u200b\u200bwhich is 1 mm2 and length 1 m. The temperature for the characteristic is 20 degrees Celsius.

Good conductors of electric current among metals are precious metals, namely gold and silver, as well as copper, chromium and aluminum. Steel and iron conductors have weaker characteristics. It should be noted that the metals pure form differ in better electroconductive properties in comparison with alloys of metals. For high resistance, if necessary, tungsten, nichrome and constant conductors are used.

With knowledge of the indicators of resistivity or conductivity, it is very easy to calculate the resistance and electrical conductivity of a particular conductor. In this case, the length and cross-sectional area of ​​​​a particular conductor must be used in the calculations.

It is important to know that the electrical conductivity index, as well as the resistance of any material, directly depends on temperature regime. This is explained by the fact that with a change in temperature, there are also changes in the frequency and amplitude of atomic vibrations. Thus, with an increase in temperature, the resistance to the flow of moving charges will increase in parallel. And as the temperature decreases, the resistance decreases, and the electrical conductivity increases.

In some materials, the dependence of temperature on resistance is very pronounced, in some it is more weak.

Let us consider the behavior of conduction electrons in a metal in a nonequilibrium state, when they move under the action of applied external fields. Such processes are called transfer phenomena.

As is known, electrical conductivity (electrical conductivity) o is a value that relates the density of the electric current and the intensity in local law Ohm: j - oE(see formula (14.15) part 1). All substances according to the nature of electrical conductivity are divided into three classes: metals, semiconductors and dielectrics.

characteristic feature metals is their metallic conductivity - a decrease in electrical conductivity with increasing temperature (at a constant concentration of current carriers). The physical cause of electrical resistance in metals is the scattering of electron waves by impurities and lattice defects, as well as by phonons.

The most significant feature semiconductors is their ability to change their properties over an extremely wide range under the influence of various influences: temperature, electric and magnetic fields, lighting, etc. For example, the intrinsic conductivity of pure semiconductors increases exponentially when heated.

At T> 300 K, the specific conductivity o of materials related to semiconductors varies in a wide range from 10 ~ 5 to 10 6 (Ohm m) -1, while for metals o is more than 10 6 (Ohm m) -1 .

Substances with low specific conductivity, of the order 10~ 5 (ohm m) -1 or less, refer to dielectrics. Their conductivity occurs at very high temperatures Oh.

Quantum theory leads to the following expression for electrical conductivity metals:

where P- concentration of free electrons; t is the relaxation time; t* - effective mass of an electron.

Relaxation time characterizes the process of establishing equilibrium between electrons and the lattice, disturbed, for example, by the sudden inclusion of an external field E.

The term "free electron" means that the electron is not affected by any force fields. The movement of a conduction electron in a crystal under the action of external force F and forces from crystal lattice in some cases can be described as the movement of a free electron, which is affected only by a force F(Newton's second law, see formula (3.5) part 1), but with an effective mass t*, different from mass t e free electron.

Calculations using expression (30.18) show that the electrical conductivity of metals about~1/T. The experiment confirms this conclusion quantum theory, while according to the classical theory

about ~l/fr.

AT semiconductors the concentration of mobile carriers is much lower than the concentration of atoms, and can change with changes in temperature, illumination, irradiation with a particle flux, exposure to an electric field, or the introduction of a relatively small amount of impurities. The charge carriers in semiconductors in the conduction band are electrons (conduction electrons), and in the valence band - positively charged quasiparticles holes. When there is no electron in the valence band for any reason, it is said that a hole (a vacant state) has formed in it. The concepts of holes and conduction electrons are used to describe electronic system semiconductors, semimetals and metals.

In the state of thermodynamic equilibrium, the concentrations of electrons and holes in semiconductors depend both on the temperature and concentration of electrically active impurities, and on the band gap A E.

A distinction is made between intrinsic and extrinsic semiconductors. Own semiconductors are chemically pure semiconductors (eg germanium Ge, selenium Se). The number of electrons in them is equal to the number of holes. Conductivity such semiconductors are called own.

In intrinsic semiconductors at T\u003d O K the valence band is completely filled, and the conduction band is free. Therefore, when T= About K and the absence of external excitation, intrinsic semiconductors behave like dielectrics. As the temperature rises due to thermal excitation, electrons with upper levels the valence band will go into the conduction band. Simultaneously, it becomes possible for the electrons of the valence band to pass to its vacated upper levels. Electrons in the conduction band and holes in the valence band will contribute to the electrical conductivity.

The energy required to transfer an electron from the valence band to the conduction band is called activation energy own conductivity.

