Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 8, Problem 55E
(a)
To determine
The effective orbit radius for
(b)
To determine
(c)
To determine
Protons to be unscreened to the
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198. In Fig. 89, four electrons, located at the vertices of a square of side a=1mm, rotate
describing a circular orbit around the proton. This is located in the center of the square. Find
the angular velocity (lattice/s) of the movement of electrons through the orbit. (m=9,1 . 10-³1
kg, k=9 x 10° N. m²/C²)
(a)1,70.105
b)1,72.105
c)1,74.10¹
Fig.89
d)1,76.105
-e
c)1,78.105
Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the total kinetic energy of the electrons?
Bohr’s model of the atom of hydrogen can be compared to the Earth-Moon system. Inthis analogy, the role of the Earth is played by the proton and the Moon by the electron, andthe gravitational attraction is replaced by the electrostatic one. The mean distance betweenan electron and a proton in the atom is approximately 0.5 ×10−10m.
(a) Given this model, what would be the frequency of rotation of the electron around theproton? Compare this to the frequency of visible light.
(b) What is the speed of the electron in this orbit? Is electrostatics a good approximationin this case? Is it appropriate to use non-relativistic mechanics?
Chapter 8 Solutions
Modern Physics
Ch. 8 - A dipole without angular momentum can simply...Ch. 8 - Prob. 2CQCh. 8 - Prob. 3CQCh. 8 - Prob. 4CQCh. 8 - Prob. 5CQCh. 8 - Prob. 6CQCh. 8 - Prob. 7CQCh. 8 - Prob. 8CQCh. 8 - Prob. 9CQCh. 8 - Prob. 10CQ
Ch. 8 - Prob. 11CQCh. 8 - Prob. 12CQCh. 8 - Prob. 13CQCh. 8 - Prob. 14CQCh. 8 - Prob. 15CQCh. 8 - Lithium is chemically reactive. What if electrons...Ch. 8 - Prob. 17CQCh. 8 - Prob. 18CQCh. 8 - Prob. 19CQCh. 8 - Prob. 20CQCh. 8 - Prob. 21CQCh. 8 - Prob. 22CQCh. 8 - Prob. 23CQCh. 8 - The total-spin singlet state for two electrons has...Ch. 8 - Prob. 25ECh. 8 - Prob. 26ECh. 8 - Show that the frequency at which an electron’s...Ch. 8 - Prob. 28ECh. 8 - Prob. 29ECh. 8 - Prob. 30ECh. 8 - Prob. 31ECh. 8 - Prob. 33ECh. 8 - Prob. 34ECh. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - Prob. 38ECh. 8 - Prob. 39ECh. 8 - Prob. 41ECh. 8 - Prob. 42ECh. 8 - The Slater determinant is introduced in Exercise...Ch. 8 - Prob. 44ECh. 8 - Exercise 44 gives an antisymmetricmultiparticle...Ch. 8 - Prob. 46ECh. 8 - Prob. 48ECh. 8 - Write the electronic configurations for...Ch. 8 - Prob. 50ECh. 8 - Prob. 51ECh. 8 - Prob. 52ECh. 8 - Prob. 53ECh. 8 - Prob. 54ECh. 8 - Prob. 55ECh. 8 - Prob. 56ECh. 8 - Prob. 57ECh. 8 - Prob. 58ECh. 8 - Prob. 59ECh. 8 - The well-known sodium doublet is two yellow...Ch. 8 - Prob. 61ECh. 8 - Prob. 62ECh. 8 - Prob. 64ECh. 8 - Prob. 65ECh. 8 - Prob. 66ECh. 8 - Prob. 67ECh. 8 - Prob. 68ECh. 8 - Prob. 69ECh. 8 - Prob. 70ECh. 8 - Repeat Example 8.6, but assume that the upper...Ch. 8 - Prob. 72ECh. 8 - Prob. 73ECh. 8 - Prob. 74ECh. 8 - Using J2=L2+S2+2LS to eliminate LS , as well as...Ch. 8 - A hydrogen atom is subjected to a magnetic field...Ch. 8 - Prob. 77ECh. 8 - Prob. 78ECh. 8 - Prob. 79ECh. 8 - Prob. 80ECh. 8 - Prob. 81ECh. 8 - As is done for helium in Table 8.3, determine for...Ch. 8 - Prob. 83CECh. 8 - Prob. 84CECh. 8 - Prob. 85CE
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- A negative helium ion would attract additional electrons. O True O Falsearrow_forwardConsider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. Determine the radius of the orbit and the orbital speed of each electron.arrow_forwardConsider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the potential energy of the system (the nucleus and the two electrons)?arrow_forward
- (1) The charge of the tin nucleus is 50e +. Calculate the voltage at a point 10 m away from it, as well as the potential energy of a proton at this point, noting that the charge of the Burton is e = 1.6 x 10 -19c + %3Darrow_forwardA monatomic ion has a charge of +2. The nucleus of the ion has a mass number of 86. The number of neutrons in the nucleus is 1.26 times that of the number of protons. How many electrons and what is the element?arrow_forwardsince charge of electron q = -1.6 x 10-19, shouldn't solution for k = -3.2 x 10-17 ? Why was the negative sign removed in the solution above, was it an error?arrow_forward
- An electron revolves around the nucleus of an atom in a circular orbit of radius 4.0Å with a speed of 6.0 x 10^6 ms-1. Calculate the linear kinetic energy.arrow_forwardConsider a two-electron atom in which the electrons, orbiting a nucleus of charge+Ze, follow Bohr-like orbits of the same radius r, with the electrons always on opposite sides of the nucleus. (a) Show that the net force on each electron is toward the nucleus and has magnitude. (b) Use the fact that this is the centripetal force to show that the square of each electron’s orbital speed v is given by as attached.arrow_forwardAs per Bohr model of a hydrogen atom for a stable orbit centripetal, Coulomb, and all forces should be in equilibrium. Therefore, for an electron with mass me and speed v₁ on the nth orbit with radius rn, (k being Coulomb/s constant) mevn = ke²/rn mevn² = ke²/rn mevn²/rn = ke²/rn 2.2 Ome²v² = ke²/r²arrow_forward
- For a K*- CF ion pair, attractive and repulsive energies E, and ER, respectively, depend on the distance between the ions r, according to 1.436 E4 -- 5.8 x 10-6 ER = For these expressions, energies are expressed in electron volts per K*- Cl- pair, and r is the distance in nanometers. a) If the net energy EN is just the sum of the two expressions above: EN = E+ ER, Find the values of r, and E,? b) If curves of E,, ER and EN are plotted in given figure, compare E, the calculated values of ro and E, with that from the graph. -0.28 nm E,-4.6 eV 0.00 0 10 0.20 0.30 0.40 0.50 060 0.70 0.80 00 1.00arrow_forwardChapter 39, Problem 043 In the ground state of the hydrogen atom, the electron has a total energy of -13.6 ev. What are (a) its kinetic energy and (b) its potential energy if the electron is a distance 4.0a from the central nucleus? Here a is the Bohr radius. (a) Number Units eV (b) Number Units eVarrow_forwardConsider the element Hydrogen. In this atom, assume the electron travels with a speed of 6.8 105 m/s. What is the radius between the nucleus and the orbiting electron in m?arrow_forward
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