The ratio of root mean square velocity and average velocity of a gas molecules, at a particular temperature, is

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$1.086 : 1$

$1.086 : 2$

$2 : 1.086$

$1 : 1.086$

answer is B.

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Detailed Solution

The relationship between the root mean square velocity (Crms) and the average velocity (Cavg) of gas molecules can be derived using their respective formulas. Both parameters are used to describe the motion of gas particles at a given temperature (T) and are functions of the molar mass of the gas (M) and the universal gas constant (R).

Root Mean Square Velocity Formula

The formula for the root mean square velocity is given as:

Crms = √(3RT / M)

Average Velocity Formula

The average velocity, also referred to as the mean velocity, is expressed as:

Cavg = √(8RT / πM)

Derivation of the Ratio

To find the ratio of the root mean square velocity to the average velocity, we divide the formulas for Crms and Cavg:

Ratio = Crms / Cavg = √(3RT / M) / √(8RT / πM)

Simplifying this expression:

Ratio = √[(3RT / M) * (πM / 8RT)] = √(3π / 8)

Numerical Value of the Ratio