3
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?
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?
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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,
=√3×8.314×2.72×10−3=183.5 m/s.
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,
=√3×8.314×2.72×10−3=183.5 m/s.
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