Almost simultaneously, two scientific groups from different parts of the world managed to realize the effect of electromagnetic-induced transparency in a single atom. What is unique is that success was achieved by some scientists using real atoms, and by others using man-made analogues.

The EIT (electromagnetically induced transparency) effect is known for creating an environment with a very narrow gap in the absorption spectrum. This phenomenon is most easily recorded when a three-level quantum system (like the one shown in the figure below) is exposed to two resonant fields, the frequencies of which are different.

This structure of energy levels, when there are two close lower states and an upper one, separated from them by the energy of a quantum of the optical range, is usually called the Λ-scheme.

Schematic representation of the experiment with the rubidium atom and a three-level system, where the energy of the state is deposited in the vertical direction. The two lower levels are horizontally spaced for clarity. Blue arrows show the measuring beam, orange arrows indicate the control beam (illustration by Martin Mucke et al.).

The essence of EIT can be described as follows: the action of the control field in one “arm” of the Λ-circuit (transition between the second and third level) makes the system transparent to the test field (transition of the first – third level) acting in the second “arm”.

In other words, the system becomes transparent to the combination of two light fields when the difference in their frequencies coincides with the transition frequency between the two lower levels.

It should be noted that the EIT effect provides interesting opportunities for studying the propagation of light. Thus, in the zone of dip in the absorption spectrum, the medium exhibits a very steep variation in the refractive index. Under certain conditions, this can lead, for example, to a colossal decrease in the group speed of light propagation in the medium.

It is the EIT effect that underlies the well-known experiments on “slowing down” light, which subsequently resulted in the creation of such an entertaining device as the “rainbow trap,” which demonstrates frozen light in the visible frequency range.

The graph shows the relative transmittance and contrast (ie, the difference in readings when the control laser is turned on and off) in experiments involving different numbers of atoms (illustration by Martin Mucke et al.).

The authors of the first work under consideration from the German Max Planck Institute for Quantum Optics (MPQ) chose rubidium atoms 87 Rb to conduct the experiment, due to the fact that the organization of the energy levels of this metal makes it possible to construct a Λ-scheme.

According to the scientists, whose article is posted in the public domain (PDF document), they used a single atom located in an optical resonator. When the control laser was turned on, the relative transmittance estimated using another (trial) laser was 96%. After turning off the control radiation, the value decreased by 20%.

Which is quite logical, with an increase in the number of atoms, the maximum relative transmittance decreased proportionally: thus, the inclusion of seven rubidium atoms in the experiment gave a coefficient of only 78%.

However, at the same time, the EIT effect became more pronounced, and in the case of seven atoms, when the control laser was turned off, the relative transmittance immediately dropped by 60%.

The black line shows the relative transmittance in the case of an “empty” optical resonator, the red line in the presence of atoms, and the blue line in the case of the EIT effect. Different plots reflect experiments with different numbers of atoms (N) (illustration by Martin Mucke et al.).

A second study on the same topic was conducted by a scientific group that included specialists from Japan, Uzbekistan, Great Britain and Russia. Not content with existing elements, physicists created an artificial “atom” in which the EIT effect was also successfully tested.

Connections in nanoelectronics, implemented using a single atom, are not as fragile as they might seem at first glance. Recent experiments by American scientists with nanoscale “bridges” between two macroscopic metal bodies show that the bond becomes rigid when the width of the “bridge” is reduced to one atom. These results are consistent with the assumption that, at such scales, surface forces.

The development of technology has finally reached atomic proportions. Devices with components whose dimensions are of the same order as the atoms of matter are no longer a sensation. Today, for example, “connecting wires” in an electronic circuit can be about 100 atoms wide, and this is not the limit. Because of the ever-shrinking size, scientists need to conduct new research showing how size affects material properties, particularly resistance and mechanical strength.

Another work in this direction was published by a group from the State University of New York (USA). Their results were published in the journal Physical Review B. The object of research was the tiny contacts formed between the gold tips and the surface. Experiments have shown that such compounds (which can be as thin as 1 atom) have specific electrical and mechanical properties.

