Entertaining tops. Experiments, competitions, production

respectively, from units to hundreds of cm -1 (h is Planck’s constant, c is the speed of light). Purely rotational Raman spectra are observed when molecules are irradiated with visible or UV radiation with a frequency v0; the corresponding wavenumber differences, measured from the Rayleigh scattering line, have the same values ​​as the wavenumbers in the purely rotational spectra of the IR and microwave ranges. When the electronic and vibrational states of molecules change, the rotational states always change, which leads to the appearance of the so-called rotational structure of the electronic and vibrational spectra in the UV, IR regions and in the vibrational-rotational Raman spectra.

For an approximate description of the rotational motion of a molecule, one can adopt a model of rigidly coupled point masses, i.e. atomic nuclei, the sizes of which are negligible compared to the molecule itself. The mass of electrons can be neglected. In classical mechanics, the rotation of a rigid body is characterized by the main moments of inertia IA, IB, IC about three mutually perpendicular principal axes intersecting at the center of mass. Each moment of inertia, where mi is the point mass, ri is its distance from the axis of rotation.

The total angular momentum G is related to the projections of the moment onto the main axes by the relation:

The rotational energy EUR, which is kinetic energy (Tvr), is generally expressed through the projections of the total angular momentum and the main moments of inertia by the relation:

According to quantum mechanical concepts, the angular momentum of a molecule can only take on certain discrete values. The quantization conditions have the form:

where Gz is the projection of the moment onto some selected z axis; J = 0, 1, 2, 3, ... - rotational quantum number; K is a quantum number that takes on each J(2J + 1) values: 0, ± 1, ±2, ±3, ... ±J.

The expressions for EUR are different for the four main types of molecules:

1) linear, for example, O-C-O, H=C N, H-C C-H; a special case is diatomic molecules, for example N2, HC1;

2) molecules of the spherical top type, for example, CC14, SF6;

3) molecules like a symmetrical top, for example. NH3, CH3C1, C6H6; 4) molecules like an asymmetric top, for example, H2O, CH2C12.

4.1 Types of rotational spectra

Linear molecules. For them, Eur = G2/2IB, since in this case one of the main moments of inertia is zero, and the other two - for rotation about the axes perpendicular to the axis of the molecule - are equal to each other (denoted IB). Such molecules are described by a model of the so-called rigid rotator - a material point with mass m, rotating

along a circle of radius r. In the quantum mechanical description, where F(J) = Eвp/hc (in cm -1) is the rotational term,

B is the rotational molecular constant. In the special case of a diatomic molecule

where r is the distance between atomic nuclei with masses m1 and m2, = m1m2/(m1 + m2) is the reduced mass. Typically, molecules are characterized by equilibrium values ​​of the parameters r (denoted by re IB and B, corresponding to the minimum potential energy; in practice, parameters slightly different from the equilibrium ones are determined from rotational spectra. Figure 5 shows the system of rotational terms of a diatomic molecule.

If a linear molecule is polar, i.e. has a non-zero electric dipole moment (for example, HC1, HCN), transitions between neighboring terms are possible, for which = 1. Microwave rotational spectra of linear molecules (Figures 8a and 9) are a series of approximately equally spaced lines; the general expression for their wave numbers with the specified selection rule has the form:

Raman spectra are formed by transitions for which = 2 (Figure 8 b). In this case

• = B(4J + 6), (25)

moreover, J, as in the case of absorption spectra, refers to the lower of the two levels between which the transition occurs. Such spectra are characteristic of both polar and nonpolar molecules. Thus, from the distance between the lines of the rotational spectra, equal to 2B in absorption spectra, and 4B in Raman spectra, B, IB and rotational terms are determined. For diatomic molecules, the internuclear distance is found from the IB values. In the case of polyatomic molecules, the rotational spectra of the isotopic species of the molecule are examined to determine all internuclear distances. In this case, to a good approximation, it is believed that during isotopic substitution, only the masses of the nuclei and, consequently, the values ​​of IB and B change, and the internuclear distances remain unchanged.

Figure 8 - Rotational terms of a diatomic molecule, as well as schemes for the formation of purely rotational absorption spectra (a) and Raman spectra (b)

Figure 9 - Rotational absorption spectrum of the HCl molecule. The corresponding quantum number J of the level from which the transition occurs is indicated above the peaks.

