Municipal educational institution gymnasium No. 1
Central district of Volgograd
Physics lesson on the topic
Movement of molecules. Experimental determination of molecular speeds
Grade 10
Prepared by: highest category physics teacher
Petrukhina
Marina Anatolyevna.
UMK: N. S. Purysheva,
N. E. Vazheevskaya,
D. A. Isaev
“Physics - 10”, a workbook for this textbook and a multimedia application for the textbook.
Volgograd, 2015
Lesson on the topic
Movement of molecules.
Experimental determination of molecular speeds
Grade 10
annotation.
Understanding the most important issues of modern physics is impossible without some, at least the most elementary ideas about statistical laws. Consideration of a gas as a system consisting of a huge number of particles allows us to give in an accessible form an idea of the probability, statistical nature of the laws of such systems, statistical distributions indicating with what probability the particles of the system have one or another value of the parameters that determine their state, and Based on this, outline the main provisions of the classical theory of gases. One of the lessons that allows us to form this idea includes the presented lesson on the teaching materials of the Drofa publishing house: a physics textbook by N. S. Purysheva, N. E. Vazheevskaya, D. A. Isaev, a workbook for this textbook and a multimedia application for textbook.
Explanatory note.
This lesson can be taught while studying the topic “Fundamentals of MCT structure of matter” in 10th grade.
The new lesson material allows students to deepen their knowledge of the basics of the kinetic theory of gases and use it when solving problems to determine the velocities of molecules of various gases.
Each stage of the lesson is accompanied by a thematic slide of a multimedia application and a video fragment.
The purpose of the lesson:
Activity: the formation of new ways of activity in students (the ability to ask and answer effective questions; discussion of problem situations; the ability to evaluate their activities and their knowledge).
Lesson objectives:
Educational: developing the ability to analyze, compare, transfer knowledge to new situations, plan one’s activities when constructing an answer, completing tasks and searching activities through physical concepts (most probable speed, average speed, root mean square speed), and intensify the mental activity of students.
Educating: instilling discipline when performing group tasks, creating conditions for positive motivation when studying physics, using a variety of activity techniques, communicating interesting information; cultivate a sense of respect for the interlocutor, an individual culture of communication.
Developmental: develop the ability to construct independent statements in oral speech on the basis of learned educational material, develop logical thinking, develop the ability of a unified mathematical approach for a quantitative description of physical phenomena based on molecular concepts when solving problems.
Lesson type: lesson of learning new material.
Teaching methods: heuristic, explanatory - illustrative, problem-solving, demonstrations and practical tasks, solving problems of physical content.
Expected results:
be able to draw conclusions based on experiment;
develop rules of discussion and follow them;
understand the meaning of the issues being discussed and show interest in the topic.
Preparatory stage: knowledge of basic equations, dependencies on this topic (a theoretical block on the topic is available to each student in the form of a lecture-note)
Equipment: device for demonstrating Stern's experiment;
a computer and a projector for demonstrating the presentation and video clip “The Stern Experience”.
Lesson stages.
Organizational stage (greeting, checking readiness for the lesson, emotional mood), (1 minute)
Stage of goal setting, lesson objectives and problems about the method of measuring the speed of molecules, (4 minutes)
The stage of studying new educational material, showing presentation slides with student comments, which allows you to create a visual impression of the topic, activate visual memory (check the level of mastery of the system of concepts on this topic), (20 minutes)
The stage of consolidating acquired knowledge when solving problems (application of knowledge in practice and its secondary comprehension), (8 minutes)
Stage of generalization and summing up the lesson (analyze the success of mastering knowledge and methods of activity), (4 minutes)
Information about homework (aimed at further development of knowledge), (1 minute)
Reflection, (2 minutes)
Lesson script.
Activities of a physics teacher
Student activity
Organizational stage.
Hello guys! I am glad to welcome you to the lesson, where we will continue to open pages in the knowledge of the classical theory of gases. Interesting discoveries await us ahead. Greet each other.
Then let's get started...
Goal setting and motivation.
In the last lesson we became acquainted with the basic principles of the molecular kinetic theory of an ideal gas. Participating in continuous chaotic motion, molecules constantly collide with each other, while the number of colliding particles their speed are different at every moment of time.
What do you think the topic of the lesson “awaits” us today?
Yes, indeed, the goal that we set for ourselves today is to get acquainted with one of the methods for determining the speed of movement of molecules - the molecular beam method, proposed by the German physicist Otto Stern in 1920.
