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- A charge of 36.3 nC is transferred to a neutral copper ball of radius 4.35 cm. The ball is not grounded. The excess electrons spread uniformly on the surface of the ball. What is the number density (number of electrons per unit surface area) of excess electrons on the surface of the ball?Calculate the speed of (a) an electron and (b) a proton with a kinetic energy of 1.00 electron volt (eV). (c) Calculate the average translational kinetic energy in cV of a 3.00 102 K ideal gas particle. (Recall from Topic 10 that 12mv2 = 32kBT.)Calculate the speed of (a) an electron and (b) a proton with a kinetic energy of 1.00 electron volt (eV). (c) Calculate the average translational kinetic energy in cV of a 3.00 102 K ideal gas particle. (Recall from Topic 10 that 12mv2 = 32kBT.)
- In the Millikan oil-drop experiment illustrated in Figure 15.21, an atomizer (a sprayer with a fine nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more excess electrons. The charge on the plates is adjusted so that the electric force on the excess electrons exactly balances the weight of the droplet. The idea is to look for a droplet dial has the smallest electric force and assume it has only one excess electron. This strategy lets the observer measure the charge on the electron. Suppose we are using an electric field of 3 104 N/C. The charge on one electron is about 1.6 1019 C. Estimate the radius of an oil drop of density 858 kg/m5 for which its weight could be balanced by the electric force of this field on one electron. (Problem 42 is courtesy of E.F. Redish. For more problems of this type, visit www.physics.umd.cdu/pcrg/.)In the classical model of a hydrogen atom, an electron orbits a proton with a kinetic energy of +13.6 eV and an electric potential energy of 27.2 eV. (a) Use the kinetic energy to calculate the classical orbital speed. (b) Use the electric potential energy to calculate the classical orbital radius.In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 10-27 kg, is a product of certain radioactive decay's. The results of the experiment led Rutherford to the idea that most of an atoms mass is in a very small nucleus, with electrons in orbit around it. (This is the planetary model of the atom, which well study in Chapter 42.) Assume an alpha particle, initially very far from a stationary gold nucleus, is fired with a velocity of 2.00 107 m/s directly toward the nucleus (charge +79e). What is the smallest distance between the alpha particle and the nucleus before the alpha particle reverses direction? Assume the gold nucleus remains stationary.
- An electron with charge e and mass m moves in a circular orbit of radius r around a nucleus of charge Ze, where Z is the atomic number of the nucleus. Ignore the gravitational force between the electron and the nucleus. Find an expression in terms of these quantities for the speed of the electron in this orbit.The probability of fusion occurring is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high- temperature gas ions or by accelerating the nuclei toward one another. (a) Calculate the potential energy of two singly charged nuclei separated by 1.001012. (b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?What is the magnitude of the repulsive force between a 3.4 mC charge and a 6.3 mC charge if they are separated by a distance of 93 centimeters? Report your answer kN rounded up to the tenths place
- You have 2.4 kg of water. One mole of waterhas a mass of 18.1 g/mole and each moleculeof water contains 10 electrons since water isH2 O.What is the total electron charge containedin this volume of water? The elementarycharge is 1.6 × 10−19 C .1. −1.17116 × 1082. −1.72253 × 1083. −9.58218 × 1074. −1.27762 × 1085. −7.45281 × 1076. −1.61487 × 1087. −2.12937 × 1078. −1.50722 × 1089. −3.22975 × 10710. −1.07658 × 108Answer in units of CI have placed an electron at the origin. The grid spacing is 1 Angstrom per small square. Now place an atomic nucleus with 8 protons on positive x-axis, at x = 7.2 Angstroms. How much work did it take you to bring this nucleus in from 1 m away? 20.8 eV 12.0 eV 16.0 eV 8.0 eVWith what electrical force do an electron and a proton located 10 ^ -7 m apart attract or repel each other?Data: qe = -1.6⋅10 ^ -19C; qp = 1.6⋅10 ^ -19C; K = 9⋅10 ^ 9N⋅m ^ 2 / C ^ 2