What is the root mean square of velocity of a typical neon gas atom as a function of temperature?

Question

Can someone please explain this to me.

Answer 1

Sure.  The average speed of a molecule depends upon its temperature and its molar mass.

u = (3RT / M)^(1/2)

or

u = (3kT / m)^(1/2)

where

u is the average, RMS speed

R is the gas constant, 8.314 J/mol K, which is defined in terms of moles

k is Boltzman's constant, 1.380 ×10^-23 J/K, which is defined in terms of a single molecule

M is the molar mass

m is the mass of a single molecule in kilograms

For neon:

u = (3RT/M)^(1/2)

u = (3 x 8.314 J/mol K x 298K / 20.179 g/mol x 1000g / 1 kg x kg m^2 /s^2 / J)^(1/2)

u = 606.9 m/s

or

u = (2.037 m/s/K) x (T)  ... where T is in kelvin

Answer 2

Tricky ?  Two ways to get the answer  , typical covers a broader area sometimes  ,