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# Most probable speed

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

Most probable speed (Vmp)

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 vrms, v and vmp

Among the speeds vrms is the largest and vmp is the least

vrms > v > vmp ### 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 Tags : Kinetic Theory of Gases , 11th Physics : UNIT 9 : Kinetic Theory of Gases
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11th Physics : UNIT 9 : Kinetic Theory of Gases : Most probable speed | Kinetic Theory of Gases