How Does Compton Scattering Affect Photon Wavelength in the Sun?

[oldspice1212]

Homework Statement

Nuclear fusion reactions at the center of the sun produce gamma - ray photons with energies of about 1 MeV (10^6 eV). By contrast, what we see emanating from the sun's surface are visible light photons with wavelengths of about 500nm. A simple model that explains this difference in wavelength is that a photon undergoes compton scattering many times, in fact 10^26 times, as suggested of the solar interior, as it travels from the center of the sun to its surface.
Estimate the increase in wavelength of a photon in an average compton - scattering event.

The Attempt at a Solution

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I'm not exactly sure what they mean by increase in wavelength what I did was calculate the wavelength using,
E = \frac{ hc }{ lambda } solving for lambda I got 1.2*10^-12m. But, I don't think it's that easy. So what is this initially asking?
I'm thinking that it's asking for the average wavelength but not sure that lambda prime is, if I have that I can use the compton scattering equation, right?

I think I just answered my own question haha, the other wavelength is 500nm, so now I can subtract and use the compton scattering right? :P

 

[voko]

The photon has an initial wavelength in the core of the Sun, and a final wavelength at its surface. It undergoes a given number of scattering events. What is the average change in the wavelength per event?