Page 359 - Physics Coursebook 2015 (A level)

Chapter 22: Ideal gases
Figure 22.3 Brownian motion of pollen grains, as drawn by the French scientist Jean Perrin.
BOX 22.1: Observing Brownian motion
The oxygen and nitrogen molecules that make up
most of the air are far too small to see; they are much smaller than the wavelength of light. To observe the effect of the air molecules we have to look at something bigger. In this experiment (Figure 22.4), the smoke cell contains air into which a small amount of smoke has been introduced. The cell is lit from the side, and the microscope is used to view the smoke particles.
microscope
cover slip smoke cell
light smoke
Figure 22.4 Experimental arrangement for observing Brownian motion.
QUESTIONS
1 Consider a smoke particle of mass M and speed V. It is constantly buffeted by air molecules. The mass of a single air molecule is m and it has speed v. It is reasonable to assume that, on average, the smoke particle will have kinetic energy approximately equal to the kinetic energy of a single air molecule. Show that, since M >> m (M is much greater
than m), it follows that the air molecules must be moving much faster than the smoke grain (v >> V ).
2 If equal numbers of air molecules hit a smoke particle from all directions, the smoke particle does not move. State three ways in which the random movement of molecules of air cause the smoke particles to move.
3 Describe and explain what you would expect to see through a microscope observing Brownian motion when the temperature increases.
4 An oxygen molecule is moving around inside
a spherical container of diameter 0.10 m. The molecule’s speed is 400 m s−1. Estimate the number of times each second the molecule collides with the walls of the container. (You can assume that the molecule’s speed is constant.)
The smoke particles show up as tiny specks of reflected light, although they are too small for any detail of their shape to be seen. What is noticeable
is the way they move. If you can concentrate on a
single particle, you will see that it follows a somewhat jerky and erratic path. This is a consequence of the repeated collisions between the smoke particles and air molecules. The erratic motion of the smoke particles provides direct evidence that the air molecules must:
■■ be moving
■■ also have haphazard motion.
Since the air molecules are much smaller than the smoke grain, we can deduce that they must be moving much faster than the smoke grain if they are to affect it in this way.
(You may observe that all of the smoke particles in your field of view have a tendency to travel in
one particular direction. This is a consequence of convection currents in the air. Also, you may have to adjust the focus of the microscope to keep track of an individual particle, as it moves up or down in the cell.)
347