We opened our notebooks, wrote down the date and topic of today's lesson: Motion of molecules. Experimental determination of the velocities of molecular motion.
Let us remember what is the speed of thermal motion of molecules?
Let's calculate the speed of silver molecules Ag during evaporation from the surface, T = 1500K.
Let me remind you that the speed of sound is 330 m/s, and the speed of silver molecules is 588 m/s, compare.
Let's calculate the speed of hydrogen molecules H 2 at a temperature close to absolute zero T=28K.
For example: the speed of a passenger plane is 900 m/s, the speed of the Moon around the Earth is 1000 m/s.
Now put yourself in the place of scientists of the 19th century, when these data were obtained, doubts arose about the correctness of the kinetic theory itself. After all, it is known that odors spread rather slowly: it takes time on the order of tens of seconds for the smell of perfume spilled in one corner of the room to spread to another corner.
So the question arises: what is the actual speed of molecules?
When the scent of perfume spreads, is there anything interfering with the perfume molecules?
How does this affect the speed of directional movement of molecules?
Let's calculate the speed of hydrogen molecules H 2 at a temperature close to room temperature T=293K.
Then what is the speed? What?
But how to measure it, determine its value in practice? Let's solve the following problem:
Let there be 1 molecule. It is necessary to determine the free path speed of molecules. How do molecules move between collisions?
Let the molecule travel 1 meter, find the time at a hydrogen speed of 1911 m/s, it turns out to be 0.00052 s.
As you can see, the time is very short.
The problem arises again!
The stage of learning new educational material.
It is impossible to solve this problem in a school setting; Otto Stern (1888-1970) did it for us in 1920, replacing translational motion with rotational motion.
Let's watch a short video clip and then discuss some issues.
What was the installation used by O. Stern?
How was the experiment carried out?
The speed values were obtained close to the speed calculated by the formula:
, 
,
Where 
– linear speed of points on the surface of cylinder B.
, That
, which is in agreement with the molecular kinetic theory. The speed of the molecules coincides with the calculated one obtained on the basis of MCT, this was one of the confirmations of its validity.
From the experiment of O. Stern, it was found that at a temperature of 120 0 C the velocities of most silver atoms lie in the range from 500 m/s to 625 m/s. When the experimental conditions change, for example, the temperature of the substance from which the wire is made, other velocity values are obtained, but the nature of the distribution of atoms in the deposited layer does not change.
Why is the silver strip in Stern’s experiment displaced and blurred at the edges, and is also non-uniform in thickness?
What conclusion can be drawn about the velocity distribution of atoms and molecules?
Consider table No. 12 of the textbook on page 98 for nitrogen molecules. What can be seen from the table?
The English physicist D.C. Maxwell also considered it incredible that all molecules move at the same speed. In his opinion, at any given temperature, most molecules have speeds that lie within fairly narrow limits, but some molecules can move at higher or lower speeds. Moreover, the scientist believed, in every volume of gas at a given temperature there are molecules with both very low and very high velocities. Colliding with each other, some molecules increase speed, while others decrease. But if the gas is in a stationary state, then the number of molecules with one or another speed remains constant. Based on this idea, D. Maxwell investigated the question of the velocity distribution of molecules in a gas in a stationary state.
He established this dependence long before O. Stern’s experiments. The results of D. K. Maxwell's work received universal recognition, but were not confirmed experimentally. This was done by O. Stern.
Think about it? What is the merit of O. Stern?
Let's look at Fig. 64 on page 99 of the textbook and examine the nature of the distribution of molecules by speed.
The form of the molecular velocity distribution function, which D. Maxwell determined theoretically, qualitatively coincided with the profile of the deposit of silver atoms on a brass plate in O. Stern’s experiment.
Studying the profile of a silver strip allowed the scientist to conclude the existence most probable average speed movement of particles (i.e. the speed at which the largest number of molecules moves).
Where does the maximum of the distribution curve shift with increasing temperature?
In addition to the most probable and average speeds, the movement of molecules is characterized by the mean square of speed:
, and the square root of this value is the root mean square speed.
Let's look again at how cognition occurred when studying the question of the speed of movement of molecules?
The stage of consolidating acquired knowledge when solving problems.
Let's make mathematical calculations and test the theory in a specific situation.
