XIX International Physics Olympiad

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XIX
International Physics Olympiad

Doctor of Pedagogical Sciences
O. F. KABARDIN,
Candidate of Pedagogical Sciences
V. A. ORLOV

This year, the International Physics Olympiad for Schoolchildren was held from June 23 to July 2 in the city of Bad Ischl (Austria). The number of pages of the Olympiad increases daily (this year by two countries). Schoolchildren from 27 countries came to Austria: Australia, Australia, Belgium, Bulgaria, Great Britain, Hungary, Vietnam, East Germany, Iceland, Italy, Canada, Cyprus, China, Colombia, Cuba, Kuvet, Inderland, Norway, Poland, Romania, USSR, USA, Finland, Germany, Czechoslovakia, Sweden, Yugoslavia.

A representative of UNESCO and correspondents from magazines for schoolchildren from Belgium, Great Britain, Hungary, Yugoslavia, and Czechoslovakia took part in the Olympiad. It’s a pity that there was no representative of the magazine «Kvant» at the Olympics.*

The USSR team, based on the results of performance at the All-Union Olympiads and the results of winter and summer training camps, included:

Yuri Kravchenko is a graduate of the secondary school. No. 820 Moscow,
Alexander Mazurenko - graduate of the secondary school. No. 50 Minsk,
Anton Malkin is a graduate of S.S. No. 30 Leningrad,
Vadim Moroz is a graduate of Physics School No. 45 in Leningrad,
Konstantin Penenen - graduate of the secondary school. No. 63, Odessa.

*) The editors also keep this in mind. We can only hope that our regret is shared by the recently created USSR State Committee for Public Education. (Note ped.).

We also note that all participants in the summer camp, including Dmitry Golovin, a graduate of the S.S. No. 29 Tambov, Sergei Panafidin - graduate of the northern school. No. 30 of Leningrad and Alexei Pushkin - a graduate of the Northern School. No. 57 in Moscow, enrolled without exams in the universities of their choice - MIPT, MSU, LSU.

The team leaders were the authors of this article - research associates of the Research Institute of Content and Methods of Teaching of the Academy of Pedagogical Sciences of the USSR.

The grand opening of the Olympiad took place in the building of the Higher School of Personnel Training in the Field of Tourism. The schoolchildren were led by the director of this school, Master R. Ginzel, the mayor of Bad Ischl, K. Saller, the representative of the International Commission, Professor of the Vienna Technical University P. Skalitsky, and the head of the section of the Ministry of Education, Art and Sports, Master L. Leitner. Professor of the University of Vienna R. Dobrozemsky read a bright report on the topic “Physics in Australia”, from which it clearly followed that Australia gave the world not only brilliant artists, musicians, poses, but also no less brilliant physicists: H. Doppler, I. Loschmidt, L. Boltzmann, W. Hecca, E. Schrödinger, W. Pauli, E. Mach (“Mach cone” was used as an emblem Olympics).

The competition took place, as always, in two rounds. At the theoretical round, schoolchildren were given three tasks, and at the experimental round, two tasks (they were given 5 hours to complete each task). Here are the conditions for these tasks.

Theoretical tour

Task 1. Determining speed using effective data.

The processes of emission and absorption of photons are reversible, therefore, even after the process of absorption of a photon by an atom, its spontaneous emission (fluorescence) can be observed. This phenomenon is used in modern methods of particle detection and identification, as well as for spectrosynthesis of atomic particle velocities.

In an ideal experimental setup (Fig. 1), particles (singlely initiated ions) move with speed v against the beam

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Fig. 1.
laser with variable wavelength $\lambda$. Rest particles ($v=0$) can be excited by radiation with a wavelength $\lambda_0=600$ nm. Particle movements, in accordance with the Doppler principle, are excited by radiation with a different particle, therefore, to excite them, the laser must be tuned to a different wavelength $\lambda(v)$. The spectrum of ion velocities in the range from $v_1=0$ to $v_2=6000$ m/s is shown in figure 2.

1. Using the classical Doppler effect, determine in what wavelength range the laser radiation must be in order to excite all particles. Imagine the qualitative distribution of the number of absorbed photons depending on the laser wavelength.

Vollee strict calculation requires the use of a relativistic formula

$$v' = v \sqrt{\frac{1+v/c}{1-v/c}}.$$

Estimate the error when using the classical approximation.