When an external electric field is applied to a crystal, electrons move against the field and create an electric current. In an external field, when a neighboring valence electron moves to a vacant place, a hole "moves" to its place. As a result, the hole, just like the electron that passed into the conduction band, will move through the crystal, but in the opposite direction to the electron movement. Formally, a particle with a positive charge equal to the absolute value of the electron charge moves along the crystal in the direction of the field. To take into account the action on elementary charges of the internal field of the crystal for holes, the concept of effective mass w* is introduced. Therefore, when solving problems, we can assume that a hole with an effective mass moves only under the action of one external field.

In an external field, the direction of the velocities of electrons and holes is opposite, but the electric current created by them has the same direction - the direction of the electric field. Thus, the current density at the intrinsic conductivity of a semiconductor is the sum of the current density of electrons y e and holes y d:

The electrical conductivity o is proportional to the number of carriers, which means that it can be proved that for intrinsic semiconductors

and depends exponentially on temperature. The contribution of electrons and holes to o is different, which is explained by the difference in their effective masses.

At comparatively high temperatures, intrinsic conduction predominates in all semiconductors. Otherwise, the electrical properties of a semiconductor are determined by impurities (atoms of other elements), and then they talk about impurity conductivity. The electrical conductivity will be composed of intrinsic and impurity conductivities.

Impurity semiconductors called semiconductors, individual atoms of which are replaced by impurities. The concentration of electrons and holes in them is significantly different. Impurities that are sources of electrons are called donors. Impurities that capture electrons from the valence band are called acceptors.

As a result of the introduction of an impurity in the band gap, additional allowed electronic energy levels arise, located in the band gap close to or to the bottom of the conduction band ( donor levels), or to the top of the valence band ( acceptor levels). This significantly increases the electrical conductivity of semiconductors.

In n-type semiconductors (from English, negative - negative) with a donor impurity, electronic mechanism of conduction. Conductivity in them is provided by excess impurity electrons, the valency of which is one greater than the valency of the main atoms.

In p-type semiconductors (from English, positive - positive) with an acceptor impurity, hole mechanism of conduction. The conductivity in them is provided by holes due to the introduction of an impurity whose valence is one less than the valency of the main atoms.

Convincing proof of the reality of positive holes is provided by hall effect(1879). This effect consists in the occurrence in a metal (or semiconductor) with a current density y placed in a magnetic field AT, additional electric field in the direction perpendicular to AT and at. The use of the Hall effect (measurement of the Hall coefficient depending on the substance) makes it possible to determine the concentration and mobility of charge carriers in a conductor, as well as to establish the nature of the conductivity of a semiconductor (electronic or hole).

Currently, in the development of materials for microelectronics, various semiconductor materials are being created, including those with a wide bandgap. Semiconductor microcircuits are considered one of the promising directions microelectronics, allowing you to create reliable and functionally complex integrated circuits.

Division solids on conductors, semiconductors and dielectrics is connected with the structure of their energy bands. The theory of energy zones is considered in the introduction to this series of works.

In a metal, the conduction band is not completely filled with electrons, but only partially, approximately up to the Fermi level. For this reason, electrons in a metal are free and can move from occupied levels to free ones under the influence of weak electric fields. The concentration of free electrons in the metal is high (of the order of ~ 10 28 m -3), so it depends weakly on temperature and other external factors. For this reason, according to (6), the temperature dependence of the specific conductivity, and hence the resistance, is determined by the change in the electron mobility. In this case, it is essential that the electron gas in the metal degenerate, i.e. its energy is not the temperature, but the concentration of electrons. Indeed, electrons in a metal occupy energy levels up to the Fermi level, which is several electron volts away from the "bottom" of the valence band. The thermal energy of electrons (~ ) at ordinary temperatures is much less, on the order of ~ 10 -2 eV. Consequently, only a few electrons from the upper levels can absorb thermal energy. Average energy electrons, therefore, almost does not change with increasing temperature.

An electron gas in a state of degeneracy has velocities chaotic movement electrons are also determined not by the temperature of the body, but by the concentration of charge carriers. These speeds can be ten times higher than average speed thermal motion calculated from the classical theory ( »10 5 m/s), i.e. »10 6 m/s.

Moving electrons have both corpuscular and wave properties. The wavelength of an electron is determined by the de Broglie formula:

, (8)

where is Planck's constant,

electron speed,

The effective mass of an electron (the concept is introduced in order to describe its carrier motion in a solid body).

Substituting the velocity value =10 6 m/s into (8), we find the de Broglie wavelength for an electron in a metal, it is 0.4 - 0.9 nm.

