The paper presents preliminary results used to design and prepare an advanced physics experiment to be carried out in Physics Laboratory II at the Institute of ...
BROWNIAN MOTION WITH DATA VIDEO
Tomasz Greczyło, Ewa D bowska
ABSTRACT The paper presents preliminary results used to design and prepare an advanced physics experiment to be carried out in Physics Laboratory II at the Institute of Experimental Physics of Wrocław University. The authors discuss the process of setting up the experiment and the results. Advantages and disadvantages of the apparatus are discussed along with descriptions of possible future uses.
1. INTRODUCTION Experimental work at advanced student physics laboratory [1] plays an important role in teaching and learning processes during science and technology studies. Therefore it is extremely useful to work on making student laboratory tasks more efficient and effective in accumulating knowledge and skills necessary for experimental work. The paper presents experimental verification of an idea of a new advanced experiment to be carried out in Physics Laboratory II at the Institute of Experimental Physics of Wroclaw University. We consider that it is possible to create one more students’ experiment [2] giving a chance to do measurements on real digital movies. This is possible due to the use of new experimental method known as Data Video. We believe that students preparing themselves to perform the experiment extend their knowledge and skills. The experiment described below helps also to work with experimental data, elaborate them, make critical conclusions and present results. Such experiment is a good chance to introduce a computer, programs and educational environments at advanced physics laboratory.
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2. SUBJECT AND APPARATUS Theory Robert Brown is well known from his observation of motion of pollen grains suspended in water which, for the very first time, he observed in 1828. Separated work of Marian Smoluchowski and Albert Einstein, carried out at the beginning of the last century, brought light to such a behavior of particles [3]. When one considers one-dimensional chaotic motion [4] he can be write that the displacement after one step is equal to unity x1 = ± 1. After two steps the displacement is
x2 = x1 ± 1,
then
x22 = x12 ± 2x1 + 1.
Knowing that
= 0
and establishing an average squared displacement one arrives at = + 1 = 2. Continuing such a way of thinking after N steps one receives = N. The similar result can be obtained from the kinetic theory of matter for three-dimensional system which explains connection between the average squared displacement for a spherical particle bombarded by much smaller particles in which it is immersed and time t:
< r 2 >=
RT t, 3πaηN A
(1)
where: R – the ideal gas constant, T – liquid temperature, a – the radius of particle, η - the viscosity of liquid, NA – Avogadro’s number. The equation is known as the EinsteinSmoluchowski’s equation.
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In 1908 Jean Perrin carried out the experiment in which he considered the validity of the equation [5] and established the value of Avogadro’s number. For this work he was awarded with Nobel prize in 1926. Experiment idea
Determination of Avogadro’s number with the use of presented set-up is possible when one knows the viscosity of liquid , its temperature T, and the radius a of spherical particles in η
use. In the case of two dimensions, which was realized in our experiment, the equation (1) has a form < r 2 >=
RT t. 2πaηN A
(2)
The experiment was carried out at room temperature T=(293±1) K, when the viscosity of liquid was equal to =(1,00±0,05)N·s/m2, and the average radius of particles a=(850±10)nm. η
The phenomenon of Brownian motion – motion of particles immersed in liquid – is often used to illustrate kinetic theory of matter [6]. Real time Brownian motion of cigarette smoke or fat suspensions in liquid is a typical illustration for oral lectures in physics. We believe that use of Data Video technique will allow preparing an experiment in which students will be able to make quantitative measurements of the phenomenon. Repetition of Jean Perrin’s experiment is an excellent subject for an advanced physics laboratory work. There are plans for the spring of 2005 to establish a new experiment called Brownian motion at the Institute of Experimental Physics of Wroclaw University. In the next chapters the experimental set-up and the results are presented.
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3. EXPERIMENTAL SET-UP
To set up the experiment we used the apparatus present at the Physics Laboratory II and the Division of Physics Teaching at our Institute. All components of experimental set-up are presented in Fig. 1: 1. optical microscope BAD
Figure 1. The view of the experimental set-up’s components
Carlzeiss Jena nr 469634 together with its holder – a table; 2. analogue video camera Unitra Polkolor TP-K16 allowing capturing black and white movies. Originally the microscope worked with a traditional camera; 3. monochromatic monitor Unitra WZT TWM-315 used to observe the quality of picture coming from the camera. The monitor was used because the window in the program for capturing movies is to small to ensure sufficient quality (brightness and sharpness); 4. computer with the operating system Windows 95 and educational environment Coach 5 which contains Data Video; 5. video card miroVIDEO DC 10 (inside the computer) along with a program for capturing and storing digital video movies.
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Experimental procedure
The experimental procedure consists of four steps: 1. preparation of the solution of water and plastic spheres and placing it under the microscope; 2. capturing the digital video sequences showing chaotic motion of the immersed particles; 3. measurements with the use of Data Video mode of Coach 5; 4. elaboration and visualization of the results with the use of Microsoft Excel® 2003 spreadsheet. The optical microscope together with the camera and the monitor has the magnifying power of 2000 times. To reach the power we used an immersion objective with the magnifying power of 100 which works with
Figure 2. The view of microscopic glass together with metallic loop
immersion oil whose refraction index for white light is n = 1,515 (20˚C). The liquid was put inside the metallic loop made of wire of radius d = (40±5) µm, placed on a microscopic glass (Fig.2) and covered with covering glass. On the top of the glass the immersion oil was put. This way we obtained
two-dimensional
Figure 3. The frame from the digital movie showing the axis, investigated particle and radius of the wire
experimental
area between optical glasses. Such geometry of the system makes it impossible for the particles to move in depth of the liquid. The movement would lead to the lost of sharpness of the observed particle image. We used plastic spheres supplied by Beckman CoulterTM.
