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CSM.10 One way to measure nuclear radii is to determine the initial speed that a proton fired at a nucleus must have to be absorbed. Suppose you fire a proton directly at the nucleus of a gold atom, which contains 79 protons and neutrons. Since both the proton and the gold nucleus are positively charged, they will repel each other electrostati cally. What must the proton's minimum initial speed (as a fraction of the speed of light) be if it is to penetrate that nucleus (whose radius is R 6 fm)? (a) Give your answer symbolically in terms of R, the Cou- lomb constant 1/4TEo, the speed of light c, the charge on the proton q, and the proton's mass m. (b) What is this fraction's numerical value? (Hints: What must the proton's speed be at its point of closest approach if the collision is head-on and it barely touches the nucleus? Note also that the particles' initial separation will be essentially infinite compared to 6 fm. Neutrons have no charge, so the charge of a gold nucleus will be 79 times that of the proton. Finally, note that this whole interaction will take only a tiny fraction of a second.)

CSM.10 One way to measure nuclear radii is to determine the initial speed that a proton fired at a nucleus must have to be absorbed. Suppose you fire a proton directly at the nucleus of a gold atom, which contains 79 protons and neutrons. Since both the proton and the gold nucleus are positively charged, they will repel each other electrostati cally. What must the proton's minimum initial speed (as a fraction of the speed of light) be if it is to penetrate that nucleus (whose radius is R 6 fm)? (a) Give your answer symbolically in terms of R, the Cou- lomb constant 1/4TEo, the speed of light c, the charge on the proton q, and the proton's mass m. (b) What is this fraction's numerical value? (Hints: What must the proton's speed be at its point of closest approach if the collision is head-on and it barely touches the nucleus? Note also that the particles' initial separation will be essentially infinite compared to 6 fm. Neutrons have no charge, so the charge of a gold nucleus will be 79 times that of the proton. Finally, note that this whole interaction will take only a tiny fraction of a second.)

Modern Physics
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter14: Nuclear Physics Applications
Section: Chapter Questions
Problem 33P
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CSM.10 One way to measure nuclear radii is to determine the initial speed that a proton fired at a nucleus must have to be absorbed. Suppose you fire a proton directly at the nucleus of a gold atom, which contains 79 protons and neutrons. Since both the proton and the gold nucleus are positively charged, they will repel each other electrostati cally. What must the proton's minimum initial speed (as a fraction of the speed of light) be if it is to penetrate that nucleus (whose radius is R 6 fm)? (a) Give your answer symbolically in terms of R, the Cou- lomb constant 1/4TEo, the speed of light c, the charge on the proton q, and the proton's mass m. (b) What is this fraction's numerical value? (Hints: What must the proton's speed be at its point of closest approach if the collision is head-on and it barely touches the nucleus? Note also that the particles' initial separation will be essentially infinite compared to 6 fm. Neutrons have no charge, so the charge of a gold nucleus will be 79 times that of the proton. Finally, note that this whole interaction will take only a tiny fraction of a second.)
Transcribed Image Text:CSM.10 One way to measure nuclear radii is to determine the initial speed that a proton fired at a nucleus must have to be absorbed. Suppose you fire a proton directly at the nucleus of a gold atom, which contains 79 protons and neutrons. Since both the proton and the gold nucleus are positively charged, they will repel each other electrostati cally. What must the proton's minimum initial speed (as a fraction of the speed of light) be if it is to penetrate that nucleus (whose radius is R 6 fm)? (a) Give your answer symbolically in terms of R, the Cou- lomb constant 1/4TEo, the speed of light c, the charge on the proton q, and the proton's mass m. (b) What is this fraction's numerical value? (Hints: What must the proton's speed be at its point of closest approach if the collision is head-on and it barely touches the nucleus? Note also that the particles' initial separation will be essentially infinite compared to 6 fm. Neutrons have no charge, so the charge of a gold nucleus will be 79 times that of the proton. Finally, note that this whole interaction will take only a tiny fraction of a second.)
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