Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 9, Problem 39SP
With the previous problem in mind, what is the
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An old model of a hydrogen atom has the charge +e of the proton uniformly distributed over a sphere of radius a0, with the electron of charge -e and mass m at its center. (a) What would then be the force on the electron if it were displaced from the center by a distance r # a0? (b) What would be the angular frequency of oscillation of the electron about the center of the atom once the electron was released?
Consider 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.
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 potential energy of the system (the nucleus and the two electrons)?
Chapter 9 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Ch. 9 - 17. A wheel spins around exactly 6 times. How many...Ch. 9 - 18. Given that a disk revolves through 81.681...Ch. 9 - 19. Convert (a) 50.0 rev to radians, (b) 48π rad...Ch. 9 - 20. Express 40.0 deg/s in (a) rev/s, (b) rev/min,...Ch. 9 - 21. A 2.00-m-long steel rod, pivoted at one end,...Ch. 9 - 22. A pendulum swings through an angle of 20.0°,...Ch. 9 - 23. A pebble is stuck in the tread of a tire...Ch. 9 - 24. A sphere rotates about a fixed axis 10.0 times...Ch. 9 - 25. A flywheel turns at 480 rpm. Compute the...Ch. 9 - 26. It is desired that the outer edge of a...
Ch. 9 - 27. Through how many radians does a point fixed on...Ch. 9 - 28. A wheel 25.0 cm in radius turning at 120 rpm...Ch. 9 - 29. The angular speed of a disk decreases...Ch. 9 - 30. A car wheel 30 cm in radius is turning at a...Ch. 9 - 31. A wheel revolving at 6.00 rev/s has an angular...Ch. 9 - 32. A thin string wound on the rim of a wheel 20...Ch. 9 - 9.33 [II] A mass of 1.5 kg out in space moves in a...Ch. 9 - 34. (a) Compute the radial acceleration of a point...Ch. 9 - 35. A mass is whirling in a circle at the end of a...Ch. 9 - 36. A mass is whirling in a circle at the end of a...Ch. 9 - 37. Imagine a weightless 2.00-kg mass far out in...Ch. 9 - 38. The old Bohr model of the hydrogen atom has a...Ch. 9 - 39. With the previous problem in mind, what is the...Ch. 9 - Prob. 40SPCh. 9 - 41. A car moving at 5.0 m/s tries to round a...Ch. 9 - 42. A box rests at a point 2.0 m from the central...Ch. 9 - 43. A stone rests in a pail which is tied to a...Ch. 9 - Prob. 44SPCh. 9 - 45. Refer back to Fig. 9-6. How large must h be...Ch. 9 - 46. If, in Fig. 9-6 and in Problem 9.33, h = 2.5R,...Ch. 9 - 47. A satellite orbits the Earth at a height of...Ch. 9 - 49. The human body can safely tolerate a vertical...Ch. 9 - 50. A 60.0-kg pilot in a glider traveling at 40.0...Ch. 9 - 51. Suppose the Earth is a perfect sphere with R =...Ch. 9 - 9.52 [III] A mass m hangs at the end of a pendulum...
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- if the chlorine molecule at 290K were to rotate at the angular frequency predicted by the equipartition theorem what would be the average centipital force ? ( the atoms of Cl are 2 x 10-10 m apart and the mass of the chlorine atom 35.45 a.m.u )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 total kinetic energy of the electrons?arrow_forwardThe velocity of electron in the first Bohr orbit of radius 0.5 A.U. is 2.24 x 106 m/s. Calculate the period of revolution of the electron in the same orbit.arrow_forward
- (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy? (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 m, how many joules of kinetic energy will it have when it reaches the ground? (c) Is it reasonable that a 30-kg child could run fast enough to have 100 J of kinetic energy?arrow_forward(a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 x 10⁰ m as the average Earth- Moon distance and 2.36 × 106 s as the period of the Moon in its orbit. (Use 7.36 × 1022 kg for the mass of the moon.) 2.889e34 kg. m²/s (b) If the angular momentum of the moon obeys Bohr's quantization rule (L = nħ) determine the value of the quantum number, n. 8.463e67 Your response differs from the correct answer by more than 10%. Double check your calculations. (c) By what fraction would the Earth-Moon radius have to be increased to increase the quantum number by 1? 2.3632e-6 X Your response differs from the correct answer by more than 100%.arrow_forwardIt may be argued on theoretical grounds that the radius of the hydrogen atom should depend only on the fundamental constants h, e, the electrostatic force constant k = 1/4πℰ0, and m (the electron’s mass). Use dimensional analysis to show that the combination of these factors that yields a result with dimensions of length is h2kme2.arrow_forward
- Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², L₂ = m₂h, 1 = 0,1,2,..., n-1 m₁ = 0, +1, +2, ..., ±l 3 1 S² = s(s+1)h²=h², S₂ = m₂h = + = h +/-ħ 4 Consider an excited electron (n > 1) on an H-atom. What is the minimum angle 0min that the S can have with the z-axis? Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forward(a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 × 108 m as the average Earth- Moon distance and 2.36 × 106 s as the period of the Moon in its orbit. (Use 7.36 × 1022 kg for the mass of the moon.) kg. m²/s 2.889e34 (b) If the angular momentum of the moon obeys Bohr's quantization rule (L: nh) determine the value of the quantum number, n. 2.7395e68 (c) By what fraction would the Earth-Moon radius have to be increased to increase the quantum number by 1? 1.825e-69 X Your response differs from the correct answer by more than 10%. Double check your calculations.arrow_forwardFor each of the following transitions in a hydrogen atom free of external fields, determine whether the electron energy increases, decreases, or remains unchanged. Indicate your answers with I, D, or U. (a) The electron moves from n = 2 to n = 4. (b) The electron moves from n = 4 ton= 3. (c) Within 3 level, the electron moves from e the n = 2 to l =-2. (d) Within the n = 4, € = 2 sublevel, the electron moves from = - 1 to me = + 1. me %3Darrow_forward
- 13.10 If the radial momentum p, and radial velocity a, for an electron in a central potential are defined by r.p-ih a.r Pr = Xr= " r r show that ihk Ba, (ap) = ar Pr + r B(o'. L + h) where k = ħarrow_forwardDetermine the distance between the electron and proton in an atom if the potential energy U of the electron is 13 eV (electronvolt, 1 eV = 1.6 x 10-19 J). Give your answer in Angstrom (1 A = 10-10 m). Answer: Choose... +arrow_forwardAn electron is orbiting a nucleus which has a charge of 14e, under the action of the Coulomb force at a radius of 1.14 × 10-¹0 m. Calculate the angular velocity of the electron, in radians per second. @=||arrow_forward
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