The atmospheric scale height H = kT/(mg) is inversely proportional to the mean molecular mass m of the atmosphere (for the same temperature T and gravity g); comparing scale heights between two atmospheres of different composition reduces to comparing the inverse ratio of their mean molecular masses.
Earth's atmosphere (80:20 N2:O2 by the problem's simplification) has mean molar mass = 0.8(28) + 0.2(32) = 22.4 + 6.4 = 28.8 g/mol. The hypothetical...
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