Typically, to assess the thickness of a contact, scientists apply a voltage to the resulting “bridge” and measure the electrical conductivity of the contact. Previous experiments have shown that in this configuration, as the distance between the surface and the tip increases (as the “bridge” lengthens and decreases in width), the conductivity decreases abruptly. This is because the contact atoms rearrange, so that the number of contact atoms is reduced from several hundred to one. A team of American scientists set themselves the task of studying this rearrangement from a mechanical point of view.

To obtain the necessary data, the scientists applied mechanical stress to the contact and changed the length of the “bridge” in increments of 4 picometers (for this, the tip was attached to a cantilever, which made it possible to measure not only changes in the size of the “bridge”, but also variations in force). As is known, the ratio of the applied mechanical force to the change in length gives a parameter such as rigidity (or a related characteristic called Young’s modulus, which determines the measure of the material’s response to external influence, regardless of geometric dimensions).

As the contact width decreases, the atomic forces change in such a way that the stiffness must increase. Previous experiments have already offered some evidence for this fact; but they were applicable over a limited range of scales. American scientists observed similar phenomena for contact widths less than 1 nm. According to their data, when the contact is narrowed to 1 atom, the rigidity of the contact turns out to be almost twice as high as that of “ordinary” gold.

In addition to the main research, the scientists explained why narrow “constrictions” formed between two metal bodies can be deformed in unexpected ways under the influence of surface forces.

Further work in this direction could explain how different microscopic properties of objects combine to form macroscopic properties.

Connections in nanoelectronics, realized using a single atom, are not as fragile as they might seem at first glance. Recent experiments by American scientists with nanoscale “bridges” between two macroscopic metal bodies show that the bond becomes rigid when the width of the “bridge” is reduced to one atom. These results are consistent with the assumption that surface forces dominate at these scales.

The development of technology has finally reached atomic proportions. Devices with components whose dimensions are of the same order as the atoms of matter are no longer a sensation. Today, for example, “connecting wires” in an electronic circuit can be about 100 atoms wide, and this is not the limit. Because of the ever-shrinking size, scientists need to conduct new research showing how size affects material properties, particularly resistance and mechanical strength.

Another work in this direction was published by a group from the State University of New York (USA). Their results were published in the journal Physical Review B. The study focused on tiny contacts formed between gold tips and the surface. Experiments have shown that such compounds (which can be as thin as 1 atom) have specific electrical and mechanical properties.

Typically, to assess the thickness of a contact, scientists apply a voltage to the resulting “bridge” and measure the electrical conductivity of the contact. Previous experiments have shown that in this configuration, as the distance between the surface and the tip increases (as the “bridge” lengthens and decreases in width), the conductivity decreases abruptly. This is because the contact atoms rearrange, so that the number of contact atoms is reduced from several hundred to one. A team of American scientists set themselves the task of studying this rearrangement from a mechanical point of view.

To obtain the necessary data, the scientists applied mechanical stress to the contact and changed the length of the “bridge” in increments of 4 picometers (for this, the tip was attached to a cantilever, which made it possible to measure not only changes in the size of the “bridge”, but also variations in force). As is known, the ratio of the applied mechanical force to the change in length gives a parameter such as rigidity (or a related characteristic called Young’s modulus, which determines the measure of the material’s response to external influence, regardless of geometric dimensions).

As the contact width decreases, the atomic forces change in such a way that the stiffness must increase. Previous experiments have already offered some evidence for this fact; but they were applicable over a limited range of scales. American scientists observed similar phenomena for contact widths less than 1 nm. According to their data, when the contact is narrowed to 1 atom, the rigidity of the contact turns out to be almost twice as high as that of “ordinary” gold.

In addition to the main research, the scientists explained why narrow “constrictions” formed between two metal bodies can be deformed in unexpected ways under the influence of surface forces.