2. Let the ions, before their excitation, be accelerated by an electric field with a voltage $U$. What is the dependence of the width of the velocity spectrum $\Delta v$ on the accelerating voltage $U$? Does the width of the particle velocity spectrum increase or decrease as a result of their acceleration?

3. An ion with a charge to mass ratio of $e/m = 4 \cdot 10^6$ C/kg has two excitation wavelengths $\lambda_1=600$ nm and $\lambda_2=\lambda_1+10^{-3}$ nm. Show that the two wavelength integrals of the laser spectrum overlap when all ions are excited. Is it possible to separate the excitation spectra of two levels as a result of the acceleration of ions in an electric field with a potential difference $U$? If yes, then determine the minimum voltage value.

Task 2. Maxwell’s disk
A homogeneous cylindrical disk (mass $M=0,40$ kg, radius $R=0,060$ m, thickness $d=0,010$ m) is suspended on two threads of equal length attached to its axis (radius $r$). The mass and thickness of the threads, as well as the mass of the axle, can be transformed. By lifting the center of gravity of the disk, winding the threads to a height of $H=1,0$ m, the disk is allowed to lower (Fig. 3). Accessible in the lowest position, the disc begins to rise again. Answer the following questions, assuming for simplicity that point $A$ is always on the same vertical as point $P$ (Fig. 4).

1. What angular velocity does the disk develop?

Fig. 2.
after its center of gravity passes the path $s$?

2. What kinetic energy of translational motion does the disk have after its center of gravity passes a distance $s=0,50$ m? What is the relationship between this energy and other types of energy if the radius of the axis is $r=0,0030$ m?

3. What is the tension force in each of the two threads as the disk is lowered?

4. Find the angular velocity of the disk as it rises as a function of the rotation angle $\varphi$ (Fig. 5). Establish, at least qualitatively, the displacement and velocity components of the center of gravity of the disk in a Cartesian coordinate system as a function of the angle $\varphi$.

5. The minimum value of the tension force at which the thread breaks is $T_{\min}=10$ N. What is the maximum height of lowering of the disk at which the thread will not break while the disk is rising?

Task 3. Recombination process in a gas discharge
In the high-temperature plasma of a gas discharge there are $(Z-1)$-fold initized notes of atoms containing $Z$ protons in the nucleus. Let us denote such atoms $A^{(Z-1)}$.

1. Let us consider the case when the only electron in the atom $A^{(Z-1)}$ is in the ground state. In this state, we define the average squared distance $r_0^2$ of the electron from the nucleus as the sum of the squared uncertainties of its coordinates $(\Delta x)^2, (\Delta y)^2$ and $(\Delta z)^2$. We define the mean square of the momentum $P_0^2$ electron as the sum of the squared uncertainties of the projections of the momentum onto the coordinates of the axis $(\Delta P_x)^2, (\Delta P_y)^2$ and $(\Delta P_z)^2$. What inequality does the product $(P_0^2) \cdot (r_0^2)$ satisfy?

2. The $A^{(Z-1)}$ ion can capture a second electron and at the same time emit a photon. Write down the equations that determine the frequency of this radiation. (The calculated frequency product is not needed.)

3. Calculate the internal energy $A^{(-1)}$ based on the fact that in the ground state it has a minimum value. Make the following approximations: a) use the value $r=r_0$ from question 1 in the expression for the electron’s potential energy; b) uses the mean square of momentum $P_0^2$ from the approximation $(P_0^2) \cdot (r^2)=\hbar^2$ in the expression for kinetic energy.

4. Calculate in a similar way the energy of the system $A^{(-2)}$ resulting from re

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Fig. 6.

Fig. 7.

Fig. 8.

cilial hole*, from which they cannot exit in the normal way (Fig. 7) even when a direction is applied to the metal (Fig. 8). However, if the metal is heated, then the electrodes, due to their thermal movement, can overcome the energy threshold $W$ and leave the cadan. The number of electrons released per unit time depends only on the materials of the cadan and its temperature. The direction of $U$ determines whether all electrodes reach the anode or not. For a given kadan, the dependence of the saturation current on temperature is shown in figure 9. For the saturation current (the charge carried away by electrons per unit time), the Richardson equation is valid:

$$I_H = CT^2 \cdot \exp(-W/kT),$$

where $W$ is the electron work function, $C$ is a constant, $T$ is the Cadan temperature on the Kelvin scale, $k$ is Boltzmann’s constant.

