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Chapter 6: Q74PP (page 1253)
In the alternate universe, how fast must an object be moving for it to have a kinetic energy equal to its rest mass?
(a) 225m/s; (b) 260m/s; (c) 300m/s; (d) The kinetic energycould not be equal to the rest mass
The speed of the object is 260m/s .
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The bonding of gallium arsenide ( ) is said to be ionic and covalent. Explain.
In photosynthesis in plants, light is absorbed in light-harvesting complexes that consist of protein and pigment molecules. The absorbed energy is then transported to a specialized complex called the reaction center.
Quantum-mechanical effects may play an important role in this energy transfer. In a recent experiment, researchers cooled rubidium atoms to a very low temperature to study a similar energy transfer process in the lab. Laser light was used to excite an electron in each atom to a state with large n. This highly excited electron behaves much like the single electron in a hydrogen atom, with an effective (screened) atomic number. Because n is so large, though, the excited electron is quite far from the atomic nucleus, with an orbital radius of approximately 1 mm, and is weakly bound. Using these so-called Rydberg atoms,the researchers were able to study the way energy is transported from one atom to the next. This process may be a model for understanding energy transport in photosynthesis. (Source: 鈥淥bserving the
Dynamics of Dipole-Mediated Energy Transport by Interaction Enhanced Imaging,鈥� by G. G眉nter et al., Science342(6161): 954鈥�956, Nov. 2013.)
Assume that the researchers place an atom in a state with,. What is the magnitude of the orbital angular momentum LS associated with this state? (a); (b); (c); (d).
Many of the stars in the sky are actually binary stars, in which two stars orbit about their common centre of mass. If the orbital speeds of the stars are high enough, the motion of the stars can be detected by the Doppler shifts of the light they emit. Stars for which this is the case are called spectroscopic binary stars. Figure p=37.68 shows the simplest case of a spectroscopic binary star: two identical stars, each with mass m, orbiting their centre of mass in a circle of radius R. The plane of the stars鈥� orbits is edge-on to the line of sight of an observer on the earth. (a) The light produced by heated hydrogen gas in a laboratory on the earth has a frequency of . In the light received from the stars by a telescope on the earth, hydrogen light is observed to vary in frequency between and . Determine whether the binary star system as a whole is moving toward or away from the earth, the speed of this motion, and the orbital speeds of the stars. (Hint: The speeds involved are much less than c, so you may use the approximate result given in Section 37.6.) (b) The light from each star in the binary system varies from its maximum frequency to its minimum frequency and back again in 11 days. Determine the orbital radius R and the massm of each star. Give your answer form in kilograms and as a multiple of the mass of the sun, . Compare the value of to the distance from the earth to the sun, . (This technique is actually used in astronomy to determine the masses of stars. In practice, the problem is more complicated because the two stars in a binary system are usually not identical, the orbits are usually not circular, and the plane of the orbits is usually tilted with respect to the line of sight from the earth.)
A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet with a speed of 0.600c. The pursuit ship is travelling at a speed of 0.800crelative to Tatooine, in the same direction as the cruiser. What is the speed of the cruiser relative to the pursuit ship?
A hydrogen atom is in a d state. In the absence of an external magnetic field, the states with different values have (approximately) the same energy. Consider the interaction of the magnetic field with the atom鈥檚 orbital magnetic dipole moment. (a) Calculate the splitting (in electron volts) of the m l levels when the atom is put in a 0.800-T magnetic field that is in the +z-direction. (b) Whichlevel will have the lowest energy? (c) Draw an energy-level diagram that shows the d levels with and without the external magnetic field
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