# Homework Help: Gas density problem

1. Feb 20, 2006

### stunner5000pt

If the exospheric temperature is 1500 K and the hydrogen atom and helium atom densities at 500 km are 1x10^4 cm-3 and 1x10^6 cm-3 respectively, determine at what height the hydrogen atom and helium atom densities will become equal. [Hint: The answer is greater than 3000 km and remember that the acceleration due to gravity g decreases with height]

wel the densities of the gases in the atmosphere is given by
$$n(z) = n_{0} \exp(\frac{-z}{H})$$
where H is the scale height $$H = \frac{RT}{Mg(z)}$$

the densities of H are 10^10 m-1 and He 10^12 m-1
when the densities are equal
$$10^{10} \exp\left(\frac{-zg(z)}{1.2 * 10^7}\right) = 10^{12} \exp\left(\frac{-zg(z)}{3.1*10^6}\right)$$
where $$g = \frac{GM}{z^2}$$

is the setup good so far? Thank you for all your help!

2. Feb 23, 2006

### stunner5000pt

bump !

can anyone help?

i jsut wanna know if the setup is correct or not!