density of electrons

[stunner5000p]

A planet with an atmosphere entirely consisting of O2 and atomic oxygen, O, is exposed to solar EUV radiation at a wavelength of λ = 80 nm. The O2 does not absorb this radiation but the atomic oxygen is ionized by it with an absorption and ionization cross section of σ = 1x10-18 cm2. The O+ ions rapidly undergo charge exchange with O2 to form O2+ ions, and the only electron and ion loss process is dissociative recombination of the O2+ ions

O2+ e→O+O k1 = 1x10-8 cm3 s-1

If the solar flux is 1x10^11 photons cm-2 s-1 at 80 nm, the atomic oxygen scale height is 50 km and the O density is 1.6x10^12 cm-3 at 100 km, calculate the peak electron density of the resulting ionospheric layer for a solar zenith angle of 0°. What is the altitude of the electron density maximum?

 

thing is we know the solar flux anbd the nergy of each photon thus we know the totla energy coming into the planet

 

is this the formula i have to be using

[math] n_{e}(h,\chi) = \sqrt{\frac{q_{max}}{keff}} \exp[0.5{1-z-\sec \chi \exp(-z)}] [/math] where

[math] z = \frac{h-h^0_{max}}{H_{O}} [/math]

where ne is the electron density at some height h and zenith angle chi