Can anybody help me in understanding this physics question, I don't know where to start?

Question

The scale height of the earth’s atmosphere is 7.60 km. A hypothetical planet has a thin isothermal atmosphere at T = 100 K and is composed of molecules with m = 3.00*10^-26 kg. What would the acceleration due to gravity on the planet need to be for its scale height to be the same as that on earth.

a) 3.63 m s^-2

b) 4.38 m s^-2

c) 6.05 m s^-2

d) 4.38*10^3 m s^-2

e) 6.05*10^3 m s^-2

Answer 1

(c) appears to be the correct answer.

This is a direct application of the equation for Scale height (http://en.wikipedia.org/wiki/Scale_heigh...

H = kT/Mg  where:

k = Boltzmann constant = 1.38 x 10−23 J·K−1

T = mean planetary surface temperature in kelvins

M = mean molecular mass of dry air (units kg·mol−1)

g = acceleration due to gravity on planetary surface (m/s²)

To obtain the answer we simply solve for g where H = 7600 m.

g = kT/HM = (1.38x10^-23 J*K^-1)*(100 K)/(7600 m)*(3.00^10^-26 kg*mol^−1)