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What is the concept of Maxwell: Boltzmann distribution of molecular speeds, at a given temperature in a gas sample?

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A gas consists of tiny particles (atoms or molecules) separated from one another by large spaces. These particles are constantly moving in all directions. During their motion, they collide with one another and also with the walls of the container. As a result of collisions, the speed and the direction of the molecules keep on changing. Thus, all the molecules present in given sample of a gas do not possess the same speed. The speeds of individual molecules are different and are distributed over a wide range. The speeds of different molecules keep on changing However, the distribution of speed among different molecules remains the same at particular temperature although the individual speeds of the molecules may change. The distribution of molecules between different possible speeds was given by Maxwell and Boltzmann. He plotted the fraction of molecules, i.e., (along y-axis) having different speeds against the speeds of the molecules (along x-axis). The curve so obtained is shown in figure below and is known as Maxwell's distribution curve.

The important features of Maxwell's distribution curve can be summarized as follows: 

(i) The fraction of molecules with very low or very high speeds is very small. 

(ii) The fraction of molecules possessing higher and higher speeds goes on increasing till it reaches the peak and then it starts decreasing. 

(iii) The maximum fraction of molecules possesses a speed corresponding to the peak in the curve. The speed corresponding to the peak in the curve is referred to as most probable speed.

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