Discussion
Which quantity is the scale height of an isothermal atmosphere?
Answer: C
Substituting the gas law into the hydrostatic equation and integrating at constant temperature gives an exponential profile with scale height \( H = RT/g \). Pressure falls by a factor of e, about 2.718, over that distance. The half-pressure height is smaller by a factor of the natural logarithm of two, which is why 5.5 kilometres and 8 kilometres are both quoted for different definitions. Checking the units of each quantity catches a wrong formula before the arithmetic begins.
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