Quantum Physics

Problems 897The probability per unit volume of finding the particleat a particular point at some instant is proportional to 2 . Quantum mechanics has been highly successfulin describing the behavior of atomic and molecularsystems.27.8 The Uncertainty PrincipleAccording to Heisenberg’s uncertainty principle, it isimpossible to measure simultaneously the exact positionand exact momentum of a particle. If x is theuncertainty in the measured position and p x theuncertainty in the momentum, the product x p x isgiven byAlso,E t [27.17]where E is the uncertainty in the energy of the particleand t is the uncertainty in the time it takes to measurethe energy.h4x p x h4[27.16]CONCEPTUAL QUESTIONS1. If you observe objects inside a very hot kiln why is itdifficult to discern the shapes of the objects?2. Why is an electron microscope more suitable thanan optical microscope for “seeing” objects of atomicsize?3. Are blackbodies black?4. Why is it impossible to simultaneously measure theposition and velocity of a particle with infinite accuracy?5. All objects radiate energy. Why, then, are we not ableto see all objects in a dark room?6. Is light a wave or a particle? Support your answer by citingspecific experimental evidence.7. A student claims that he is going to eject electronsfrom a piece of metal by placing a radio transmitterantenna adjacent to the metal and sending a strongAM radio signal into the antenna. The work functionof a metal is typically a few electron volts. Will thiswork?8. Light acts sometimes like a wave and sometimes like aparticle. For the following situations, which best describesthe behavior of light? Defend your answers.(a) The photoelectric effect. (b) The Compton effect.(c) Young’s double-slit experiment.9. In the photoelectric effect, explain why the stoppingpotential depends on the frequency of the light butnot on the intensity.10. Which has more energy, a photon of ultraviolet radiationor a photon of yellow light?11. Why does the existence of a cutoff frequency in thephotoelectric effect favor a particle theory of lightrather than a wave theory?12. What effect, if any, would you expect the temperatureof a material to have on the ease with whichelectrons can be ejected from it via the photoelectriceffect?13. The cutoff frequency of a material is f 0 . Are electronsemitted from the material when (a) light of frequencygreater than f 0 is incident on the material? (b) Less thanf 0 ?14. The brightest star in the constellation Lyra is thebluish star Vega, whereas the brightest star in Boötes isthe reddish star Arcturus. How do you account for thedifference in color of the two stars?15. If the photoelectric effect is observed in one metal,can you conclude that the effect will also be observedin another metal under the same conditions?Explain.16. A beam of blue light and a beam of red light carry thesame total amount of energy. Which beam contains thelarger number of photons?17. An x-ray photon is scattered by an electron which isinitially at rest. What happens to the frequency ofthe scattered photon relative to that of the incidentphoton?