Please do 2 Exercise #5 (updated)In class we found the number of standing wave modes (with polarizations) contained inbetween w and w + dw,Vw?N(w) dw =(1)where V is the volume of the cabity, V = L³. With this number density N(w), the totalmean energy of the blackbody radiation inside the cavity is obtained as|E(w, T) N (w)dw = | plw) dwE =(2)where E(w, T) =ehw /kpTand p(w) = E(w,T') N (w) is called the blackbody spectrum.a. What is the SI unit for the blackbody spectrum p(w)?b. Do the integral of Eq.(2) to find the energy density u = E/V of the blackbody radiationinside the cavity. Use the following formula:73(3)c. Borrowing a formula from electro-magnetic theory, the radiation flux J from the surfaceof the cavity can be written in terms of the energy density as J = cu/4. For theblackbody radiation, this can be written as J = oT with o the Stefan-Boltzmannconstant. Find the expression of o in terms of kg, h, and c, then compute the value.(If your calculator cannot handle it, you will need to work out powers by hand.)d. What is the SI unit for o supposed to be? Does your o have the correct unit?e. Find the peak frequency of p(w) as a function of T by solvingdp= 0dw(4)for w. Use the solution for 3+ e"(x – 3) = 0, x = 2.824.f. What is the total power of the black body radiation from an object whose surface areais A and temperature is T? Use the Stefan-Boltzmann law, J = oTª.2. The Sun can be modeled as a sphere of gas in thermal equilibrium. This is justified bythat the spectrum of sunlight is well approximated by the blackbody spectrum.(a) The peak frequency of the spectrum is f = 3.4× 1014 Hz. What is the temperatureof the Sun?(b) The radius of the Sun is estimated to be 700,000 km. Find the total energyradiated by the Sun in a day (24 hours) in units of Joules and of eV. Hint: theStefan-Boltzmann law.

Question

Please do 2 Exercise #5 (updated)In class we found the number of standing wave modes (with polarizations) contained inbetween w and w + dw,Vw?N(w) dw =(1)where V is the volume of the cabity, V = L³. With this number density N(w), the totalmean energy of the blackbody radiation inside the cavity is obtained as|E(w, T) N (w)dw = | plw) dwE =(2)where E(w, T) =ehw /kpTand p(w) = E(w,T') N (w) is called the blackbody spectrum.a. What is the SI unit for the blackbody spectrum p(w)?b. Do the integral of Eq.(2) to find the energy density u = E/V of the blackbody radiationinside the cavity. Use the following formula:73(3)c. Borrowing a formula from electro-magnetic theory, the radiation flux J from the surfaceof the cavity can be written in terms of the energy density as J = cu/4. For theblackbody radiation, this can be written as J = oT with o the Stefan-Boltzmannconstant. Find the expression of o in terms of kg, h, and c, then compute the value.(If your calculator cannot handle it, you will need to work out powers by hand.)d. What is the SI unit for o supposed to be? Does your o have the correct unit?e. Find the peak frequency of p(w) as a function of T by solvingdp= 0dw(4)for w. Use the solution for 3+ e&#34;(x – 3) = 0, x = 2.824.f. What is the total power of the black body radiation from an object whose surface areais A and temperature is T? Use the Stefan-Boltzmann law, J = oTª.2. The Sun can be modeled as a sphere of gas in thermal equilibrium. This is justified bythat the spectrum of sunlight is well approximated by the blackbody spectrum.(a) The peak frequency of the spectrum is f = 3.4× 1014 Hz. What is the temperatureof the Sun?(b) The radius of the Sun is estimated to be 700,000 km. Find the total energyradiated by the Sun in a day (24 hours) in units of Joules and of eV. Hint: theStefan-Boltzmann law.

Accepted Answer

Using Wein's displacement Law

Where T = Temperature,   = Peak wavelength, b = Wein displacement…