1. The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is a. 1.086 : 1 b. 1 : 1.086 c. 2 : 1.086 d. 1.086 : 2

Sol. The two types of speeds are defined as; Root mean square speed (urms) = √(3RT/M) Average speed (uavg) = √(8RT/πM) For the same gas, at a given temperature, M and T are same, therefore u_rms/u_avg = √(3RT/M) ∶ √(8RT/πM) = √3 ∶ √(8/π )= √3 ∶ √2.54=1.085∶1

Dear Student,
Please find below the solution to your problem.

The two types of speeds are defined as;
Root mean square speed (urms) = √(3RT/M)
Average speed (uavg) = √(8RT/πM)
For the same gas, at a given temperature, M and T are same,
therefore
u_rms/u_avg = √(3RT/M) ∶ √(8RT/πM)
= √3 ∶ √(8/π )
= √3 ∶ √2.54
= 1.085∶1

Thanks and Regards