68 A muon of charge -e and mass m = 207m. (where m, is theтmass of an electron) orbits the nucleus of a singly ionized heliumatom (He*). Assuming that the Bohr model of the hydrogen atomcan be applied to this muon-helium system, verify that the energylevels of the system are given by11.3 keVE =n-

Answered: 68 A muon of charge -e and mass m =…

College Physics

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Chapter28: Special Relativity

Section: Chapter Questions

Problem 56PE: A positron is an antimatter version of the electron, having exactly the same mass. When a positron...

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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.
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.)
List all the possible values of s and msfor an electron. Are there particles for which these values are different? The same?
(a) Calculate the mass of a proton using the charge-to-mass ratio given for it in this chapter and its known charge. (b) How does your result compare with the proton mass given in this chapter?
An atom can be formed when a negative muon is captured by a proton. The muon has the same charge as the electron and a mass 207 times that of the electron. Calculate the frequency of the photon emitted when this atom makes the transition from n=2 to the n=1 state. Assume that the muon is orbiting a stationary proton.
Nobel laureate Richard Feynman (19181088) once said that if two persons stood at arms length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a weight equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion.
The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.061010 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20106 m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?
An electron is to be accelerated in a uniform electric field having a strength of 2.00106 V/m. (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?
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.
Review. From a large distance away, a particle of mass m1, and positive charge q1 is fired at speed in the positive x direction straight toward a second particle, originally stationary but free to move, with mass m2, and positive charge q2. Both particles are constrained to move only along the x axis. (a) At the instant of closest approach, both particles will be moving at the same velocity. Find this velocity, (b) Find the distance of closest approach. After the interaction, the particles will move far apart again. At this time, find the velocity of (c) the particle of mass m1, and (d) the particle of mass m2.
Use the laws of conservation of momentum and energy to explain how a shape charge can direct most of the energy released in an explosion in a specific direction. (Note that this is similar to the situation in guns and cannonsmost of the energy goes into the bullet.)

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