Task No. 1
What speed did the silver vapor molecule have if its angular displacement in Stern’s experiment was 5.4º at a rotational speed of the device of 150 sˉ¹? The distance between the inner and outer cylinders is 2 cm.
Generalization stage and summing up the lesson
Today in class we learned about one of the methods for determining the speed of movement of molecules - the molecular beam method, proposed by the German physicist Otto Stern.
What is the significance of O. Stern’s experience in the development of ideas about the structure of matter?
Information about homework.
Reflection.
During our lesson, you showed yourself to be observant theorists, capable of not only noticing everything new and interesting around you, but also independently conducting scientific research.
Our lesson has come to an end.
Let's answer the question: “What did you like about the lesson?” and “What did you remember about the lesson?”
And in conclusion, I want to quote Virey’s words:
“All discoveries in the sciences and in philosophy often stem from generalizations or from applications of a fact to other similar facts.”
Thanks guys for working together. I was glad to meet you. See you!
Lesson topic: Determining the speed of movement of molecules.
(students write down the date and topic of the lesson in their notebooks)
(answers from several students)
, on the other side
knowing that 
, from here
, or 
, Where
– universal gas constant, 
8,31 
Speed of silver molecules supersonic.
590m/s, same!!! Can't be!
What speed should we find and measure?
Air molecules interfere.
It is decreasing.
We got high speed, and nothing prevents the molecules from moving?
Free path speed of molecules.
Evenly.
How to measure it?
(watch video)
The installation consisted of: a platinum thread coated with a thin layer of silver, which was located along the axis inside a cylinder with a radius 
and outer cylinder 
. The air is pumped out of the cylinder.
When an electric current was passed through the wire, it heated up to a temperature above the melting point of silver 961.9 0 C. The walls of the outer cylinder were cooled so that the silver molecules would better settle in the path of the screen. The installation was rotated at an angular speed of 2500 – 2700 rpm.
When the device was rotated, the strip of silver acquired a different appearance because if all the atoms flying out of the thread had the same speed, then the image of the slit on the screen would not change in shape and size, but would only shift slightly to the side. The blurriness of the silver strip indicates that the atoms escaping from the hot filament move at different speeds. Atoms moving quickly move less than atoms moving at a slower speed.
The distribution of atoms and molecules by speed represents a certain pattern that characterizes their movement.
The table shows that the largest number of nitrogen molecules have speeds from 300 m/s to 500 m/s.
91% of molecules have velocities included in the range from 100m/s to 700m/s.
9% of molecules have speeds less than 100 m/s and greater than 700 m/s.
O. Stern, using the molecular beam method invented by the French physicist Louis Dunoyer (1911), measured the speed of gas molecules and experimentally confirmed the distribution of gas molecules by speed obtained by D. C. Maxwell. The results of Stern's experiment confirmed the correctness of the estimate of the average speed of atoms, which follows from the Maxwell distribution.
From the graph it was possible to determine the displacement for the middle of the slit image and, accordingly, calculate average speed
movement of atoms.
At T 2 T 1 the maximum of the distribution curve shifts to the region of higher speed values.
N. S. Purysheva, N. E. Vazheevskaya, D. A. Isaev, textbook “Physics - 10”, workbook for this textbook.
Physics: 3800 problems for schoolchildren and entering universities. – M.: Bustard, 2000.
Rymkevich A.P. Collection of problems in physics. 10-11 grades – M.: Bustard, 2010.
L.A. Kirik “Independent and test work in physics.” Grade 10. M.: Ilexa, Kharkov: Gymnasium, 1999.
Encyclopedia for children. Technique. M.: Avanta+, 1999.
Encyclopedia for children. Physics. Part I. M.: Avanta+, 1999.
Encyclopedia for children. Physics. Ch.P.M.: Avanta+, 1999.
Physical experiment at school./ Comp. G. P. Mansvetova, V. F. Gudkova. - M.: Education, 1981.
Glazunov A. T. Technology in the course of high school physics. M.: Education, 1977.
Initially, it was hypothesized that molecules move at different speeds.
These speeds are related to temperature and there is a certain law for the distribution of molecules by speed, which followed from observations, in particular, of Brownian motion.
The experiment is one of the fundamental physical experiments. Currently, atomic-molecular teaching has been confirmed by numerous experiments and is generally accepted.
Reflection of educational actions.
Today I found out...
It was interesting…
It was difficult…
I realized that...I learned...
I was surprised...