Real molecules are not rigid systems; when they rotate, in particular, centrifugal distortion of the structure occurs. The intensity of the lines of rotational spectra is determined by the probability of quantum transitions (depending on the wave functions of states and electric moment operators) and the population of states, i.e. fractions NJ of molecules in a given state relative to the total number of molecules N0. If, when considering the wave functions of states, we take into account the influence of nuclear spins, then it turns out to be possible to explain the features of the rotational Raman spectra of centrosymmetric linear molecules (H2, O2, CO2). If the nuclear spin is zero, every second rotational level cannot be occupied, for example, in the O2 molecule - every level with an even J, and the spectrum will not have half (every other) lines. When the nuclear spin is not equal to zero, alternating intensities of the lines of the Raman spectra are observed. For example, in the case of H2 (proton spin is 1/2), the ratio of the intensities of “even” to “odd” lines is 1:3, which corresponds to the ratio of para- and ortho-modifications of H2.

Molecules like a spherical top. In such molecules all the main moments of inertia are the same (denoted IB); the expressions for Eur in the classical theory and in the quantum mechanical description are the same as for linear molecules. However, molecules of the type under consideration do not have purely rotational spectra, since they are isotropic (have a spheroid of polarizability) and do not have a dipole moment. In this case, transitions between rotational terms are prohibited both in the absorption and Raman spectra. However, the corresponding molecular parameters can be obtained by studying the rotational structure of the vibrational and electronic spectra of substances in the gas phase.

Molecules like a symmetrical top. In such molecules, one main moment of inertia differs from the other two, which are equal to each other: (an extreme special case is linear molecules). The expression for the rotation term is:

where is the rotational constant.

An elongated symmetrical top is distinguished when IA< IB = IC, и сплюснутый, когда IA >IB = IC In the first case (A - B) > O, i.e., for a given J, as the absolute value of Kv increases, the energy of the levels increases, and in the second case (A - B)< О и энергия с ростом K2 уменьшается. Поскольку по правилам отбора для таких молекул переходы возможны только без изменения квантового числа К, то из вращательных спектров определяется лишь одна вращательная постоянная В и момент инерции IB = IC, а для определения IA и геометрических параметров необходимы дополнительные данные, например, по изотопно-замещенным молекулам.

Molecules like an asymmetric top. In this case, all moments of inertia are different, there is no exact analytical expression for the rotation term as a function of quantum numbers, and the system of energy levels can be represented as something intermediate between the cases of elongated and oblate symmetrical tops. The complexity of the system of levels and selection rules also leads to a complication of the observed rotational spectra. Nevertheless, for a number of molecules of the type under consideration, for example, SO2, CH2C12, ethylene oxide and others, a complete analysis of the rotational spectra was carried out and bond lengths and bond angles were determined.

4.2 Meaning and application

Rotational spectra are highly individual, which makes it possible to identify specific molecules (conformations, isotopic species, etc.) using several lines. It is from rotational spectra that the existence of free molecules in interstellar space is discovered. From the fine structure of rotational spectra caused by vibrational-rotational interactions, it is possible to determine the potential functions of internal rotation, inversion and other types of intramolecular motions with large amplitudes. Modern technology (optical-microwave double resonance using lasers) makes it possible to observe purely rotational transitions in highly excited (electronic and vibrational) states of molecules, i.e. study the properties of molecules in these states using rotational spectra. Studying the parameters of spectral lines (broadening, frequency shift) provides information about intermolecular interactions.

When an external electric or magnetic field is applied, the rotational energy levels of molecules are split; Accordingly, the rules for selection and rotational spectra become more complicated. It becomes possible to obtain additional information, in particular about electric dipole and quadrupole moments, magnetic moments and anisotropy of the magnetic susceptibility of molecules. The rotational spectra of paramagnetic molecules can be observed selectively in a mixture with other molecules.

Molecular constants determined from rotational spectra make it possible to find the rotational sum (sum over states) Qrev - one of the main components of the total sum over states, which is necessary for calculating the thermodynamic functions of substances and the equilibrium constants of chemical reactions in the gas phase.

High-resolution spectrometers make it possible to measure very fine splittings of the rotational spectra of molecules and determine molecular parameters with high accuracy. Thus, bond lengths are found from rotational spectra with an accuracy of thousandths of a nm, bond angles - to tenths of a degree. Microwave spectroscopy, along with gas electron diffraction, is the main method for studying the geometry of molecules. Laser Raman spectroscopy and Fourier transform spectroscopy are also increasingly used for these purposes.

