Times change, especially at the scientific frontiers. In problem #42, update you

Question

Times change, especially at the scientific frontiers. In problem #42, update your RMS speed noting that more recent experiments on ultracold gases now achieve temperatures of hundreds of pico-Kelvin or less (pico-Kelvin = 10^-12 K). What is the RMS speed of Na gas at 100 pK, in m/s? Consider an atom with the RMS speed of part a), above. How long in seconds would that atom take to travel from the front to the back of our lecture hall? (Assume no intermolecular collisions.) For this, make a reasonable estimate of the length of our lecture hall, stating your rationale clearly. How long (in seconds) would an H_2 molecule and which is traveling at its RMS speed at 300 K take to move the same distance as in part b), above (also with no intermolecular collisions)? What is the ratio of the time for part c) to that of part b)?

Explanation / Answer

2.

a) RMS speed of Na gas = sq.rt.(3RT/M)

= sq.rt.(3 x 8.31447 x 100 x 10^-12/0.023) = 3.30 x 10^-4 m/s

b) Let the distance be 30 m

then, velocity = distance/time

so time the Na gas atom would take = 30/3.30 x 10^-4 = 9.10 x 10^4 s to travel

c) RMS speed of H2

= sq.rt.(3 x 8.31447 x 300/0.002016) = 1926.61 m/s

Time H2 would take to travel 30 m = 30/1926.61 = 0.0156 s

d) The ratio of time in c to b

= 0.0156/9.10 x 10^4 = 1.71 x 10^-7

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