The task is to change the work function of the $W$ electron from a given material. To do this, you are provided with the following devices: an AZ41 electronic tube (a two-hand vacuum rectifier tube with a knurled direction of no more than 4 V), a universal electronic measuring device (its internal resistance when the voltage changes is 10 MΩ), a 1.5 V battery, 4 9 V batteries (batteries can be contained in series), three resistors, the resistance of which can be determined by colored stripes (the resistance of the resistors is 1000 Ohm ± 2 %, 100 Ohm±2% and 47.5 Ohm±1%), 4 resistors of about 1 Ohm each (they are numbered), 12 screw terminals, 6 connected wires about 20 cm long each, 2 plug connections (suitable for a 9V battery), screwdriver, logarithmic paper, graph paper.

A graph of the resistivity of kadan materials versus the kadan temperature is shown in figure 10. The room temperature is known.

1. Determine the resistance values ​​of the numbered resistors. Do not use an ohmmeter.

2. Determine the saturation current at different incandescent temperatures, i.e., at different incandescents. Use a 1.5 V battery for the nakadaba current and control it using numbered resistors. By saturation current you should remember the current that is obtained by constantly pumping 36-40 V between the anomer and the cathode. Create this arrangement using four 9V batteries in series. Briefly explain how you determined the temperature of the pot.

3. Determine the work function $W$ from equation (*). Explain how you did it.

Further, a simple look at the conditions of the problem shows that all the tasks, in their content, significantly go beyond the scope of the basic physics course program in our secondary school, and in a number of problems, beyond the scope of the elective course program (advanced level). For-

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malbio the authors of the problems “obeying the letter of the law,” since the topics of all problems are outlined in the program of the International Physics Olympiad, adopted by the International Commission in 1985 *). But the depth of interpretation of the topic outlined in the program can be any. The line in the program “Polarization of electromagnetic waves” corresponded to an experimental task, the successful implementation of which required a deep understanding of the phenomenon of polarization, birefringence, the phenomenon of integration of polarized light, and the existence of the phenomenon of elliptical polarization. Two words from the program - “Uncertainty relation” - allowed the author to include quantum mechanical problems both in theory and in experiment. The situation is similar with the interpretation of the words of the “Doppler Effect” program. This, of course, needs to be taken into account by schoolchildren and their teachers when preparing for subsequent Olympiads.

How did our schoolchildren cope with the proposed tasks?

The Soviet team scored 41 points out of 50 for the first problem (each problem in the theoretical and experimental rounds of evaluation is worth 10 points), for the second - 43 points, for the third - 25.5 points, for the fourth - 14 points, for the fifth - 32.13 points. Comparing these scores with the scores of other teams, we can conclude that the result for the first two problems is good, and for the fifth - absolutely the best. Our guys did a little worse on the third theoretical and first experimental tasks (for example, the Romanian team managed to score 39.5 points for the third task, and the Polish team received the maximum number of points - 23.5 - for the fourth task).

In terms of total points (155.63), the USSR team was second after the Romanian team (166.75). Teams

*) This program was published in the book by O. F. Kabardin and V. A. Orlov “International Physics Olympiads for Schoolchildren” (M.: Nauka, 1985, series “Viblotechka «Kvant»”).

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urban, republican and even weighty. When preparing for international optimids, adaptation to new conditions, “new rules of the game” is necessary, additional new knowledge is needed. At the same time, an important role is played by the dynamics of the student’s progress in learning new material, his rapid adaptation to the new requirements imposed on international optimids: the ability to present a concise and complete solution to a problem, the ability to “unravel” the “scoring” of a problem pre-compiled by the authors, etc. (A striking example of the “successful” dynamics of the conditions of a new one was shown at one time by Ruslan Sharipov from the village of Karakul, Bukhara region, who before the start of the training camp had seen little physical equipment and in many performance was inferior to the rest of the team. However, in one month he managed to gain technical knowledge and take absolute first place at the X International Optimide in 1977.)

Probably, it is a mandatory condition for all future candidates for the USSR team to be familiar with the tasks of the All-Union and International Optimids of the procedure at the winter selection camp by a special test of 120-150 tasks with the choice of the correct answer. These tasks are used and offered at the All-Union and International Optimids. An analysis of such a “legacy” of an MFO can be carried out, for example, to identify task topics that have not yet been used and thereby predict the possibility of the content of future tasks. Sometimes it was actually possible to do this.

(For the ending see p. 71)