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Question

Our universe has been continuously expanding since its formation at the Big Bang, thus gradually reducing the density of its major constituents - hydrogen and helium, and the average temperature to 2.7K (associated with the so-called microwave background radiation left over from the Big Bang). What is the rms speed of hydrogen molecules at this temperature?


A

183 m/s

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B

125 m/s

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C

240 m/s

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D

314 m/s

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Solution

The correct option is A

183 m/s


Since the H2 molecules in outer space can be considered an ideal gas on a very large scale, our kinetic theory should give good results (the theory works best for low gas densities in large volumes). We can use out vrms -T relation -

vrms=3RTM,

where M = 2 gms,

=3×8.314×2.72×103=183.5 m/s.


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