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Announcements

Announcements. Homework: Supplemental Problems 2 nd Project is due at the final exam which is 4:00pm Tues day May 6 . A list of potential projects is posted.

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Announcements

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  1. Announcements • Homework: Supplemental Problems • 2nd Project is due at the final exam which is 4:00pm Tuesday May 6. A list of potential projects is posted. • Final Exam will be another hour exam covering the material we cover in the last four weeks of class. It will be the second thing during the final exam period (project presentation first)

  2. The Heisenberg Uncertainty Principle is one of the fundamental tenants of Quantum Mechanics DE is the energy. Basically the rest mass energy of the particles (E = mc2). Dt is how long a virtual pair exists for and is Planck’s constant divided by 2p

  3. A consequence of the Uncertainty Principle is that empty space isn’t empty

  4. Steven Hawking applied the uncertainty principle to the space near a black hole

  5. Example An electron-positron virtual pair is created near the event horizon of a black hole. How long can the pair last for? If the electron is moving at almost the speed of light, how close to the event horizon must it be to fall in before the pair annihilates?

  6. Example Solution Now that we know how long the pair can last we can find how far they can travel during that time This is larger than the diameter of a nucleus (10-15 m) but smaller than the diameter of an atom (10-12 m)

  7. The Temperature of a black hole depends on its mass h = Planck constant = 6.626 x 10-34 J-s Kb = Boltzmann constant = 1.38065 x 10-23 J/K The emission of a black hole is very similar to that of a perfect black body at the given temperature

  8. Because they radiate, the will eventually evaporate away The lifetime of a black hole is proportional to its mass raised the third power

  9. Examples Determine the temperature and lifetime of a 5.0 solar mass black hole. Determine the temperature and lifetime of the supermassive black hole at the center of the Milky Way which has a mass of 4.1 x 106 solar masses

  10. Example Solution For a 5.0 solar mass black hole

  11. Example Solution 2

  12. Just for the fun of it! We now know the temperature and radius of a one solar mass black hole. Assuming it is a perfect black body, what is it’s luminosity? RS = 2952 m T = 3.88 x 10-7 K As a comparison, the energy of a single photon of visible light with a wavelength of 500 nm is about 4 x 10-19 J so this is the equivalent of emitting a single photon of visible light every 2.82 x 106 s or every 32.6 days. That’s dim!!!

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