Used Books:
Electronic applications:
L. Ya. Borevsky “Course of physics of the XXI century”, basic + for schoolchildren and applicants. MediaHouse. 2004
Interactive physics course for grades 7 – 11. Physikon LLC, 2004. Russian version of “Living Physics”, Institute of New Technologies
Physics, grades X-XI. Multimedia course-M.: Russobit Publishing LLC.-2004 (http://www. russobit-m. ru/)
Open physics. In 2 hours (CD) / Ed. CM. Goat. – M.: Physikon LLC. - 2002 (http://www.physicon.ru/.)
The study of diffusion and Brownian motion provides some insight into the speed of chaotic movement of gas molecules. One of the simplest and most visual experiments for its determination is the experiment of O. Stern, performed by him in 1920. The essence of this experiment is as follows.
On a horizontal table, which can rotate around the O axis (Fig. 3.2), cylindrical surfaces A and B are strengthened perpendicular to the table. Surface B is solid, and in surface A there is a narrow slot parallel to the O axis. A silver-plated platinum wire is located vertically along the O axis, which is included in the electrical circuit. When current is passed through, the wire glows and silver evaporates from its surface. Silver molecules fly in all directions and mainly settle on the inner side of the cylindrical surface A. Only a narrow beam of silver molecules flies through the gap in this
surface and settles in area M on surface B. The width of the deposit in M is determined by the width of the gap in surface A. To prevent silver molecules from being scattered during collisions with air molecules, the entire installation is covered with a cap, from under which air is pumped out. The narrower the gap in surface A, the narrower the coating in area M and the more accurately the speed of movement of molecules can be determined.
The very definition of speed is based on the following idea. If the entire installation is brought into rotation around the O axis with a constant angular velocity, then during the time during which the molecule flies from the slit to surface B, the latter will have time to rotate and the deposit will shift from region M to region K. Consequently, the flight time of the molecule along the radius and the time the displacement of point M of surface B by the same distance. Since the molecule flies uniformly, then
where is the desired speed, is the radius of the cylindrical surface A. Since the linear speed of points on surface B is equal to south, time can be expressed by another formula:
Thus,
Since during the experiment they remain constant and are determined in advance, then by measuring you can find the speed of the molecule. In Stern's experiment it turned out to be close to 500 m/s.
Since the deposit in region K appears blurred, we can conclude that the silver molecules fly to surface B at different speeds. The average molecular speeds can be expressed mathematically by the formula
As an example, we note that at 0 °C the average speed of hydrogen molecules is 1840 m/s, and that of nitrogen is 493 m/s. The change in plaque thickness in the K region gives an idea of the distribution of molecules according to the speed of their movement. It turns out that a small number of molecules have speeds several times higher than the average speed.
(Think where in Fig. 3.2 they left a trace of molecules whose speeds are greater than the average speed and how the position of the deposit will change if the current in the wire O is increased.)
BROWN Robert (), English botanist Described the nucleus of a plant cell and the structure of the ovule. In 1828 he published “A Brief Report on Observations with a Microscope...”, in which he described the motion of Brownian particles that he discovered. Described the nucleus of a plant cell and the structure of the ovule. In 1828 he published “A Brief Report on Observations with a Microscope...”, in which he described the motion of Brownian particles that he discovered.
Brownian motion is the thermal movement of particles suspended in a liquid or gas. He observed the phenomenon by examining moss spores suspended in water through a microscope. Brownian motion never stops; particles move randomly. This is thermal movement.
PERRIN Jean Baptiste (), French physicist. Perrin's experimental studies of Brownian motion () finally proved the reality of the existence of molecules. Nobel Prize (1926).
Perrin's experiments Observed Brownian particles in very thin layers of liquid Concluded that the concentration of particles in the gravity field should decrease with height according to the same law as the concentration of gas molecules. The advantage is that the mass of Brownian particles occurs faster due to the large mass. Based on counting these particles at different heights, we determined Avogadro's constant in a new way.
MAXWELL James Clerk ((), English physicist, creator of classical electrodynamics, one of the founders of statistical physics Maxwell was the first to make a statement about the statistical nature of the laws of nature. In 1866 he discovered the first statistical law, the law of the distribution of molecules by speed (Maxwell distribution).
