Black holes are objects in Outer Space that have so much mass in such a small volume, nothing can escape from them, not even light. Suppose a black hole is eating a companion star. As the gas from the companion star falls into the black hole, just before it passes the point of no return, the black hole’s tremendous gravity compresses the gas so that its temperature rises to 10 million K. Because this gas is so dense, it is opaque, so it radiates X-rays into space. At what wavelength does this gas radiate its maximum intensity?
) (a) Black holes are objects in Outer Space that have so much mass in such a small volume, nothing can
escape from them, not even light. Suppose a black hole is eating a companion star. As the gas from the
companion star falls into the black hole, just before it passes the point of no return, the black hole’s
tremendous gravity compresses the gas so that its temperature rises to 10 million K. Because this gas is so
dense, it is opaque, so it radiates X-rays into space. At what wavelength does this gas radiate its maximum
intensity?
(b) How many kiloelectron-volts (or keV) does each X-ray photon in (8)(a) have?
(c) An electron microscope uses magnets to accelerate electrons with negligible initial speed through a
potential difference of 50 million volts. Calculate the ratio of the resolution of this electron microscope to the
resolution of a microscope that uses visible light with a wavelength of 5.00 × 10−7 m through a circular
aperture with an aperture of 5.00 mm.
(d) A common science-fiction concept is the transporter unit (like in Star Trek), sometimes alternatively called
a transmat beam. Such a (fictional) device turns matter into energy and then beams this energy across space,
to be re-assembled into matter somewhere else. Calculate how many meters one could transport a person with
a mass of 75 kg at the
like this with individual electrons: numerous electronic devices such as tunnel diodes make use of it.
(e) Cosmic rays are high-energy protons from Outer Space. They are accelerated to relativistic speeds by
supernovae, which are exploding stars. The highest-energy cosmic ray ever observed had an energy of
3.0 × 1020 eV. That is about as much as the kinetic energy of a tennis ball with a speed of over 90
miles/hour—for one proton.
The Universe is filled with a thin soup of microwaves that are left over from when the Universe originated
13.80 ± 0.02 billion years ago in a hot, dense state widely referred to as the Big Bang. These microwaves are
called the Cosmic Background Radiation. They fit a thermal spectrum with a temperature of 2.725 K.
If cosmic rays with higher energies existed, astronomers could not detect them directly, because they would
lose energy by colliding with the photons of the Cosmic Background Radiation. The process by which they
lose energy is called the inverse Compton effect, in which a fast charged particle collides with a low-energy
photon and become a slower charged particle and a higher-energy photon.
Suppose a cosmic ray with E = 3.0 × 1020 eV collides head-on with a microwave photon in the Cosmic
Background Radiation. The photon is scattered straight backward. The cosmic ray does not change direction
in the collision. The collision is otherwise elastic, with the total energy of both particles being the same before
and after the collision. How many electron-volts (eV) does the cosmic ray lose in the collision?
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