1) (a) How can neutron stars in a binary system generate X rays? (b) What do the
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Question
1) (a) How can neutron stars in a binary system generate X rays?(b) What do the words absolute and visual mean in the definition of absolute visual magnitude?
2) To demonstrate the relative strengths of the electrical and gravitational forces of attraction between the electron and the proton in the Bohr atom, suppose the hydrogen atom were held together solely by the force of gravity. Determine the radius of the ground state orbit (in units of nm and AU) and the energy of the ground state (eV).
3) Show that the relativistic kinetic energy of the particle can be written as
Where is the magnitude of the particle’s relativistic momentum. This demonstrates that in the low-speed Newtonian limit of , (as expected).
Explanation / Answer
A two-solar-mass neutron star would not be more compact than 10,970 meters radius (AP4 model). Its mass fraction gravitational binding energy would then be 0.187, -18.7% (exothermic). This is not near 0.6/2 = 0.3, -30%. A neutron star is so dense that one teaspoon (5 milliliters) of its material would have a mass over 5.5×1012 kg, about 900 times the mass of the Great Pyramid of Giza.[14] The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7.2 million kilometers per hour.[15] The temperature inside a newly formed neutron star is from around 1011 to 1012 kelvin.[7] However, the huge number of neutrinos it emits carries away so much energy that the temperature falls within a few years to around 106 kelvin.[7] Even at 1 million kelvin, most of the light generated by a neutron star is in X-rays. In visible light, neutron stars probably radiate approximately the same energy in all parts of visible spectrum, and therefore appear white.
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