5 TYPES OF GOPS

As a molecular model, we will choose a system of interconnected particles (effective atoms). These particles are point masses connected by weightless springs and must have certain electrical properties, for example, they must carry a certain charge, be polarized under the influence of an external electric field, and have nuclear spin. then the entire system of particles (molecule) could have a constant dipole moment or acquire a variable dipole moment under the influence of the field. We will conventionally call such particles “atoms”.

To simplify the problem, we consider rotation separately from oscillations. In addition, we will consider a rotating molecule to be a rigid body, that is, a body in which the distances between the atoms do not change. This means that the springs connecting all point masses will be considered rigid, not allowing a change in the distance between the atoms. Therefore, the potential energy of the system can be taken equal to zero. This is the rigid rotator model.

The rotation of a three-dimensional body can be very complex, and it is convenient to decompose it into components in three mutually perpendicular directions passing through the center of gravity. - main axes of rotation. Accordingly, the body has three main moments of inertia, one about each axis, denoted as In accordance with this, all molecules can be divided into groups, which is equivalent to classifying molecules by shape.

Linear tops. All atoms in such molecules are located along a straight line, for example, an HCl or OCS molecule:

Three directions of rotation can be chosen as follows: a - around the direction of the bond, b - rotation of the ends of the molecule in the plane of the sheet, c - rotation of the ends of the molecule perpendicular to this plane. It is obvious that a relative to the a axis the moment is very small, i.e.

Symmetrical tops. Consider a molecule like methyl fluoride, in which three hydrogen atoms are tetrahedrally bonded to a carbon atom. The rotation of the ends of the molecule in the plane of the page and perpendicular to it are identical and the moment of inertia relative to the direction C-F connections(which is chosen as the main axis of rotation, since the center of gravity is located on it) cannot be neglected in this case due to the contribution from the rotation of three hydrogen atoms located outside this axis. A molecule rotating around a given axis looks like a top, hence the name. So, for a symmetrical top

This group includes two subgroups:

This is an elongated symmetrical top,

This is a flattened symmetrical top.

Spherical tops. If all three moments of inertia of a molecule are equal, then it belongs to spherical tops, for example, a tetrahedral methane molecule. .

Due to their symmetry, these molecules do not have, and rotation itself does not lead to changes in the dipole moment, so a rotational spectrum is not observed for them.

Asymmetrical tops. For such molecules, all three moments of inertia are different:

A simple example is a water molecule - .

LIST OF USED SOURCES OF LITERATURE

1. “Atomic and molecular spectroscopy” M., Elyashevich 1969

2. “Electronic spectra in organic chemistry” 2nd ed., Sverdlova O.V., 1985

3. “Vibrational spectra of polyatomic molecules” M., Sverdlov L.M., Kovner M.A., Krainev E.P., 1970

4. “Vibrations of molecules” 2nd ed., M. Yu. A. Peptin, 1972

5. “Vibrational and rotational spectra of polyatomic molecules” trans. from English, M., Yu. A. Pentin, 1949

6. http://www.femto.com.ua/articles/part_1/2342.html

Short description

A molecule is a microparticle formed from two or more atoms and capable of independent existence. It has a constant composition, atomic nuclei included in it and a fixed number of electrons and has a set of properties that make it possible to distinguish one molecule from others, including from molecules of the same composition. A molecule as a system consisting of interacting electrons and nuclei can be in different states and move from one state to another forcedly (under the influence of external influences) or spontaneously.
The theory of vibrations and rotation of polyatomic molecules comes from considering the energy of vibrations and rotation of the molecule as one of the parts total energy molecules.

Table of contents

Introduction 3
1 Place of rotation in the energetics of types of molecular motion 5
1.1 Molecular spectra 5
2 Electronic spectra 8
2.1 Classification of electronic states 9
2.2 Selection rules 10
2.3 Vibrational structure of electronic spectra 11
2.4 Absorption spectra 12
2.5 Emission spectra 14
2.6 Application of electronic spectra 14
2.7 Vibrational structure of electronic spectra 15
2.8 Rotational structure of electronic spectra 19
3 Vibrational spectra 21
3.1 Interpretation and application 24
3.2 Rotational structure of vibrational spectra 26
4 Rotational spectra 28
4.1 Types of rotational spectra 29
4.2 Meaning and application 33
5 Types of tops 35
List of references used

