Suppose a star with radius 8.66 times 10^8 m has a peak wavelength of 684 nm in

Question

Suppose a star with radius 8.66 times 10^8 m has a peak wavelength of 684 nm in the spectrum of its emitted radiation. (a) Find the energy of a photon with this wavelength. 2.91e - 19 J/photon (b) What is the surface temperature of the star? 4.24e3 K (c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e = 1). 1.69e18 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. W (d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star. 6 73e36 You. response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully, photon/s

Explanation / Answer

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(8.66*10^8m)²}(1 x 5.67*10^-8)(4240K)^4 .. .. P = 1.73*10^26 W

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

E(J) x N/s = P (J/s)
N/s = P / E = 1.72*10^26 J/s / 2.91*10^-19 J .. .. N/s = 5.93*10^44 s¹

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