So, in metal conductors, where the electron wavelength is about 0.5 nm, microdefects create a significant scattering of electron waves. In this case, the speed of the directed motion of electrons decreases, which, according to (4), leads to a decrease in mobility. The mobility of electrons in a metal is relatively low. Table 1 lists the electron mobilities for some metals and semiconductors.

Table 1. Electron mobility in various materials at =300 K

As the temperature increases, the fluctuations of the lattice nodes increase and more and more obstacles appear in the path of the directed movement of electrons, and the electrical conductivity decreases, and the resistance of the metal grows.

Experience shows that for pure metals the dependence on temperature is linear:

, (9)

where is the thermal coefficient of resistance,

Temperature by Celsius scale,

Resistance at =0°C.

To determine and it is necessary to build a dependency graph.

Fig.1. Dependence of metal resistance on temperature

The point of intersection of the line with the axis will give the value. The value is found by the formula:

(10)

Electrical conductivity is the ability of a body to pass an electric current under the influence of an electric field. To characterize this phenomenon is the value of electrical conductivity σ. As theory shows, the value of σ can be expressed in terms of the concentration n of free charge carriers, their charge e, mass m, free path time τ e , free path length λe and average drift velocity< v >charge carriers. For metals, free electrons act as free charge carriers, so that:

σ = ne 2 τе / m = (n e 2 / m) (λe /< v >) = e n u

where u is the carrier mobility, i.e. physical quantity, numerically equal to the drift velocity acquired by the carriers in the field of unit intensity, namely

u=< v >/ E = (e τ e) / m

Depending on σ, all substances are subdivided; on conductors - with σ\u003e 10 6 (Ohm m) -1, dielectrics - with σ\u003e 10 -8 (Ohm m) -1 and semiconductors - with an intermediate value of σ.

From the point of view of the band theory, the division of substances into conductors, semiconductors and dielectrics is determined by how the valence band of the crystal is filled with electrons at 0 K: partially or completely.

The energy imparted to electrons even by a weak electric field is comparable to the distance between the levels in the energy band. If there are free levels in the band, then the electrons excited by the external electric field will fill them. The quantum state of the system of electrons will change, and a preferential (directed) motion of electrons against the field will appear in the crystal, i.e. electricity. Such bodies (Fig. 10.1, a) are conductors.

If the valence band is completely filled, then a change in the state of the system of electrons can occur only when they pass through the band gap. The energy of an external electric field cannot make such a transition. The permutation of electrons inside a completely filled zone does not cause a change in the quantum state of the system, since electrons themselves are indistinguishable.

In such crystals (Fig. 10.1, b), an external electric field will not cause an electric current to appear, and they will be non-conductors (dielectrics). From this group of substances, those with a band gap ΔE ≤ 1 eV (1eV = 1.6 10 -19 J) have been selected.

The transition of electrons through the band gap in such bodies can be carried out, for example, by means of thermal excitation. In this case, a part of the levels - the valence band - is released and the levels of the free band following it (the conduction band) are partially filled. These substances are semiconductors.

According to expression (10.1), a change in the electrical conductivity (electrical resistance) of bodies with temperature can be caused by a change in the concentration n of charge carriers or a change in their mobility u.

Metals

n = (1 / 3π 2) (2mE F / ђ 2) 3/2

where ђ \u003d h / 2π \u003d 1.05 10 -34 J s is the normalized Planck constant, E F is the Fermi energy.

Since E F practically does not depend on temperature T, the concentration of charge carriers does not depend on temperature either. Consequently, the temperature dependence of the electrical conductivity of metals will be completely determined by the electron mobility u, as follows from formula (10.1). Then at high temperatures

u ~ λ e / ~T-1

and in the area low temperatures

u ~ λ e / ~const(T).

The degree of mobility of charge carriers will be determined by scattering processes, i.e. interaction of electrons with the periodic field of the lattice. Since the field of an ideal lattice is strictly periodic, and the state of electrons is stationary, scattering (the appearance of the electrical resistance of a metal) can only be caused by defects (impurity atoms, structure distortions, etc.) and thermal vibrations of the lattice (phonons).

Near 0 K, where the intensity of thermal vibrations of the lattice and the concentration of phonons are close to zero, scattering by impurities (electron-impurity scattering) predominates. In this case, the conductivity practically does not change, as follows from formula (10.4), and the resistivity

has a constant value, which is called the specific residual resistance ρ rest or specific impurity resistance ρ approx, i.e.

