A black hole acts like a blackbody. Consider a mini black hole having a mass of

Question

A black hole acts like a blackbody. Consider a mini black hole having a mass of 2^*10^19kg. Assuming it radiated just like a blackbody, what is the total power in W/m radiated by the black hold and at what frequency would the spectral radiancy function be maximum? Say the Earth was at rest relative to this far away black hole and this light made it to the Earth's surface. What would a person on the surface of the Earth observe the wavelength of this light to be? (Earth's radius is 6.371^*10^6m and Earth's mass is 5.97219^*10^24,kg)

Explanation / Answer

Temperature of black hole T = 6150 K

Power = sigma T^4

P = 5.67 e -8 * 6150^4

P = 8.11 e 7 W/m^2

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from Weins Dispalcement law L T = 0.0029

L = 0.0029/(6150

L = 471.2 nm

use V = Lf

f = V/L = 3 e8/(471.1 e -9) = 6.4 e 14 Hz

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part B :

delta L/L = V/c

Lambda L' = L*(1 + V/c)

Lambda = 848.2 nm

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