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Chapter 36: Q. 5 (page 1059)
An out-of-control alien spacecraft is diving into a star at a speed of . At what speed, relative to the spacecraft, is the starlight approaching?
The speed will be speed of light c.
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The radioactive element radium (Ra) decays by a process known as alpha decay, in which the nucleus emits a helium nucleus. (These high-speed helium nuclei were named alpha particles when radioactivity was first discovered, long before the identity of the particles was established.) The reaction is , where Rn is the element radon. The accurately measured atomic masses of the three atoms are , , and . How much energy is released in each decay? (The energy released in radioactive decay is what makes nuclear waste “hot.”)
The sun radiates energy at the rate . The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is .
a. How much mass does the sun lose each year?
b. What percent is this of the sun’s total mass?
c. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun’s lifetime, giving your answer in billions of years.
A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 * 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes.
a. Is it possible that the explosion of Alpha is in any way responsible for the explosion of Beta? Explain.
b. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?
On a futuristic highway, a long rocket travels so fast that a red stoplight, with a wavelength of , appears to the pilot to be a green light with a wavelength of . What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?
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