Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 37, Problem 83GP
To determine
The ratio of the gravitational force to the electric force for the electron in a hydrogen atom and to check whether the gravitational force can be ignored.
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Say you have a point charge of one Coulomb and a hydrogen atom some distance away. Within what distance would the difference of forces on the proton and electron from the Coulomb charge exceed the attraction between the proton and electron that holds the hydrogen atom together. Treat the hydrogen atom as a proton and electron 0.53 × 10−10 m (a.k.a., one Bohr radius) apart.
Using the virial theorem for a particle, determine the energy (in 10-18 J) of a charge electron revolving
around a nucleus of charge "Ze" at a distance "r".
Apply to the hydrogen atom whose radius is approximately r = 0,53x10-¹⁰ m
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Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 37.2 - Prob. 1AECh. 37.2 - Prob. 1BECh. 37.4 - Prob. 1CECh. 37.7 - Prob. 1DECh. 37.7 - Prob. 1EECh. 37.11 - Prob. 1FECh. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4Q
Ch. 37 - Prob. 5QCh. 37 - Prob. 6QCh. 37 - Prob. 7QCh. 37 - Prob. 8QCh. 37 - Prob. 9QCh. 37 - Prob. 10QCh. 37 - Prob. 11QCh. 37 - Prob. 12QCh. 37 - Prob. 13QCh. 37 - Prob. 14QCh. 37 - Prob. 15QCh. 37 - Prob. 16QCh. 37 - Prob. 17QCh. 37 - Prob. 18QCh. 37 - Prob. 19QCh. 37 - Prob. 20QCh. 37 - Prob. 21QCh. 37 - Prob. 22QCh. 37 - Prob. 23QCh. 37 - Prob. 24QCh. 37 - Prob. 25QCh. 37 - Prob. 26QCh. 37 - Prob. 27QCh. 37 - Prob. 28QCh. 37 - Prob. 1PCh. 37 - Prob. 2PCh. 37 - Prob. 3PCh. 37 - Prob. 4PCh. 37 - Prob. 5PCh. 37 - Prob. 6PCh. 37 - Prob. 7PCh. 37 - Prob. 8PCh. 37 - Prob. 9PCh. 37 - Prob. 10PCh. 37 - Prob. 11PCh. 37 - Prob. 12PCh. 37 - Prob. 13PCh. 37 - Prob. 14PCh. 37 - Prob. 15PCh. 37 - Prob. 16PCh. 37 - Prob. 17PCh. 37 - Prob. 18PCh. 37 - Prob. 19PCh. 37 - Prob. 20PCh. 37 - Prob. 21PCh. 37 - Prob. 22PCh. 37 - Prob. 23PCh. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 28PCh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43PCh. 37 - Prob. 44PCh. 37 - Prob. 45PCh. 37 - Prob. 46PCh. 37 - Prob. 47PCh. 37 - Prob. 48PCh. 37 - Prob. 49PCh. 37 - Prob. 50PCh. 37 - Prob. 51PCh. 37 - Prob. 52PCh. 37 - Prob. 53PCh. 37 - Prob. 54PCh. 37 - Prob. 55PCh. 37 - Prob. 56PCh. 37 - Prob. 57PCh. 37 - Prob. 58PCh. 37 - Prob. 59PCh. 37 - Prob. 60PCh. 37 - Prob. 61PCh. 37 - Prob. 62PCh. 37 - Prob. 63PCh. 37 - Prob. 64PCh. 37 - Prob. 65PCh. 37 - Prob. 66PCh. 37 - Prob. 67PCh. 37 - Prob. 68PCh. 37 - Prob. 69PCh. 37 - Prob. 70PCh. 37 - Prob. 71PCh. 37 - Prob. 72GPCh. 37 - Prob. 73GPCh. 37 - Prob. 74GPCh. 37 - Prob. 75GPCh. 37 - Prob. 76GPCh. 37 - Prob. 77GPCh. 37 - Prob. 78GPCh. 37 - Prob. 79GPCh. 37 - Prob. 80GPCh. 37 - Prob. 81GPCh. 37 - Prob. 82GPCh. 37 - Prob. 83GPCh. 37 - Prob. 84GPCh. 37 - Prob. 85GPCh. 37 - Prob. 86GPCh. 37 - Prob. 87GPCh. 37 - Prob. 88GPCh. 37 - Prob. 89GPCh. 37 - Prob. 90GPCh. 37 - Prob. 91GPCh. 37 - Prob. 92GPCh. 37 - Prob. 93GPCh. 37 - Show that the wavelength of a particle of mass m...Ch. 37 - Prob. 95GPCh. 37 - Prob. 96GPCh. 37 - Prob. 97GPCh. 37 - Prob. 98GPCh. 37 - Prob. 99GPCh. 37 - Prob. 100GP