Further work in this direction could explain how different microscopic properties of objects combine to form macroscopic properties.

Oxidation state

On the visibility of the conditional charge

Every teacher knows how much the first year of chemistry means. Will it be understandable, interesting, important in life and when choosing a profession? Much depends on the teacher’s ability to answer “simple” questions from students in an accessible and visual way.

One of these questions is: “Where do the formulas of substances come from?” – requires knowledge of the concept of “oxidation state”.

The formulation of the concept of “oxidation state” as “the conditional charge of atoms of chemical elements in a compound, calculated on the basis of the assumption that all compounds (both ionic and covalently polar) consist only of ions” (see: Gabrielyan O.S. Chemistry-8. M.: Bustard, 2002,
With. 61) is accessible to few students who understand the nature of the formation of chemical bonds between atoms. Most people find it difficult to remember this definition; they need to cram it. And for what?

A definition is a step in cognition and becomes a tool for work when it is not memorized, but remembered because it is understandable.

When starting to study a new subject, it is important to clearly illustrate abstract concepts, which are especially abundant in the 8th grade chemistry course. This is exactly the approach I want to propose, and to form the concept of “oxidation state” before studying the types of chemical bonds and as the basis for understanding the mechanism of its formation.

From the first lessons, eighth-graders learn to use the periodic table of chemical elements as a reference table for drawing up diagrams of the structure of atoms and determining their properties based on the number of valence electrons. When starting to formulate the concept of “oxidation state,” I teach two lessons.

Lesson 1.
Why are non-metal atoms
connect with each other?

Let's get creative. What would the world look like if atoms did not connect, if there were no molecules, crystals and larger formations? The answer is amazing: the world would be invisible. The world of physical bodies, animate and inanimate, simply would not exist!

Next, we discuss whether all atoms of chemical elements combine. Are there single atoms in nature? It turns out that there are – these are atoms of noble (inert) gases. We compare the electronic structure of noble gas atoms and find out the peculiarities of completed and stable external energy levels:

The expression “external energy levels are complete and stable” means that these levels contain the maximum number of electrons (the helium atom has 2 e, for atoms of other noble gases – 8 e).

How can we explain the stability of the outer eight-electron level? There are eight groups of elements in the periodic table, which means the maximum number of valence electrons is eight. Noble gas atoms are single because they have the maximum number of electrons in the outer energy level. They do not form molecules, like Cl 2 and P 4, or crystal lattices, like graphite and diamond. Then we can assume that the atoms of the remaining chemical elements tend to take on a shell of the noble gas - eight electrons at the outer energy level - connecting with each other.

Let's check this assumption using the example of the formation of a water molecule (the formula H 2 O is known to students, as well as the fact that water is the main substance of the planet and life). Why is the formula of water H 2 O?

Using atomic diagrams, students guess why combining two H atoms and one O atom into a molecule is beneficial. As a result of the displacement of single electrons from two hydrogen atoms, the oxygen atom has eight electrons in its outer energy level. Students suggest different ways of atoms' mutual arrangement. We choose a symmetrical option, emphasizing that nature lives according to the laws of beauty and harmony:

The connection of atoms leads to the loss of their electrical neutrality, although the molecule as a whole is electrically neutral:

The resulting charge is defined as conditional, because it is “hidden” inside an electrically neutral molecule.

Let’s formulate the concept of “electronegativity”: the oxygen atom has a conditional negative charge of –2, because he displaced two electrons from the hydrogen atoms towards himself. This means that oxygen is more electronegative than hydrogen.

We write down: electronegativity (EO) is the property of atoms to displace valence electrons from other atoms towards themselves. We work with the electronegativity series of nonmetals. Using the periodic table, we explain the highest electronegativity of fluorine.

Combining all of the above, we formulate and write down the definition of the oxidation state.

The oxidation state is the conditional charge of the atoms in a compound, equal to the number of electrons displaced to atoms with higher electronegativity.

