Answer to Question #166937 in Astronomy | Astrophysics for Marie

Question

a) . If the emitted infrared radiation from Pluto, has a wavelength of maximum intensity at 75,000 nm, what is the temperature of Pluto assuming it follows Wien’s law?

b) What is the energy of the photon with the wavelength of 150 nm? 

c) Would you prefer to be irradiated by radio wavelength radiation or gamma ray wavelength radiation? Why? 

Answer 1

a) According to Wien's law, the temperature of maximum the spectral radiance of black-body radiation is

$T = \dfrac{0.002898\,\mathrm{m\cdot K}}{\lambda\,\mathrm{m}} = \dfrac{0.002898\,\mathrm{m\cdot K}}{7.5\cdot10^4\cdot10^{-9}\,\mathrm{m}} = 38.64\,\mathrm{K}.$

b) The energy of photon may be obtained as

$E = h\nu = h \cdot \dfrac{c}{\lambda} = 6.626\cdot10^{−34}\,\mathrm{J\cdot s} \cdot \dfrac {3\cdot10^8\,\mathrm{m/s}}{150\cdot10^{-9}\,\mathrm{m}} = 1.33\cdot10^{-18}\,\mathrm{J}.$

c) The energy of radiation is proportional to the frequency. We know that gamma ray radiation has significantly larger frequency than radio wavelength radiation, so gamma ray radiation will have a much greater impact on our body. Therefore, I'll prefer radiation with smaller energy.