Answer: Nuclear fusion reactions at the center of the sun

Chapter 38, Problem 38.33

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Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about 1 MeV 1106 eV2. By contrast, what we see emanating from the suns surface are visiblelight photons with wavelengths of about 500 nm. A simple model that explains this difference in wavelength is that a photon undergoes Compton scattering many timesin fact, about 1026 times, as suggested by models of the solar interioras it travels from the center of the sun to its surface. (a) Estimate the increase in wavelength of a photon in an average Compton-scattering event. (b) Find the angle in degrees through which the photon is scattered in the scattering event described in part (a). (Hint: A useful approximation is cosf 1 - f2>2, which is valid for f V 1. Note that f is in radians in this expression.) (c) It is estimated that a photon takes about 106 years to travel from the core to the surface of the sun. Find the average distance that light can travel within the interior of the sun without being scattered. (This distance is roughly equivalent to how far you could see if you were inside the sun and could survive the extreme temperatures there. As your answer shows, the interior of the sun is very opaque.)