The term “oxidation” can also be explained as the donation of electrons to the atoms of a more electronegative element, emphasizing that when atoms of different non-metals combine, only a shift of electrons to a more electronegative non-metal often occurs. Thus, electronegativity is a property of non-metal atoms, which is reflected in the name “Electronegativity Series of Non-Metals”.

According to the law of constancy of the composition of substances, discovered by the French scientist Joseph Louis Proust in 1799–1806, every chemically pure substance, regardless of location and method of production, has the same constant composition. This means that if there is water on Mars, then it will be the same “ash-two-o”!

To consolidate the material, we check the “correctness” of the formula of carbon dioxide by drawing up a diagram for the formation of a CO 2 molecule:

Atoms with different electronegativity combine: carbon (EO = 2.5) and oxygen (EO = 3.5). Valence electrons (4 e) carbon atoms are shifted to two oxygen atoms (2 e– to one atom O and 2 e– to another O atom). Therefore, the oxidation state of carbon is +4, and the oxidation state of oxygen is –2.

By connecting, the atoms complete, make their external energy level stable (complement it to 8 e). This is why the atoms of all elements, except the noble gases, combine with each other. Atoms of noble gases are single, their formulas are written with the sign of the chemical element: He, Ne, Ar, etc.

The oxidation state of noble gas atoms, like all atoms in a free state, is zero:

This is understandable, because atoms are electrically neutral.

The oxidation state of atoms in molecules of simple substances is also zero:

When atoms of the same element join, no displacement of electrons occurs, because their electronegativity is the same.

I use the paradox technique: how do non-metal atoms in diatomic gas molecules, for example, chlorine, supplement their external energy level to eight electrons? Let's schematically present the question like this:

Valence electron displacements ( e) does not happen, because The electronegativity of both chlorine atoms is the same.

This question confuses students.

As a hint, it is proposed to consider a simpler example - the formation of a diatomic hydrogen molecule.

Students quickly figure out that since electron displacement is impossible, atoms can combine their electrons. The scheme of such a process is as follows:

The valence electrons become shared, joining the atoms into a molecule, and the outer energy level of both hydrogen atoms becomes complete.

I propose to depict valence electrons as dots. Then the common pair of electrons should be located on the axis of symmetry between the atoms, because When atoms of the same chemical element combine, electron displacement does not occur. Consequently, the oxidation state of hydrogen atoms in the molecule is zero:

This lays the foundation for further study of covalent bonds.

Let's return to the formation of a diatomic chlorine molecule. One of the students guesses to propose the following scheme for combining chlorine atoms into a molecule:

I draw students’ attention to the fact that the common pair of electrons connecting chlorine atoms into a molecule is formed only by unpaired valence electrons.

This way, students can make their own discoveries, the joy of which is not only remembered for a long time, but also develops creative abilities and personality as a whole.

Students receive a homework assignment: to draw diagrams of the formation of common electron pairs in the molecules of fluorine F 2, hydrogen chloride HCl, oxygen O 2 and determine the oxidation states of the atoms in them.

In homework you need to be able to move away from the template. Thus, when drawing up a diagram for the formation of an oxygen molecule, students need to depict not one, but two common pairs of electrons on the axis of symmetry between atoms:

In the diagram for the formation of a hydrogen chloride molecule, one should show the displacement of a common pair of electrons to a more electronegative chlorine atom:

In the HCl compound, the oxidation states of the atoms are: H – +1 and Cl – –1.

Thus, the definition of the oxidation state as the conditional charge of atoms in a molecule, equal to the number of electrons displaced to atoms with higher electronegativity, makes it possible not only to formulate this concept clearly and accessible, but also to make it the basis for understanding the nature of a chemical bond.

Working on the principle of “first understand, and then remember,” using the paradox technique and creating problem situations in the classroom, you can get not only good learning results, but also achieve understanding of even the most complex abstract concepts and definitions.

Lesson 2.
Compounding metal atoms
with non-metals

At checking homework I invite students to compare two options for a visual representation of the connection of atoms into a molecule.