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- The force on an electron is “negative the gradient of the potential energy function.” Use this knowledge and Equation 8.1 to show that the force on the electron in a hydrogen atom is given by Coulomb’s force law. Ur=ke2r(8.1)arrow_forwardIn the simple Bohr model of the ground state of the hydrogen atom, the electron travels in a circular orbit around a fixed proton. The radius of the orbit is 5.281011m , and the speed of the electron is 2.18106m/s . The mass of an electron is 9.111031kg . What is the force on the electron?arrow_forward. In the Bohr model of the hydrogen atom, an electron in the lowest energy state follows a circular path. [ Charge (q) = 1.6 x 10-19 C Coulomb's constant (k) = 8.89 x 10° N.m²/C?. Mass of electron (me) = 9.109 x 10-31 kg Plank's constant (h) = 6.63 x 10 34 J.s Bohr radius (ao) = 0.0529 nm] a) What distance does an electron in the ground state travel? b) Determine the velocity of the electron around its orbit. c) What is the effective current associated with this orbiting electron? %3D %3Darrow_forward
- Question 2 The Thomson model of a hydrogen atom is a sphere of positive charge with an electron (a point charge) at its center. The total positive charge equals the electronic charge e. Prove that when the electron is at a distance r from the center of the sphere of positive charge, it is attracted with a force F = 4TE,R where R is the radius of the sphere.arrow_forwardAn electron is 0.5 Å away from a carbon nucleus which contains 6 protons. Find the mutual force of attraction between the nucleus and the electron. 1Å (Angstrom)= 10^-10m, e=1.6x10^-19C.arrow_forward1.00g of hydrogen contains 6.02x10^23 atoms, each with one electron and one proton. Suppose that 1.00g of hydrogen is separated into protons and electrons, that the protons are placed at Earth's north pole, and that electrons are placed at Earth's south pole. Find the magnitude of the resulting compressional force on Earth. (The radius of Earth is approximately 6.38x10^6 m). * 5.12x10^5 N 4.23x10^5 N 6.43x10^6 N 6.87x10^6 N None of the Abovearrow_forward
- electrons Two protons (p) and two (e) are arranged on a circle of 5 [cm], with angles 0₁ = 20°, 0₂ = 60°, 03 = 20° and 04 = 60°, as radius r shown in the figure. (qp = +1.6 x 10-1⁹ [C] and qe = -1.6 × 10-19 [C]). The figure is not to scale. 04 y a. Find Enet, the net electric field vector produced at the center of the circle. Enet =([ ])i + ( ]) Ĵ [N/C] b. Where on the circle should a fifth point charge qo be placed (give its angle relative the +x-axis) and what is its value (calculate qo) in order to have Ēnet (the net electric field at the center of the circle) equals zero (Type the detailed solution to this question in the below box, Show all your calculation steps by typing in the box). Р Xarrow_forward198. 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)1,78.105arrow_forwardThe classic Millikan oil drop experiment setup is shown below. In this experiment oil drops are suspended in a vertical electric field against the gravitational force to measure their charge. If the mass of a negatively charged drop suspended in an electric field of 1.76 ✕ 10−4 N/C strength is 8.620 ✕ 10−21 g, find the number of excess electrons in the drop.arrow_forward
- An 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_forwardE (eV) -0.54 -0.85 n = ∞ n = 5 n = 4 -1.51 n = 3 -3.40 n = 2 -13.59 n = 1 The figure shows some energy levels of hydrogen. If the magnitude of the elementary charge were 10e instead of e, how would the ground state energy of hydrogen be affected?arrow_forwardDetermine the gravitational force and the electric force between the electron and the proton inthe hydrogen atom of they are 5.3×10^-11 meters apart. Then calculate the ratio of Fe to Fg.arrow_forward
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