Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 23, Problem 44PQ
(a)
To determine
The speed of the electron.
(b)
To determine
The frequency for the circular motion of electron.
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In one model of the hydrogen atom, the electron revolves in a circular orbit of radius 5.3 x 10-11 m. Calculate the speed of the electron.
An electron has a mass of 9.11x10-31 kg. In the Bohr model of the hydrogen atom, the electron was viewed as orbiting the lone proton of the nucleus; the centripetal force requirement was met by the electrical attraction between the oppositely charged proton and electron. The radius of orbit was 5.29x10-11 m. Use circular motion and electrostatic principles to determine the speed at which the electron moves as it orbits the proton.
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Chapter 23 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 23.2 - Initially a glass rod and a piece of silk are...Ch. 23.3 - a. In Figure 23.8, why are there three plus signs...Ch. 23.3 - When wool is rubbed against amber, the wool...Ch. 23.3 - Prob. 23.4CECh. 23.4 - The following scenarios involve a metal ball and a...Ch. 23.4 - Prob. 23.6CECh. 23 - What is the difference between a contact force and...Ch. 23 - Many textbooks claim Franklin decided that moving...Ch. 23 - An object has a charge of 35 nC. How many excess...Ch. 23 - As part of a demonstration, a physics professor...
Ch. 23 - A single coulomb represents a large amount of...Ch. 23 - A sphere has a net charge of 8.05 nC, and a...Ch. 23 - A glass rod is initially neutral. After it is...Ch. 23 - After an initially neutral glass rod is rubbed...Ch. 23 - A 50.0-g piece of aluminum has a net charge of...Ch. 23 - Prob. 10PQCh. 23 - A silk scarf is rubbed against glass, and a wool...Ch. 23 - CASE STUDY A person in Franklins time may have...Ch. 23 - Prob. 13PQCh. 23 - Prob. 14PQCh. 23 - A charge of 36.3 nC is transferred to a neutral...Ch. 23 - Prob. 16PQCh. 23 - Prob. 17PQCh. 23 - An electrophorus is a device developed more than...Ch. 23 - Prob. 19PQCh. 23 - An electroscope is a device used to measure the...Ch. 23 - Two particles with charges of +5.50 nC and 8.95 nC...Ch. 23 - Particle A has a charge of 34.5 nC, and particle B...Ch. 23 - Prob. 23PQCh. 23 - Prob. 24PQCh. 23 - Particle A has charge qA and particle B has charge...Ch. 23 - Two charged particles are placed along the y axis....Ch. 23 - A 1.75-nC charged particle located at the origin...Ch. 23 - A 1.75-nC charged particle located at the origin...Ch. 23 - Two particles with charges q1 and q2 are separated...Ch. 23 - An electron with charge e and mass m moves in a...Ch. 23 - Two electrons in adjacent atomic shells are...Ch. 23 - Two small, identical metal balls with charges 5.0...Ch. 23 - Two identical spheres each have a mass of 5.0 g...Ch. 23 - One end of a light spring with force constant k =...Ch. 23 - Two 25.0-g copper spheres are placed 75.0 cm...Ch. 23 - Three charged particles lie along a single line....Ch. 23 - Given the arrangement of charged particles shown...Ch. 23 - Given the arrangement of charged particles in...Ch. 23 - Given the arrangement of charged particles in...Ch. 23 - Three charged metal spheres are arrayed in the xy...Ch. 23 - Charges A, B, and C are arrayed along the y axis,...Ch. 23 - Three identical conducting spheres are fixed along...Ch. 23 - Charges A, B, and C are arranged in the xy plane...Ch. 23 - Prob. 44PQCh. 23 - A particle with charge q is located at the origin,...Ch. 23 - Figure P23.46 shows four identical conducting...Ch. 23 - Prob. 47PQCh. 23 - Two metal spheres of identical mass m = 4.00 g are...Ch. 23 - Figure P23.49 shows two identical small, charged...Ch. 23 - Two small spherical conductors are suspended from...Ch. 23 - Four equally charged particles with charge q are...Ch. 23 - Four charged particles q, q, q, and q are Fixed...Ch. 23 - A metal sphere with charge +8.00 nC is attached to...Ch. 23 - Prob. 54PQCh. 23 - Three small metallic spheres with identical mass m...Ch. 23 - How does a negatively charged rubber balloon stick...Ch. 23 - How many electrons are in a 1.00-g electrically...Ch. 23 - Prob. 58PQCh. 23 - Prob. 59PQCh. 23 - Prob. 60PQCh. 23 - Three charged particles are arranged in the xy...Ch. 23 - A We saw in Figure 23.16 that a neutral metal can...Ch. 23 - Prob. 63PQCh. 23 - A Figure P23.65 shows two identical conducting...Ch. 23 - Two helium-filled, spherical balloons, each with...Ch. 23 - Two small metallic spheres, each with a mass of...Ch. 23 - A Two positively charged spheres with charges 4e...Ch. 23 - Prob. 69PQCh. 23 - Three charged spheres are at rest in a plane as...Ch. 23 - Prob. 71PQCh. 23 - Three particles with charges of 1.0 C, 1.0 C, and...Ch. 23 - A Two positively charged particles, each with...Ch. 23 - Prob. 74PQCh. 23 - Eight small conducting spheres with identical...Ch. 23 - Prob. 76PQCh. 23 - Prob. 77PQCh. 23 - Prob. 78PQCh. 23 - Prob. 79PQ