Options for depicting the formation of molecules

M o l e c u l a f t o r F 2

Option 1.

Atoms of one chemical element are combined.

The electronegativity of the atoms is the same.

There is no displacement of valence electrons.

How the fluorine molecule F2 is formed is not clear.

Option 2.
Pairing of valence electrons of identical atoms

We depict the valence electrons of fluorine atoms as dots:

Unpaired The valence electrons of the fluorine atoms formed a common pair of electrons, depicted in the diagram of the molecule on the axis of symmetry. Since there is no displacement of valence electrons, the oxidation state of fluorine atoms in the F 2 molecule is zero.

The result of combining fluorine atoms into a molecule using a common pair of electrons was the completed outer eight-electron level of both fluorine atoms.

The formation of the oxygen molecule O2 is considered in a similar way.

M o l e c l u c l o f o r O 2

Option 1.
Using atomic structure diagrams

Option 2.
Pairing of valence electrons of identical atoms

Hydrogen chloride mole cule HCl

Option 1.
Using atomic structure diagrams

The more electronegative chlorine atom displaced one valence electron from the hydrogen atom. Conditional charges arose on the atoms: the oxidation state of the hydrogen atom is +1, the oxidation state of the chlorine atom is –1.

As a result of the combination of atoms into an HCl molecule, the hydrogen atom “lost” (according to the diagram) its valence electron, and the chlorine atom added its outer energy level to eight electrons.

Option 2.
Pairing of valence electrons of different atoms

The unpaired valence electrons of the hydrogen and chlorine atoms formed a common pair of electrons, shifted to the more electronegative chlorine atom. As a result, conventional charges were formed on the atoms: the oxidation state of the hydrogen atom is +1, the oxidation state of the chlorine atom is –1.

When atoms are combined into a molecule using a shared pair of electrons, their outer energy levels become complete. The outer level of the hydrogen atom becomes two-electron, but shifted to the more electronegative chlorine atom, and the outer level of the chlorine atom becomes stable eight-electron.

Let us dwell in more detail on the last example - the formation of the HCl molecule. Which scheme is more accurate and why? Students notice a significant difference. The use of atomic diagrams in the formation of the HCl molecule involves the displacement of the valence electron from the hydrogen atom to the more electronegative chlorine atom.

Let me remind you that electronegativity (the property of atoms to displace valence electrons from other atoms) is inherent in all elements to varying degrees.

Students come to the conclusion that using atomic diagrams for the formation of HCl does not make it possible to show the shift of electrons to a more electronegative element. The representation of valence electrons by dots more accurately explains the formation of the hydrogen chloride molecule. When the H and Cl atoms bond, a shift occurs (in the diagram - deviation from the axis of symmetry) of the valence electron of the hydrogen atom to the more electronegative chlorine atom. As a consequence, both atoms acquire a certain oxidation state. Unpaired valence electrons not only formed a common pair of electrons that connected the atoms into a molecule, but also completed the outer energy levels of both atoms. Schemes for the formation of F 2 and O 2 molecules from atoms are also more understandable when valence electrons are depicted as dots.

Following the example of the previous lesson with its main question “Where do the formulas of substances come from?” Students are asked to answer the question: “Why does table salt have the formula NaCl?”

FORMATION OF SODIUM CHLORIDE NaCl

Students make the following diagram:

Let’s say: sodium is an element of subgroup Ia, it has one valence electron, therefore, it is a metal; chlorine is an element of subgroup VIIa, has seven valence electrons, therefore, it is a non-metal; in sodium chloride, the valence electron of the sodium atom will be shifted to the chlorine atom.

I ask the guys: is everything in this diagram correct? What is the result of combining sodium and chlorine atoms to form a NaCl molecule?

Students answer: the result of combining atoms into a NaCl molecule was the formation of a stable eight-electron outer level of the chlorine atom and a two-electron outer level of the sodium atom. Paradox: the sodium atom does not need two valence electrons on the outer third energy level! (We work with the diagram of the sodium atom.)

