Mean free path formula is attached from the book. Thank you. vtFIGURE 9.6 Mean free path, l, of a hydrogen atom.atoms per cubic meter is roughly= 1.25 x 1023 m-3where mH is the mass of a hydrogen atom. In an approximate sense, two of these8.we may consider the equivalent problem of a single atom of radius 2ao moving withthrough a collection of stationary points that represent the centers of the other atomamount of time t, this atom has moved a distance vt and has swept out a cylindricalvalV = 1 (2a0)²vt = o vt, where o = 1 (2a0)² is the collision cross section of the atom:classical approximation. Within this volume V are nV = nơ vt point atoms with wthe moving atom has collided. Thus the average distance traveled between collisionpeəds%3DIGIL MIC%Dno vt nơgs ne) omulovThe distance l is the mean free path between collisions.° For a hydrogen atom,10o = 1 (2a0)² = 3.52 x 10-20 m².odeib Thus the mean free path in this situation is 00of1.= 2.27 x 10-4 m.l = ÷AVLK||%DouThe mean free path is several billion times smaller than the temperature scale height. As.result, the atoms in the gas see an essentially constant kinetic temperature between collisioeThey are effectively confined within a limited volume of space in the photosphere. O1this cannot be true for the photons as well, since the Sun's photosphere is the visible im8This treats the atoms as solid spheres, a classical approximation to the quantum atom.The concept of cross section, which will be discussed in more detail in Section 10.3, actually 1epprobability of particle interactions but has units of cross-sectional area.1ºA more careful calculation, using a Maxwellian velocity distribution for all of the atoms, resuis npath that is smaller by a factor of /2. The central density of the Sun is calculated to be p=1.53x10$ kg/m³ and the averaged opacityat the center to be k=0.217 m²/kg.a) Calculate the mean free path of a photon at the center of the Sunb) Calculate the average time it would take for the photon to escape from the Sun ignoringintensity changes.

Given, The central density of the sun is, ρ=1.53×105kg/m3 And average opacity at the center is,…

The central density of the Sun is calculated to be p=1.53x10$ kg/m³ and the averaged opacity at the center to be k=0.217 m²/kg. a) Calculate the mean free path of a photon at the center of the Sun b) Calculate the average time it would take for the photon to escape from the Sun ignoring intensity changes.

The central density of the Sun is calculated to be p=1.53x10$ kg/m³ and the averaged opacity at the center to be k=0.217 m²/kg. a) Calculate the mean free path of a photon at the center of the Sun b) Calculate the average time it would take for the photon to escape from the Sun ignoring intensity changes.