ρ rest (or ρ prime) = const (T)

In the region of high temperatures, the electron-phonon scattering mechanism becomes predominant in metals. With such a scattering mechanism, the electrical conductivity is inversely proportional to the temperature, as can be seen from formula (10.3), and the resistivity is directly proportional to the temperature:

A graph of the dependence of resistivity ρ on temperature is shown in fig. 10.2

At temperatures other than 0 K and enough in large numbers impurities, both electron-phonon and electron-impurity scattering can take place; the total resistivity has the form

Expression (10.6) is Mathyssen's rule on the additivity of resistance. It should be noted that both electron-phonon and electron-impurity scattering is chaotic.

Semiconductors

Quantum-mechanical calculations of the carrier mobility in semiconductors have shown that, firstly, the carrier mobility u decreases with increasing temperature, and the scattering mechanism that causes the lowest mobility is decisive in determining the mobility. Second, the dependence of the charge carrier mobility on the doping level (impurity concentration) shows that, at a low doping level, the mobility will be determined by scattering by lattice vibrations and, therefore, should not depend on the impurity concentration.

At high levels doping, it should be determined by scattering on the ionized dopant and decrease with increasing impurity concentration. Thus, the change in the mobility of charge carriers should not make a significant contribution to the change in the electrical resistance of the semiconductor.

In accordance with expression (10.1), the main contribution to the change in the electrical conductivity of semiconductors should be made by a change in the concentration n of charge carriers.

The main feature of semiconductors is the activation nature of conductivity, i.e. a pronounced dependence of the carrier concentration on external influences, such as temperature, irradiation, etc. This is due to the narrow band gap (ΔЕ< 1 эВ) у собственных полупроводников и наличием дополнительных уровней в запрещенной зоне у примесных полупроводников.

The electrical conductivity of chemically pure semiconductors is called own conductivity. The intrinsic conductivity of semiconductors arises as a result of the transition of electrons (n) from the upper levels of the valence band to the conduction band and the formation of holes (p) in the valence band:

σ = σ n + σ ρ = e n n u n + e n ρ u ρ

where n n and n ρ is the concentration of electrons and holes,
u n and u ρ - respectively their mobility,
e is the charge of the carrier.

As the temperature increases, the concentration of electrons in the conduction band and holes in the valence band increases exponentially:

n n = u nо exp(-ΔE / 2kT) = n ρ = n ρо exp(-ΔE / 2kT)

where n nо and n pо are the concentrations of electrons and holes at T → ∞,
k \u003d 1.38 10 -23 J / K - Boltzmann's constant.

Figure 10.3,a shows a plot of the logarithm of the electrical conductivity ln σ of its own semiconductor on the reciprocal temperature 1 / T: ln σ \u003d ƒ (1 / T). The graph is a straight line, the slope of which can be used to determine the band gap ∆E.

For lightly doped semiconductors at low temperatures, transitions involving impurity levels predominate. As the temperature increases, the concentration of impurity carriers increases, which means that the impurity conductivity also increases. Upon reaching t. A (see Fig. 10.3, b; curve 1) - impurity depletion temperature T S1 - all impurity carriers will be transferred to the conduction band.

Above the temperature T S1 and up to the transition temperature to intrinsic conductivity T i1 (see t. B, curve 1, Fig. 10.3, b), the electrical conductivity drops, and the resistance of the semiconductor increases. Above the temperature T i1, intrinsic electrical conductivity predominates, i.e. due to thermal excitation, their own charge carriers pass into the conduction band. In the intrinsic conduction region, σ increases, while ρ decreases.

For heavily doped semiconductors, in which the impurity concentration is n ~ 1026 m–3, i.e. is commensurate with the concentration of charge carriers in metals (see curve 3, Fig. 10.3, b), the dependence of σ on temperature is observed only in the intrinsic conduction region. With an increase in the concentration of impurities, the value of the interval AB (AB\u003e A "B"\u003e A "B") decreases (see Fig. 10.3, b).

Both in the region of impurity conductivity and in the region of intrinsic conductivity, the electron-phonon scattering mechanism prevails. In the region of impurity depletion (intervals AB, A"B", A"B") near the temperature T S, electron-impurity scattering prevails. As the temperature increases (transition to T i), electron-phonon scattering begins to predominate. Thus, the interval AB (A"B" or A"B"), called the region of impurity depletion, is also the region of transition from the mechanism of impurity conduction to the mechanism of intrinsic conduction.

The passage of current through metals (conductors of the first kind) is not accompanied by a chemical change in them (§ 40). This circumstance suggests that the metal atoms do not move from one section of the conductor to another during the passage of current. This assumption was confirmed by the experiments of the German physicist Carl Victor Eduard Rikke (1845-1915). Rikke made a chain, which included three cylinders closely pressed against each other, of which the two outermost ones were copper, and the middle one was aluminum. An electric current was passed through these cylinders for a very long time (more than a year), so that the total amount of electricity that flowed reached an enormous value (over 3,000,000 C). Producing then a thorough analysis of the place of contact between copper and aluminum, Rikke could not find traces of penetration of one metal into another. Thus, when current passes through metals, the metal atoms do not move with the current.