A symmetrical top will be a molecule in which two main moments of inertia are equal ( I B = I C for an elongated top or I A = I B for a flattened top). The third moment of inertia is not zero and does not coincide with the other two. An example of an elongated symmetrical top is the methyl fluoride molecule FCH 3, in which three hydrogen atoms are tetrahedrally bonded to the carbon atom, and the fluorine atom is at a greater distance than the hydrogen from the carbon atom. Rotation of such a molecule around the C axis – F (the axis of symmetry of the molecule) differs from rotation around the other two axes perpendicular to this one. The moments of inertia about the other two axes are equal I B= I C. Moment of inertia relative to the direction of connection C – F( I A) although small, it cannot be neglected. Contribution to the rotation around this axis (it coincides with the symmetry axis of the molecule) is made by three hydrogen atoms located outside this axis.

The energy levels of a symmetrical top can be found through the squares of the corresponding angular momentum

For a symmetrical elongated top Ix= I y, A Iz< Iy. Axis Z coincides with the axis of the smallest moment of inertia

Formula (2.40) can be rewritten as follows:

in formula (2.40) we added and subtracted the expression ). The first term of expression (2.41) includes the square of the total moment p 2, which is quantized and equal B.J.(J+ 1) (see 2.2), and the second term includes the projection of the squared moment onto the axis Z, which is the axis of symmetry of the top. Moment projection P z quantizes and takes on values P z= ћk. Thus, the quantized expression for the rotation energy will have the form:

Introducing rotational constants, we obtain

(A>B), (2.43)

(J= 0, 1, 2, ...; k= 0, ±1, ±2, ...).

For the case of a flattened top, the axis Z is the axis of the greatest moment of inertia I C and given that I A =I B, we can write

, (C<B) (2.44)

(J= 0, 1, 2, ...; k= 0, ±1, ±2, ...).

In these formulas the rotational constant B corresponds to the moment of inertia about the axes perpendicular to the axis of symmetry.

What values ​​can the quantities take? k And J. According to the laws of quantum mechanics, both quantities can be equal to either an integer or zero. The total moment of inertia of a molecule (quantum number J) can be quite large, i.e. J can take values ​​from 0, 1, 2,..., ¥. However, infinitely large J difficult to achieve, since a real molecule at a high rotation speed can break into pieces. If the value J selected, then to the number k restrictions are immediately imposed: k cannot exceed J because J characterizes the total moment. Let J= 2, then for k values ​​can be realized k= 2, 1, 0, –1, –2. The more energy is required for rotation around an axis perpendicular to the axis of symmetry, the less k. Since energy depends quadratically on k, That k can also take negative values. From visual representations of positive and negative values k rotation can be correlated clockwise and counterclockwise relative to the axis of symmetry.

Thus, for a given value J the following values ​​can be realized k:

k = J, J– 1, J– 2, ..., 0, ... ,– (j– 1) ,–J,

i.e. only 2 J+ 1 values.

The first term in formulas (2.43) and (2.44) coincides with the energy expression (2.16) for a linear molecule ( k squared is included in formulas (2.43) and (2.44)).

Each rotational energy level with a given value J with degeneracy factor 2 J+ 1 splits into J+ 1 component in relation to absolute value | k|, which takes values ​​from 0 to J. Since energy depends on k 2, then for the quantity k indicate its absolute value. Degree of degeneracy of levels with given values J And k equals 2(2 J+ 1), and levels with a given value J and with k= 0 equals 2 J+ 1. For levels k = 0only the degeneracy associated with the independence of energy from the quantum number is preserved m J, receiving 2 J+ 1 values. Other levels ( k¹ 0) are doubly degenerate with respect to k.

Distance between levels with different k(for a given J) depends for an elongated top on the value A – B, and for a flattened top from the value WITH – IN, i.e., the greater the difference, the greater the difference between the corresponding moments of inertia. For an elongated top, the higher the energy levels ( A – B> 0), and for a flattened top the levels are located lower, the more k (C – B< 0). In Fig. Figure 2.11 shows the location of the rotational energy levels and transitions between them for an elongated top with k from 0 to 3 ( IN = WITH= 1.0 cm –1, A= 1.5 cm –1 , left side of the figure) and for a flattened top (B = A = 1.5 cm –1 , C = 1.0 cm –1 right side of the figure). Between them the energy levels of the asymmetric top are marked (A = 1.5 cm–1, B = 1.25 cm–1, C = 1.0 cm–1).

