Most probable speed

Most probable speed (V_mp)

It is defined as the speed acquired by most of the molecules of the gas.

The derivation of equations (9.20), (9.22) is beyond the scope of the book

Comparison of v_rms, v and v_mp

Among the speeds v_rms is the largest and v_mp is the least

v_rms > v > v_mp

EXAMPLE 9.3

Ten particles are moving at the speed of 2, 3, 4, 5, 5, 5, 6, 6, 7 and 9 m s-1. Calculate rms speed, average speed and most probable speed.

Solution

The average speed

The most probable speed is 5 ms^-1 because three of the particles have that speed.

EXAMPLE 9.4

Calculate the rms speed, average speed and the most probable speed of 1 mole of hydrogen molecules at 300 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 = 1.67 × 10⁻²⁷kg.

One hydrogen molecule = 2 hydrogen atoms = 2 × 1.67 × 10⁻²⁷kg.

The average speed