Absorption of Solar Radiation by Formaldehyde

The Table below lists solar flux intensities (I) at an altitude of 1km and north latitude 40^o at the summer solstice (June 21) together with absorption cross sections for the formaldehyde molecule. If the concentration of formaldehyde at 1km on Jun 11 at that location is 5 ppbv, calculate the total photon flux deposited into a cubic centrimetre of air at midday as a consequence of formaldehyde absorption of solar radiation.

Wavelength (nm)	295-305	305-315	315-325	325-335	335-345	345-355	355-365
I (photons/cm2 / sec/ (10nm) )	2.66. 1013	4.20. 1014	1.04. 1015	1.77. 1015	1.89. 1015	2.09. 1015	2.15. 1015
sigma (10-20 cm2/molecule)	2.62	2.45	1.85	1.76	1.18	0.42	0.06

• Work out the total number of molecules in 1 cm³ (As an approximation, use a pressure of 1 atm = 100 kPa, see p46-47.)
  pV = nRT is a useful relation, multiply the number of moles with Avogadros number. (Get data from Tables or from CODATA86 on-line
• Work out number of formaldehyde molecules
• Work out the absorption in each of the wavelength interval, assuming constant flux and cross section within the interval.
• Sum all contributions, as an approximation to the integral in (3.9), p 43

p=1e5;                   % Air pressure (neglecting decrease due to altitute)
                         % See p46-47 in the book)
T=273;
V=1e-6;                  % Convert cm^3  to m^3
R=8.31451;               % "Molar gas constant" in J/mol/K
n=p*V/R/T ;               % number of moles

NA=6.022E23;             % Avogadros Number
N=NA*n;                  % Number of molecules in V
Nf=5E-9*N;	         % Number of formaldehyde molecules (5 ppbv or N)										


I  =  [2.66E13  4.20E14  1.04E15  1.77e15  1.89e15  2.09e15  2.15e15 ];
sigma=[2.62e-20 2.45e-20 1.85e-20 1.76e-20 1.18e-20 0.42e-20 0.06e-20];
lamda=[300:10:360]*1E-9; 

Is=I.*sigma*Nf ;
plot (lamda,Is)          % Plot the absorption as a function of wavelength
hold on 
plot(lamda,Is,'o')

abs=sum(Is)              % Total absorption by formaldehyde (photons/ cm^3/ s)

abs2=Nf*I*sigma'         % Alternative evaluation using matrix and transpose (')