How does charge transfer occur when a current passes through a metal?

According to the concepts of electronic theory, which we have repeatedly used, negative and positive charges, which are part of each atom, differ significantly from each other. The positive charge is attached to the atom itself and normal conditions inseparable from the main part of the atom (its nucleus). Negative charges - electrons with a certain charge and mass, almost 2000 times less than the mass of the lightest atom - hydrogen, can be relatively easily separated from the atom; an atom that has lost an electron forms a positively charged ion. In metals, there is always a significant number of "free" electrons separated from atoms, which wander around the metal, passing from one ion to another. These electrons, under the action of an electric field, easily move through the metal. Ions, on the other hand, make up the backbone of the metal, forming its crystal lattice (see Volume I).

One of the most convincing phenomena that reveals the difference between positive and negative electric charges in a metal is the photoelectric effect mentioned in § 9, which shows that electrons can be torn out of the metal relatively easily, while positive charges are tightly bound to the substance of the metal. Since, during the passage of current, the atoms, and, consequently, the positive charges associated with them, do not move along the conductor, free electrons should be considered carriers of electricity in the metal. These ideas were directly confirmed by the important experiments carried out for the first time in 1912 by L. I. Mandelstam and N. D. Papaleksi, but not published by them. Four years later (1916) R. C. Tolman and T. D. Stuart published the results of their experiments, which turned out to be similar to those of Mandelstam and Papaleksi.

When staging these experiments proceeded from the following thought. If there are free charges in the metal that have mass, then they must obey the law of inertia (see Volume I). A conductor moving rapidly, for example, from left to right, is a collection of metal atoms moving in this direction, which carry free charges along with them. When such a conductor suddenly stops, the atoms that make up it stop; free charges, by inertia, must continue to move from left to right until various interferences (collisions with stopped atoms) stop them. The occurring phenomenon is similar to what is observed during a sudden stop of a tram, when “free” objects and people not attached to the car, by inertia, continue to move forward for some time.

In this way, short time after the conductor stops, the free charges in it must move in one direction. But the movement of charges in a certain direction is an electric current. Therefore, if our reasoning is correct, then after a sudden stop of the conductor, we must expect the appearance of a short-term current in it. The direction of this current will make it possible to judge the sign of those charges that moved by inertia; if positive charges move from left to right, then a current will be found that is directed from left to right; if negative charges move in this direction, then a current should be observed that has a direction from right to left. The current that arises depends on the charges and the ability of their carriers to keep their motion more or less long due to inertia, despite interference, i.e., on their mass. Thus, this experiment not only allows us to verify the assumption of the existence of free charges in the metal, but also to determine the charges themselves, their sign and the mass of their carriers (more precisely, the ratio of charge to mass).

In the practical implementation of the experiment, it turned out to be more convenient to use not progressive, but rotary motion conductor. The scheme of such an experiment is shown in fig. 141. On the coil, in which two half-axes isolated from each other, a wire spiral 1 is fixed. then suddenly slowed down. Experiment indeed revealed that in this case an electric current arose in the galvanometer. The direction of this current showed that negative charges move by inertia. By measuring the charge carried by this transient current, one could find the ratio of the free charge to the mass of its carrier. This ratio turned out to be equal to C/kg, which agrees well with the value of such a ratio for electrons determined by other methods.

Rice. 141. Study of the nature of electric current in metals

So, experiments show that there are free electrons in metals. These experiments are one of the most important confirmations of the electronic theory of metals. Electric current in metals is an ordered movement of free electrons (as opposed to their random thermal movement, which is always present in a conductor).

86.1. An uncharged metal disk is brought into rapid rotation and thus becomes an "electron centrifuge". A potential difference arises between the center and periphery of the disk (Fig. 142; 1 - disk, 2 - contacts, 3 - electrometer). What will be the sign of this difference?

Rice. 142. To exercise 86.1

86.2. A current of 1 A passes through a silver wire with a cross section of 1 mm2. Calculate the average speed of the ordered movement of electrons in this wire, assuming that each silver atom gives one free electron. The density of silver is kg/m3, its relative atomic mass equals 108. Avogadro's constant mol-1.

86.3. How many electrons must pass through the cross section of the wire every second for a current of 2 A to flow in the wire? The charge of an electron is Cl.