In the example considered, the rotational constants do not differ very much from each other, therefore, for a given J levels with different k close to each other. When there is a large difference in the moments of inertia, which is often the case for real molecules, the normal order of levels with different J may be violated. For example, for an elongated top, level c J= 3, k= 0, will lie below level c J= 2, k= 2.

To obtain the IR absorption spectrum of a symmetric rotator, it is necessary to know the selection rules for quantum numbers J And k. Calculations show that for dipole absorption and emission D J= ±1 (selection rule similar to that for a diatomic molecule) and D k = 0. Last relation for D k=0 means that during transitions the projection of the angular momentum onto the axis of the top should not change. This is true for both absorption and emission spectra and Raman spectra. In Fig. 2.11, arrows indicate transitions in absorption and emission.

The position of the lines of purely rotational spectra can be determined if, using formula (2.43) or (2.44), we take the energy difference E VR between adjacent levels

For IR absorption D J = 1, J"= J""+1,J"= J"", That

Thus, in absorption and emission a series of equally spaced lines is obtained, analogous to a current, as was the case for a diatomic molecule.

For the CD, possible transitions are determined by the following selection rules

D J= ±1, ±2, (2.46)

what gives (with J" = J""+ 1,J" = J""+ 2, J" = J)the following series of lines

at D J= 2 (J= 1, 2, ...) and

at D J= 1 (J = 1, 2, 3, ...).

In the latter case, the transition J""= 0 ® J"= 1 is prohibited by additional selection rules. Indeed, the selection rules D k= 0, means that the change in angular momentum for rotation around the axis of symmetry ( k– rotational quantum number for axial rotation) does not lead to a change in polarizability, i.e., during this rotation there is no Raman spectrum. Availability for states with k= 0 only transitions from D J= ±2 means that in transitions D J= ±1 the ground state cannot participate ( J= 0). For all non-zeros J number k may be non-zero and transitions D J= ±1 are allowed.

Thus, in the Raman spectrum we obtain two series of lines, one of which (2.48) coincides with a similar series for a diatomic molecule (), and, accordingly, a second series (the lines of which are located twice as often as the lines of the first series. The lines of the second series coincide every other with lines of the first series, which leads to an alternation of intensities. This alternation should not be confused with the alternation of intensities due to nuclear spin.

As we see, formulas (2.43 and 2.44) imply that they contain only one rotational constant IN. Therefore, from the distance between the rotational lines of a molecule such as a symmetrical top, one can determine the moment of inertia relative to the axes perpendicular to the axis of symmetry of the top. Moment of inertia relative to the axis of symmetry of the elongated object (constant A) or oblate (constant WITH) the top cannot be determined. An example of molecules that have characteristic rotational absorption spectra and which are modeled by symmetrical tops are the molecules NH 3, PH 3, etc.

It is necessary to take into account that the resulting formulas (2.43 and 2.44) are approximate and do not take into account changes in the spectra that occur as a result of centrifugal stretching. For a symmetrical top, centrifugal stretching depends not only on the quantum number J, but also from the number k. When taking centrifugal tension into account in formulas (2.43) and (2.44), terms of the fourth order are added with respect to J And k. In formulas (2.43) and (2.44) terms appear that depend on [ J (J+ 1)] 2 , from k 4 and from J (J+ 1) k 2. Taking these terms into account for the rotational energy of a symmetrical elongated top, we obtain the formula

Permanent D J, Dk And D J,k too small compared to IN, A And WITH. At IR absorption (D J= 1, D k) for possible transitions we have the formula

The second term in the formula causes only a slight change in the distances between the lines, the last term depending on k, causes line splitting J® J+ 1 on J+ 1 components corresponding to the values k from 0 to J. To estimate the values ​​of constants D J And D J,k Let us present their values ​​obtained by Gordy for the methyl fluoride molecule FCH 3: IN= 0.851 cm –1 D J = 2.00×10 –6 cm –1 , D J,k= 1.47 ×10 –5 cm –1.

Although D J,k is small (10 –4 ¸ 10 –6 V), the specified splitting can be observed for rotational lines due to the high resolution of the modern spectrometers used.

