Problem 2: Black hole – the ultimate blackbody A black hole emits blackbody radiation called Hawking radiation. A black hole with mass M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of hc³/167²KGM. a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole. b) Calculate the total power radiated by a one-solar mass black hole. c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing. As it loses energy, its mass must decrease; one could say "evaporates". Derive a differential equation for the mass as a function of time, and solve to obtain an expression for the lifetime of a black hole in terms of its mass.

Part C At a local high school track meet, an athlete in the 100 m spring reaches a top speed of 6.6 V(vm m/s)). If the athlete's mass is 59 V{vm kg}\) , what is their de Broglie wavelength? 1.55x10-28 (vm m)\) O 3.41x10-36 vvm m)) 1.70x10-36 V(vm m)\) O 5.87x1035 V{\vm m}\) Submit Request Answer Part D What is the longest wavelength of the Balmer series (\(n'=2\))? O 1.82x10-7 v\m m}\) O 1.22x10-7 {\m m}\) O 3.65x10-7 {\vm m}\) O 6.56x10-7 Vm m}\) O 5.47x10-7 vm m)) Submit Request Answer

) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?

What is the wavelength (in m) of a 2.06 eV photon? Find its frequency in hertz.