Homework 12 due Wednesday, March 31

  1. Black holes are object whose gravity is so strong that not even an object moving at the speed of light cannot escape from their surface. Hence, black holes do not themselves emit light. But it is possible to detect radiation from material falling toward a black hole. Calculations suggest that as this matter falls, it is compressed and heated to temperatures around 106 K. Calculate the wavelength of maximum emission for this temerature. In what part of the electromagnetic spectrum does this wavelength lie?

    2. l = .0029/T = 2.9 x 10-9 m = 2.9 nm This is in the X-ray region of the spectrum.

  2. The bright star Rigel in the constellation Orion has a surface temperature of 12000 K. How much more energy is emitted each second from each square meter of Rigel's surface than from each square meter of the Sun's surface?

    3. F = sT4

    FRigel/FSun = sTRigel4/sTSun4 = 120004/58004 = 18

    Rigel emits18 times more energy per second per square meter than does the Sun.

  3. The spaces between the galaxies are filled with a very cold, very thin gas of hydrogen atoms. Ultraviolet radiation with any wavelength shorter then 91.2 nm cannot pass through this gas; instead it is absorbed. Explain why.

    A wavelength of 91.2 nm corresponds to an energy of 13.2 eV--the ionization energy of hydrogen. Thus any photon with a wavelength < 91.2 nm will free an electron from the hydrogen nucleus. If the photon has an even smaller wavelength, part of the energy is used to free the electron and the other part goes into the kinetic energy (energy of motion) of the electron.

  4. An imaginary atom has just 3 energy levels; 1 eV, 2 eV and 5 eV. Draw an energy level diagram for this atom. Show all possible transitions between these energy levels. For each transition, determine the photon energy and the photon wavelength. Which transitions (if any) involve the emission or absorption of visible light?

  5. A line in a star's spectrum lies at 400.0 nm. In the laboratory, that same line lies at 400.2 nm. How fast is the star moving along the line of sight; that is, what is its radial velocity? Is it moving toward or away from us?

    Because the observed line has a wavelength that is shorter than the laboratory (stationary) wavelength, the object is blueshifting and hence is moving toward us.

    Dl/l = v/c

    v = .2 * c/400.0 = 5 x 10-4 c