2.3.4. Energy levels and spectra of molecules of type
asymmetrical top

To obtain a picture of the location of the energy levels of an asymmetric top, it is necessary to consider the energy levels of tops close to the two simplest extreme cases - an elongated and flattened symmetric top. The general expression for rotational energy is:

In the case of an asymmetric top, all three are constants ( A, IN And WITH) are different. If we arrange them in descending order, then A> B> C(For I A<I B< I C). An elongated symmetrical top corresponds to the case when IN = WITH, and oblate – when A = IN. Different meanings IN in the interval between A And WITH correspond to varying degrees of asymmetry of the top. If IN differs from A And WITH by a small amount, then the top can be called slightly asymmetrical. Rice. 2.11 shows the change in energy levels when changing IN from WITH before A. The levels on the left correspond to an elongated symmetrical top ( IN = WITH), and the levels on the right are flattened ( IN = A). The presence of a slight asymmetry leads to a splitting of energy levels with opposite signs k (k – And k +). These levels are degenerate for symmetrical tops. Doubly degenerate levels of rotational energy of symmetric tops correspond to pairs of very close levels of asymmetric tops. The latter can be called components of doublet levels. In this case, the rotational levels of the oblate symmetric top correspond to the lower doublets of the asymmetric top, for which t< 0 (t = k ––k +), and the levels of an elongated symmetrical top are the upper doublets of an asymmetrical top, for which t ³ 0 (t.= – J, –J + 1, ..., +J). So the lowest level will be J–J, and the top one J+J. For the special case when A= 1.5 cm –1, IN= 1.25 cm –1, WITH= 1.0 cm –1 ( c= 0) the corresponding arrangement of levels is shown in Fig. 2.11 in the center. As we see, with increasing at characteristic is the proximity of the two lower levels and the two upper levels. For J= 2 lower level corresponds to level c k= 0 for an elongated top and level c k= 2 for a flattened top, i.e. denoted as 2 02. Index t equal to the difference k–1 and k 1 can be used to indicate the levels of an asymmetric top. For example, for levels J= 2 the symbols 2 02 = 2 –2, 2 12 = 2 –1, 2 11 = 2 0, 2 21 = 2 +1 and 2 20 = 2 +2 will be used.

In table Table 2.3 shows the rotational levels of the water molecule (H 2 O – A= 27.79 cm –1, IN=14.51 cm –1 . WITH= 9.29 cm –1), as the first case of interpretation of a rotational structure such as an asymmetric top.

Table 2.3

Energy values ​​of rotational levels of the H 2 O molecule, cm –1

Varieties

• Kubar- Russian version of the top trompo.
• Levitron- on a magnetic cushion.

There are also varieties of tops launched using a handle and a rope; their shapes and sizes are varied.

Top toys

There is a game reminiscent of billiards called Tyrolean roulette, in which a spinning top, placed in a plate-shaped form, throws the balls in different directions. These balls can fall into holes, each of which means a certain number of points to be awarded to the player.

In fine arts

In cinema and other human activities

• Volchok (2009) - Russian feature film, psychological drama by Vasily Sigarev.
• Inception - 2010 feature film, USA.
• What? Where? When? - an intellectual television program in which questions for experts are chosen by a spinning top with an arrow pointer.

see also

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Excerpt characterizing the Top (toy)

When Pierre returned home, he was given two Rastopchin posters that had been brought that day.
The first said that the rumor that Count Rostopchin was prohibited from leaving Moscow was unfair and that, on the contrary, Count Rostopchin was glad that ladies and merchant wives were leaving Moscow. “Less fear, less news,” the poster said, “but I answer with my life that there will be no villain in Moscow.” These words clearly showed Pierre for the first time that the French would be in Moscow. The second poster said that our main apartment was in Vyazma, that Count Wittschstein defeated the French, but that since many residents want to arm themselves, there are weapons prepared for them in the arsenal: sabers, pistols, guns, which residents can get at a cheap price. The tone of the posters was no longer as playful as in Chigirin’s previous conversations. Pierre thought about these posters. Obviously, that terrible thundercloud, which he called upon with all the strength of his soul and which at the same time aroused involuntary horror in him - obviously this cloud was approaching.