Ludwig BOLZMANN, Austrian physicist, one of the founders of statistical physics and physical kinetics. He derived the distribution function named after him and the basic kinetic equation of gases. Boltzmann generalized the law of distribution of velocities of molecules in gases located in an external force field, and established a formula for the distribution of gas molecules along coordinates in the presence of an arbitrary potential field ().
Otto STERN (), physicist. Born in Germany, since 1933 he lived in the USA. Otto Stern measured (1920) the speed of thermal motion of gas molecules (Stern's experiment). The experimental determination of the rates of thermal motion of gas molecules, carried out by O. Stern, confirmed the correctness of the foundations of the kinetic theory of gases. Nobel Prize, 1943.
Stern's experiment The cylinders began to rotate at a constant angular velocity. Now the atoms that passed through the slit no longer settled directly opposite the slit, but were displaced by a certain distance, since during their flight the outer cylinder managed to rotate through a certain angle. When the cylinders rotated at a constant speed, the position of the strip formed by atoms on the outer cylinder shifted by a certain distance.
Stern's experiment Knowing the radii of the cylinders, the speed of their rotation and the magnitude of the displacement, it is easy to find the speed of movement of the atoms. The flight time of the atom t from the slot to the wall of the outer cylinder can be found by dividing the path traveled by the atom and equal to the difference in the radii of the cylinders by the speed of the atom v. During this time, the cylinders rotated through an angle φ, the value of which can be found by multiplying the angular velocity ω by time t. Knowing the value of the rotation angle and the radius of the outer cylinder R 2, it is easy to find the value of the displacement L and obtain an expression from which one can express the speed of movement of the atom
Think... Multiple repetitions of Stern's experiment made it possible to establish that with increasing temperature, the section of the strip with the maximum thickness shifts to the beginning. What does it mean? Answer: as the temperature increases, the speeds of the molecules increase, and then the most probable speed is in the region of high temperatures.
In the middle of the 19th century, the molecular kinetic theory was formulated, but then there was no evidence of the existence of the molecules themselves. The whole theory was based on the assumption of the movement of molecules, but how to measure the speed of their movement if they are invisible?
Theorists were the first to find a way out. From the equation of the molecular kinetic theory of gases it is known that
A formula has been obtained for calculating the root mean square velocity, but the mass of the molecule is unknown. Let's write the value of υ sq differently:
 |
(2.1.2) |
And we know that, then
| (2.1.3) |
Where R- pressure; ρ - density. These are already measured quantities.
For example, with a nitrogen density equal to 1.25 kg/m3, at t = 0 °C and P= 1 atm, speed of nitrogen molecules. For hydrogen: .
It is interesting to note that the speed of sound in a gas is close to the speed of molecules in this gas, where γ - Poisson's ratio. This is explained by the fact that sound waves are carried by gas molecules.
The fact that atoms and molecules of ideal gases in a thermally equilibrium beam have different velocities was verified by the German physicist Otto Stern (1888-1969) in 1920. A diagram of its installation is shown in Fig. 2.1.
Rice. 2.1
Platinum thread A, coated on the outside with silver, is located along the axis of the coaxial cylinders S1, S3,. A low pressure of the order of Pa is maintained inside the cylinders. When current is passed through a platinum filament, it heats up to a temperature above the melting point of silver (961.9 ° C). The silver evaporates and its atoms pass through narrow slits in the cylinder S 1, and aperture S 2, fly to the cooled surface of the cylinder S 1, on which they are deposited. If the cylinders S1, S3 and the diaphragm does not rotate, the beam is deposited in the form of a narrow strip D on the surface of the cylinder S 3. If the entire system is rotated with angular velocity, then the image of the slit is shifted to the point D´ and becomes blurry.
Let l- distance between D And D´, measured along the surface of the cylinder S 3, it is equal to where is the linear velocity of points on the surface of the cylinder S 3, radius R; is the time it takes silver atoms to travel the distance. Thus, we have where it is possible to determine the speed of thermal motion of silver atoms. The filament temperature in Stern's experiments was 1200 °C, which corresponds to the root mean square speed. In the experiment, the value obtained for this value was from 560 to 640 m/s. In addition, the image of the slit D´ always appeared blurred, indicating that the Ag atoms were moving at different speeds.
Thus, in this experiment the velocities of gas molecules were not only measured, but it was also shown that they have a large spread in velocities. The reason is the randomness of the thermal movement of molecules. Back in the 19th century, J. Maxwell argued that molecules, randomly colliding with each other, are somehow “distributed” in speed, and in a very definite way.