In 2003 a dilute gas of sodium atoms was cooled to 045 nK na

In 2003 a dilute gas of sodium atoms was cooled to 0.45 nK (nano Kelvin). According to the law of equipartition, what is the RMS velocity square root (v^2) of a sodium atom at this low temperature? Neglect gravity.

Solution

Since it is a dilute gas, we can assume it to be ideal (this is a tricky approximation since it is a very low temperature). Then using the equipartition theorem,

RMS velocity = sqrt(3RT/M) = .69 mm/s