1. Energy layer
The new energy layer of Achilles's zetas has become larger in diameter than the previous version. Along the edges there are metal blades in the shape of a scythe. They add significant weight, and the peripheral location increases the centrifugal force of the bey's rotation.
On the left and right are the already familiar small blue wings, which open during battle, like Voltraek B5, and serve as a break blocker. But it is worth considering that this block only increases resistance to breaking, and does not completely eliminate it.
There are another pair of blue wings located symmetrically above and below. On the one hand, they slightly increase endurance during rotation. On the other hand, they smooth out the contour so that it is more difficult for attacking opponents to latch onto and “blow the roof off” the Super Z Achilles A5. In addition, any retractable elements absorb shock, which reduces rebound during collisions. Thanks to this, the beyblade will be more difficult to knock out of the arena;

2. Power disk
The new disc is truly new. It was designated by the number 00 (double zero). Previously, the zero disk was the heaviest of all, but now it has a competitor in terms of weight. If you surprise with a new beyblade, then surprise in everything, Takara Tomy decided;

3. Driver (tip)
The updated driver is called Dimension (Dm). In essence, this is a modified Xtend driver from the previous version of Achilles. It also has two basic modes (attack and defense) and also changes its height. However, it has changed in appearance and the mechanism for switching modes has become different. Inside there is a black rod on which rotation occurs. In the old system there was a ring on top that had to be pulled back and turned to set the desired mode. Now a third element has appeared. The ring itself has become geared for ease of rotation, and when turned, a small bushing comes out of it, in which the rod is hidden;

4. The kit also includes a left-right trigger.

A top is a children's toy that, when rotating around its axis, maintains a vertical position, and when the rotation slows down, it falls. In addition, when rotating a painted top, you can observe the optical effects of mixing and even decomposition of colors into components.

Materials:
Cardboard, paint, toothpicks or even better, skewers, glue (PVA) or plasticine.

Tops do not have to be made of cardboard; you can use thick paper or thin plastic. You can try to make a large top from a CD, or a top whose axis is a pencil or felt-tip pen - then you can see interesting traces of rotation.

Manufacturing process:
On cardboard or thick paper, draw several circles using a compass, approximately 5 cm in diameter. Color according to the diagrams and cut out. If the child does not yet use a compass, you can use a round glass or coffee cup as a template, the main thing is then to find the center. You can make one circle a template - find the center there by folding it in half and in half again, pierce the middle, and then apply it to the painted circles and transfer the center to them.

In the center of the circle, make a small hole with an awl (toothpicks break), into which a toothpick or cut wooden skewer (necessarily with a sharp end) is inserted. We fix the stick with PVA glue (it takes a long time to dry) or a piece of plasticine (it will be faster here).
It turned out to be a top.

These are the tops that we made from thick paper, drawing a pattern with watercolors and inserting toothpicks and skewers.

Experiments with color

The simplest top schemes are by sector. The circle is divided into an even number of sectors and painted, for example, yellow and blue or yellow and red. When rotating we will see green and orange respectively.
In this experience you can see how colors mix.
Here you can experiment with the number of color sectors.

If you divide the top into seven parts and paint them (very pale with watercolors) in accordance with the arrangement of colors in the spectrum, then when you rotate the top, it should turn white. We will observe the process of “collecting” colors, since white is a mixture of all colors.
This effect is difficult to achieve; my daughter and I didn’t succeed; apparently we painted the top (in the photo) very brightly. Maybe we didn’t get the white color, but we got a beautiful rainbow effect, and even with some kind of three-dimensionality.

The most interesting patterns come from spiral patterns. They look especially fascinating when the rotation of the toy slows down.

Explanation of what was seen: This optical illusion occurs because the brain mistakenly reproduces areas where black and white change as colors (first experience). As we said above, white is a mixture of all colors. Black is the absence of color. When the eye sees a blurry combination of black and white, it perceives it as color. The color depends on the proportion of white and black and on the rotation speed.
Explanation from the book: “Fun Experiments with Paper” by Stephen W. Moye

Interesting: The ability of a top to assume a vertical state when rotating is widely used in modern technology. There are various gyroscopic(based on the rotational property of the top) instruments - compasses, stabilizers and other useful devices that are installed on ships and airplanes. Such is the useful use of a seemingly simple toy.

Active games for children
Playing with tops not only contributes to the development of a child’s fine motor skills, but can also amuse and keep a group of children entertained at a party. We play and compete with children.

Competitions at children's parties:

• The players launch all the tops at the same time. Whose top spins the longest is the winner.
• Or organize obstacles on the table in the form of small objects - you need to try not to touch them or, on the contrary, knock them down, depending on the conditions.
• Draw a playing field with sectors. Each participant has his own sector, whose top flies out of the sector - he lost.
• Or also a game on the playing field: whose top knocks down the other tops and is left alone is the winner.