stunner5000pt
- 1,447
- 5
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
[tex]n(z) = n_{0} \exp(\frac{-z}{H})[/tex]
where H is the scale height [tex]H = \frac{RT}{Mg(z)}[/tex]
the densities of H are 10^10 m-1 and He 10^12 m-1
when the densities are equal
[tex]10^{10} \exp\left(\frac{-zg(z)}{1.2 * 10^7}\right) = 10^{12} \exp\left(\frac{-zg(z)}{3.1*10^6}\right)[/tex]
where [tex]g = \frac{GM}{z^2}[/tex]
is the setup good so far? Thank you for all your help!
wel the densities of the gases in the atmosphere is given by
[tex]n(z) = n_{0} \exp(\frac{-z}{H})[/tex]
where H is the scale height [tex]H = \frac{RT}{Mg(z)}[/tex]
the densities of H are 10^10 m-1 and He 10^12 m-1
when the densities are equal
[tex]10^{10} \exp\left(\frac{-zg(z)}{1.2 * 10^7}\right) = 10^{12} \exp\left(\frac{-zg(z)}{3.1*10^6}\right)[/tex]
where [tex]g = \frac{GM}{z^2}[/tex]
is the setup good so far? Thank you for all your help!