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- In a classical model of a hydrogen atom, there is a proton at the center of the atom and an electron travelling in a circular orbit around the proton. If the radius of the electron’s orbit is r = 5x10^-10 metres, how long does it take the electron to go around the proton once?arrow_forwardTwo plane parallel plates A and B situated in a vacuum at a distance of 3 cm. An electron starts from rest at the negative plate and reaches the half-way between plates after 4.8 x 10-9 s. Calculate (i) the impact velocity. (ii) the time the electron takes to reach a speed of 7.5 x 106 m/s. (iii) the position of the electron after 3.6 x 10-9 s.arrow_forwardA hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 9.2 *105 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.arrow_forward
- A hydrogen atom when in its lowest energy state consists of a proton nucleus of charge +e (remember that +e = 1.6 x 10-19 C) and an electron of charge -e and mass of 9.1 x 10-31 kg. In the Bohr model of the atom, the electron moves around the nucleus in an approximately circular orbit with a radius of 0.52 x 10-10 m. The speed of the electron when in this lowest energy orbit is approximately 2.3 x 106 m/s. Imagine that we want to ionize this atom (that is free up the electron from its nucleus) by launching ANOTHER electron at the atom to break it apart. If we were to launch this electron from very far away from the atom, then how fast must it be launched in order to break apart the atom, so that all three particles (the proton and two electrons) end up at rest, very far apart?arrow_forwardAn electron has a mass of 9.11x10-31 kg. In the Bohr model of the hydrogen atom, the electron is viewed as orbiting the single proton in the nucleus; the centripetal force is provided by the electrical attraction between the oppositely charged proton and electron. The radius of orbit is 5.29x10-11 m. What is the speed at which the electron moves as it orbits the proton. (Hint: Centripetal acceleration is v2/r.) A) 2.28*106 m/s B) 5.33*104 m/s C) None of these.arrow_forwardIn the Rutherford model of the hydrogen atom, a proton (mass M, charge Q) is the nucleus and an electron (mass m, charge q) moves around the proton in a circle of radius r. Let k denote the Coulomb force constant (1/4TTE0) and G the universal gravitational constant. The ratio of the electrostatic force to the gravitational force between electron and proton is: O kMm/GQq O kQq/GMm O GQq/kMm O GMm/kQq O kQq/GMmr²arrow_forward
- In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius rB = 0.053 nm around a stationary proton. (a) Ignoring the gravitational attraction between the electron and the proton, how many revolutions per second does the electron make? (b) Which force is larger, the electric force the proton exerts on the electron or the gravitational force the proton exerts on the electron? By how much?arrow_forwardA uranium ion and an iron ion are separated by a distance of, R=23.30 nm, as shown in the figure. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance r from the uranium atom at which an electron will be in equilibrium. Ignore the gravitational attraction between the particles. What is the magnitude ?UFU of the force on the electron from the uranium ion?arrow_forwardIn a classical model of a hydrogen atom, there is a proton at the centre of the atomand an electron travelling in a circular orbit around the proton. If the radius of theelectron’s orbit is r = 0.5 × 10^-10 metres, how long does it take the electron to goaround the proton once?arrow_forward
- A uranium ion and an iron ion are separated by a distance of ?=57.10 nm, as shown in the figure. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance ? from the uranium atom at which an electron will be in equilibrium. Ignore the gravitational attraction between the particles. ?= What is the magnitude ?U of the force on the electron from the uranium ion?arrow_forwardr -e Physical constants (A) What is the radius of the orbit with n = 4? (B) What is the speed of the orbit with n = 4? The old Bohr model of the hydrogen atom was based on... (1) the assumption that the electron travels on a circle h = 6.626 x 10-34 Js; -28 (A) (in m) Bohr Model mv² r mvr = n and obeys Newton's second law, and (2) the hypothsis that angular momentum is quantized. For the Bohr model, Ke² = 2.307 x 107 Jm; 31 m9.11 x 10 kg. (B) (in m/s) Ke² 12. (1) (2) OA: 2.034x10-10 OB: 2.706x10-10OC: 3.598x10-10 OD: 4.786x10-10 OE: 6.365x10-10 OF: 8.466x10-10 OG: 1.126x109 OH: 1.497x109 OA: 8.533x104 OB: 1.237x105 OC: 1.794x105 OD: 2.601x105 OE: 3.772x105 OF: 5.470x105 OG: 7.931x105 OH: 1.150x106arrow_forwardCalculate the angular velocity ω of an electron orbiting a proton in an atom, assuming the radius of the orbit is 5.02×10^-11 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.arrow_forward
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