A hypothetical gas container holds exactly five molecules. At a given instant, their speeds are v, 2v, 3v, 4v , and 5v . The ratio of their root mean square speed to their average speed is

Step-by-step solution

The average speed of the molecules is the arithmetic mean of their speeds: v_ avg = v + 2v + 3v + 4v + 5v 5 = 15v 5 = 3v The root mean square (rms) speed is the square root of the mean of the squares of their speeds: v_ rms = v^2 + (2v)^2 + (3v)^2 + (4v)^2 + (5v)^2 5 v_ rms = v^2 + 4v^2 + 9v^2 + 16v^2 + 25v^2 5 = 55v^2 5 = 11 v The ratio of the root mean square speed to the average speed is: v_ rms v_ avg = 11 v 3v = 11 3 Answer: 11 3