91Ó°ÊÓ

The intensity of light is expressed by the equation$\mathbf{l}\mathbf{=}\frac{\mathbf{P}}{\mathbf{A}}\mathbf{=}\frac{\mathbf{P}}{\mathbf{4}{\mathbf{Ï„Ï„°ù}}^{\mathbf{2}}}$where A is the cross-sectional area of the beam, P is the rate of energy emission r is the sun radius. The radiation pressure at sun surface is given as ${\mathbf{P}}_{\mathbf{rad}}\mathbf{=}\frac{\mathbf{l}}{\mathbf{c}}$l is the intensity at the sun's surface, c is the speed of the light

The rate of energy emission is$3.9×{10}^{26}\mathrm{W}$, radius of sun is$6.96×{10}^5\mathrm{km}$. The intensity at sun surface, is$\mathrm{l}=\frac{\mathrm{P}}{\mathrm{A}}$ Substitute the values we have,

role="math" localid="1663995886324" $$\begin{gathered} \mathrm{l}=\frac{3.9×{10}^{26}\mathrm{W}}{4\mathrm{π}{\left(6.96×{10}^5\mathrm{km}\right)}^2} \\ =6.4×{10}^{7}W/m^2 \end{gathered}$$

If the sun's radius is r = R/2 then,

The intensity at sun's interior r = R/2 is

$$\begin{gathered} \mathrm{l}=\frac{3.9×{10}^{26}\mathrm{W}}{4\mathrm{π}{\left(3.48×{10}^5\mathrm{km}\right)}^2} \\ =2.6×{10}^8\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

The radiation pressure at sun surface is${\mathrm{P}}_{\mathrm{rad}}=\frac{\mathrm{l}}{\mathrm{c}}$.Substitute the values we have,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{rad}}=\frac{6.4×{10}^7\mathrm{W}/{\mathrm{m}}^2}{3×{10}^8} \\ =0.21\mathrm{Pa} \end{gathered}$$

The radiation pressure at sun's interior, is${\mathrm{P}}_{\mathrm{rad}}=\frac{\mathrm{I}}{\mathrm{c}}$ Substitute the values we have

$$\begin{gathered} {\mathrm{P}}_{\mathrm{rad}}=\frac{2.6×{10}^8\mathrm{W}/{\mathrm{m}}^2}{3×{10}^8} \\ =0.86\mathrm{Pa} \end{gathered}$$

Thus, the intensity of the electromagnetic radiation is at sun's surface $6.4×{10}^7\mathrm{W}/{\mathrm{m}}^2$and the radiation pressure at sun's surface 0.21 Pa and the intensity of the electromagnetic radiation in sun's interior $2.6×{10}^8\mathrm{W}/{\mathrm{m}}^2$and the radiation pressure in sun's interior 0.86 Pa

The gas pressure at sun's surface is $1.0×{10}^4\mathrm{Pa}$, in the sun's interior r = R/2 the gas pressure is $4.7×{10}^{13}\mathrm{Pa}$. Compare the given values with the results of part (a), at sun's surface the gas pressure ($1.0×{10}^4\mathrm{Pa}$) is 50000 greater than the radiation pressure at sun's surface (0.21 Pa x 50000 =$1.0×{10}^4\mathrm{Pa}$) and for sun's interior r = R/2 the gas pressure $4.7×{10}^{13}\mathrm{Pa}$is $6×{10}^{13}\mathrm{Pa}$ times greater than the radiation pressure. Therefore, radiation pressure is an important factor for determine the structure