Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137488179
Author: Douglas Giancoli
Publisher: PEARSON+
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Chapter 37, Problem 77GP
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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Determine the distance between the electron and proton in an atom if the potential energy U of the electron is 13.8 ev (electronvolt, 1 eV = 1.6 × 10-19 J). Give your answer in
Angstrom (1 A = 10-10 m).
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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.
Determine the distance between the electron and proton in an atom if the potential energy U of the electron is 13.8 ev (electronvolt, 1 eV
-19
1.6 x 10 J). Give your answer in Angstrom (1 A = 10"1º m).
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Chapter 37 Solutions
Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
Ch. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4QCh. 37 - Prob. 5QCh. 37 - Prob. 6QCh. 37 - Prob. 7QCh. 37 - Prob. 8QCh. 37 - Prob. 9QCh. 37 - Prob. 10Q
Ch. 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. 1PCh. 37 - Prob. 3PCh. 37 - Prob. 7PCh. 37 - Prob. 9PCh. 37 - Prob. 13PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 32PCh. 37 - Prob. 34PCh. 37 - Prob. 37PCh. 37 - Prob. 45PCh. 37 - Prob. 52PCh. 37 - Prob. 76GPCh. 37 - Prob. 77GP
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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_forwardThe electron of a hydrogen atom is at a distance 5.3x10 m from the nucleus. If the charge of the nucleus is 1.6x10¹9 C, then the electrostatic potential energy (in electron volt (eV)) of the electron is: Select one: a. -1.5 b. 27.2 c. 1.5 d. -27.2 e. zeroarrow_forward
- Coulomb's Law yields an expression for the energy of interaction for a pair of point charges. V = 2.31x10^-19 Q1Q2 r V is the energy (in J) required to bring the two charges from infinite distance separation to distance r (in nm).Q1 and Q2 are the charges in terms of electrons.(i.e. the constant in the above expression is 2.31×10-19 J nm electrons-2) For a group of "point" charges (e.g. ions) the total energy of interaction is the sum of the interaction energies for the individual pairs.Calculate the energy of interaction for the square arrangement of ions shown in the diagram below. d = 0.545 nmarrow_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_forwardThe nucleus of a certain atom is 7.30 fm in diameter and has 76.0 protons. What is the acceleration of another proton 4.00 fm from the surface of the nucleus? - 2.35×1027 m/s2, away from the nucleus- 8.20×1028 m/s2, towards the nucleus- 6.55×1029 m/s2, towards the nucleus- 1.79×1029 m/s2, away from the nucleusarrow_forward
- 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)1,78.105arrow_forwardWhat is the electric field of a proton at the first Bohr orbit for hydrogen (r = 5.29 × 10−11 m)? What is the force on the electron in that orbit?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
- Consider 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_forwardIn a simple model of a hydrogen atom, the single electron orbits the single proton (the nucleus) in a circular path. Calculate (a) the electric potential set up by the proton at the orbital radius of 52.9 pm, (b) the electric potential energy of the atom, and (c) the kinetic energy of the electron. (d) How much energy is required to ionize the atom (that is, to remove the electron to an infinite distance with no kinetic energy)? Give the energies in electron-volts.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_forward
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