Question

to larger objects, like smoke particles in the air. Suppose you see a 10???? – sided

particle of smoke under a microscope. What do you expect for the rms speed of such a smoke particle at room temperature? Model the particle as a cube. Its density would be similar to graphite. Express you answer in ??m/s. This motion is called Brownian motion. It can be observed under a simple optical microscope.

Answer 1

According to the kinetic theory of gases, the kinetic energy of a gas particle with 3 degrees of freedom(in a 3D box) is

Equating this with the formula for kinetic energy of particles,

Where K_B is the Boltzman constant 1.3806*10^-23 m² kg/s²K

For a cubic particle with 10*10^-6 m side, volume is

V = 10^-15 m³

Density of graphite is 2.266 g/cm³ = 2.266*10³ kg/m³

Thus, mass = density*volume = 2.266*10³ * 10^-15 =2.266* 10^-12 kg.

Taking room temperature to be 300 K,