The rms speed of oxygen molecule in a vessel at particular temperature is 1 + 5 x 1 2 v , when v is the average speed of the molecule. The value of x will be: (take π = 22 7 )

Step-by-step solution

The RMS speed is given by v rms = 3 R T M The average speed is given by v avg = 8 R T π M The ratio is ⇒ v rms v avg  = 3 R T M 8 R T π M = 3 π 8 = 3 8 × 22 7 ⇒ v rms v avg  = 33 28 Comparing it with the given value 1 + 5 x 1 2 , v rms v avg  = 1 + 5 28 ⇒ x = 28