speed are indicated in the Figure . . It can be seen that the rms speed is greatest among the three. EXAMPLE .
Calculate the rms speed, average speed and the most probable speed of mole of hydrogen molecules at K. Neglect the mass of electron. Solution The hydrogen atom has one proton and one electron. The mass of electron is negligible compared to the mass of proton.
Mass of one proton = . × − kg . One hydrogen molecule = hydrogen atoms = × . × − kg .
The average speed kT kT π ( . ) ) ( . ) ( ms − (Boltzmann Constant k = . × − J K - ) The rms speed kT kT rms = = ( .
) ( ) ( . ) m s Most probable speed v kT kT mp = ( . ) ( ) ( . ) ms − Note that v rms > v > v mp .
. Maxwell-Boltzmann speed distribution function In a classroom, the air molecules are moving in random directions. The speed of each molecule is not the same even though macroscopic parameters like temperature and pressure are fixed. Each molecule collides with every other molecule and they exchange their speed.
In the previous section - - - - Unit Kinetic theory of gases . Interestingly once the gas molecule attains equilibrium, the number of molecules in the given range of speeds are fixed. For example if a molecule initially moving with speed m s - , collides with some other molecule and changes its speed to m s - , then the other molecule initially moving with different speed