At what temperature does the rms speed of (a) H_2 (molecular hydrogen) and (b) O

Question

At what temperature does the rms speed of (a) H_2 (molecular hydrogen) and (b) O_2 (molecular oxygen) equal the escape speed from Earth? At what temperature does the rms speed of (c) H_2 and (d) O_2 equal the escape speed from the Moon (where the gravitational acceleration at the surface has magnitude 0.160g)? Considering the answers to parts (a) and (b), should there be much (e) hydrogen and (f) oxygen high in Earth's upper atmosphere, where the temperature is about 1000 K? Earth radius is 6.37 times 10^6 m, Moon radius is 1.74 times 10^6 m.

Explanation / Answer

a) Vrms =  (3RT/M)½

11186=(3RT/M)½

125129081=(3RT/M)

T=125129081M/3R....putting molar mass =0.002kg

= 10050 kelvin

b)T=125129081M/3R putting molar mass = 0.032kg

=160808 kelvin

c) 2400=(3RT/M)½

5760000=3RT/M

T=5760000M/3R putting value of R, M=0.002

= 462 Kelvin

D) T=5760000M/3R

=7400 Kelvin

e) yes

f)yes

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