a Find the energy of a photon with this wavelength Jphoton b

(a) Find the energy of a photon with this wavelength.
  J/photon

(b) What is the surface temperature of the star?
K

(c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e = 1)
in W

(d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star.
photons/s

Solution

a) Using Planck\'s equation .. E = hc/
E = 6.626^-34 x 3.0^8m/s / 676^-9m .. .. E = 2.9386^-19 J

b) Using Wien\'s displacement law .. (max) x T= 2.898^-3 mK
T = 2.898^-3mK / 676^-9m .. .. T = 4.2863^3 K (4230 K)

c) Using Stefan\'s black-body equation .. (P/A) = T^4
emissivity = 1, Stefan constant = , (P/A) = emission intensity (W/m²) ..

Energy emission rate (J/s) = power .. P = A T^4 .. (A = star surface area 4R²)

P = {4(8.53^8m)²}(1 x 5.70^-8)(4230K)^4 .. .. P = 2.107^27 W

d) Photon rate = N/s (number per sec)

E(J) x N/s = P (J/s)
N/s = P / E = 2.107^27 J/s / 2.9386^-19 J .. .. N/s = 7.170^45 s¹