This means that it is “unfavorable” for a sodium atom to combine with a chlorine atom, and the NaCl compound should not exist in nature. However, students know from geography and biology courses about the prevalence of table salt on the planet and its role in the life of living organisms.

How to find a way out of this paradoxical situation?

We work with diagrams of sodium and chlorine atoms, and students guess that it is beneficial for the sodium atom not to shift, but to give up its valence electron to the chlorine atom. Then the sodium atom will have a completed second external – pre-external – energy level. The chlorine atom will also have an eight-electron outer energy level:

We come to the conclusion: it is advantageous for metal atoms having a small number of valence electrons to donate rather than shift their valence electrons to non-metal atoms. Therefore, metal atoms do not have electronegativity.

I propose to introduce a “capture sign” of a foreign valence electron by a non-metal atom – a square bracket.

When valence electrons are represented by dots, the diagram of the connection of metal and non-metal atoms will look like this:

I draw students’ attention to the fact that when a valence electron is transferred from a metal atom (sodium) to a non-metal atom (chlorine), the atoms turn into ions.

Ions are charged particles into which atoms are transformed as a result of the transfer or addition of electrons.

The signs and magnitudes of the ion charges and oxidation states are the same, and the difference in design is as follows:

1 –1
Na, Cl – for oxidation states,

Na + , Cl – – for ion charges.

FORMATION OF CALCAL FLUORIDE CaF 2

Calcium is an element of subgroup IIa, it has two valence electrons, it is a metal. The calcium atom donates its valence electrons to the fluorine atom, a nonmetal and the most electronegative element.

In the diagram we arrange the unpaired valence electrons of the atoms so that they “see” each other and can form electron pairs:

The binding of calcium and fluorine atoms into the CaF 2 compound is energetically favorable. As a result, the energy level of both atoms becomes eight-electron: for fluorine it is the outer energy level, and for calcium it is the outer one. Schematic representation of electron transfer in atoms (useful when studying redox reactions):

I point out to students that, just as negatively charged electrons are attracted to the positively charged nucleus of an atom, oppositely charged ions are held together by the force of electrostatic attraction.

Ionic compounds are solids with a high melting point. Students know from life that they can heat table salt for several hours to no avail. The temperature of the gas burner flame (~500 °C) is not enough to melt the salt
(t pl (NaCl) = 800 °C). From here we conclude: the bond between charged particles (ions) - the ionic bond - is very strong.

Let us generalize: when metal atoms (M) combine with non-metal atoms (Nem), there is not a displacement, but a donation of valence electrons by the metal atoms to the non-metal atoms.

In this case, electrically neutral atoms turn into charged particles - ions, the charge of which coincides with the number of electrons donated (for a metal) and attached (for a non-metal).

Thus, in the first of two lessons the concept of “oxidation state” is formed, and in the second the formation of an ionic compound is explained. New concepts will serve as a good basis for further study of theoretical material, namely: the mechanisms of chemical bond formation, the dependence of the properties of substances on their composition and structure, and consideration of redox reactions.

In conclusion, I want to compare two methodological techniques: the technique of paradox and the technique of creating problem situations in the classroom.

A paradoxical situation is created logically in the course of studying new material. Its main advantage is strong emotions and surprise among students. Surprise is a powerful impetus to thinking in general. It “turns on” involuntary attention, activates thinking, forces you to explore and find ways to solve the issue that has arisen.

Colleagues will probably object: creating a problematic situation in class leads to the same thing. It does, but not always! As a rule, a problematic question is formulated by the teacher before studying new material and does not stimulate all students to work. It remains unclear to many where this problem came from and why, in fact, it needs a solution. The paradox technique is created in the course of studying new material and encourages students to formulate the problem themselves, and therefore understand the origins of its occurrence and the need for a solution.

I dare to say that the use of paradox is the most successful way to enhance student activity in the classroom, develop their research skills and creative abilities.