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Concentration of particles was adjusted carefully to have a number of visible particles in the experimental area – see Fig. 3. Then the camera, computer with digital capturing card and miroMEDIA Manager software have been used to register a 10-second movie showing particles in motion. The first frame of the movie is shown in Fig 3. Information about motion of certain particles (their location in time) came from digital movie thanks to the use of Data Video procedure realized with Coach 5. Data in the form of triplets – time (t), location X (PX) and location Y (PY), were achieved by clicking with the mouse on the investigated particle at each chosen frame. To be able to perform the measurements accurately one has to calibrate the movie – to show the real distance on its reference frame. Real distance was pointed by putting information about the radius of the wire used to make a metallic loop. In the process of calibration also location of the Cartesian axis has to be established. The center of the axis had always been chosen at the location of the investigated particle at the first frame of the movie. The location of the axis had not been changed during Data Video measurements. Measurements had been carried out on each fifth frame of the movie covered with the rate of 25 frames per second which resulted in 50 measured points. With the use of information about location PX, PY and time t gathered from the movie it was possible to calculate the average squared displacement of the particle changing in time. Calculations and visualization were done with the help of Microsoft Excel® 2003 spreadsheet.
3. RESULTS OF THE PRELIMINARY MEASUREMENTS AND FUTURE PLANS To establish the value of Avogadro’s number we measured location of particles during their chaotic motion registered on the digital movie. In Fig. 4 the location of one particle in time is presented.
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y [µm]
10
6
2
-20
-15
-10
-5
0 -2
-6 x [µm]
Figure 4. Location of one particle in Cartesian frame (x, y) along 10 s interval of time. 7 6 y = 0,71x - 0,78
[x10-12 m2]
5 4 3 2 1 0 0
2
4
6
8
-1 czas [s]
Figure 5. Experimental plot of average squared displacement versus time. The figure from measurements of 5 particles during 10s.
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Results of observation for 5 particles had been used to calculate average squared displacement versus time t. The plot is presented in Fig. 5 and shows linear dependence. The Avogadro’s number calculated from the slope of the linear dependence is: NA = 6,47 × 1023 mol-1,
u(NA) = 0,64 × 1023 mol-1,
where u(NA) – standard uncertainty [7]. The result, in uncertainty limits, is equal to the common scientific result obtained by different methods. The results allowed us to design and establish students' experiment aimed to find Avogadro’s number based on phenomenon of chaotic motion. We plan that all results from the experiment will be analyzed and presented by students in a form of a rapport. Detailed requirements will be pronounced by individual teacher during laboratory.
4.
CONCLUSIONS
The experimental set-up described in the paper and Data Video software for video analysis allow creating an advanced physics experiment to investigate chaotic motion, in particular to verify Einstein-Smoluchowski’s equation and to find the value of Avogadro’s number. Our value is in agreement with the common one. We believe that use of the presented apparatus allows to improve experimental skills of future physicists. The results can also be used to create experiments in which one measures: •
Avogadro’s number when viscosity of the liquid, its temperature and radius of immersed plastic spheres are known;
•
viscosity of different liquids when their temperature and radius of immersed plastic spheres are known.
To improve experimental results it would be useful to:
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•
use a digital camera what should result in better quality of captured movies (sharpness and accurateness),
•
prolong the measurement's time (length of video) and increase the number of investigated particles but it will significantly extend the time necessary to proceed with the experiment and make it more time and effort consuming.
5.
ACKNOWLEDGEMENT
We express our thanks to dr Izabela Czekaj from the Institute of Catalysis and Surface Chemistry Polish Academy of Sciences in Cracow for solution of spherical plastic particles and prof. Antoni Ciszewski, dr. Piotr Mazur and MSc. Piotr Wieczorek from our Institute for their help in preparation and realization of the work.
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LITERATURE
[1] H. Szydłowski, Pracownia fizyczna wspomagana komputerowo, Wydawnictwo Naukowe PWN, Warszawa 2003 [2] T. Greczyło, E. D bowska, Aparat rentgenowski w zaawansowanej pracowni fizycznej, Aparatura Badawcza i Dydaktyczna, tom IX, nr 2 (2004), 118-125 [3] S. Chandrasekhar, Stochastic problems in physic and astronomy, Rev. Mod. Phys. 15, 1 (1943) [4] R. Salmon, C. Robbins, K. Forinash, Brownian motion using video capture, Eur. J. Phys. 23 (2002), 249-253
[5] J. B. Perrin, Mouvement brownien et réalité moléculaire, Annales de chimie et de physiqe VIII 18, 5-114 (1909). English translation: Brownian Movement and Molecular Reality,
London, Taylor and Francis, 1909 [6] A. K. Wróblewski, J. A. Zakrzewski, Wst p do fizyki, tom I, Wydawnictwo Naukowe ę
PWN, Warszawa 1976 [7] Guide to the Expression of Uncertainty in Measurement, ISO, Switzerland 1995
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