University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Chapter 7, Problem 104AP
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A 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.
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?
Calculate 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.
Chapter 7 Solutions
University Physics Volume 2
Ch. 7 - Check Your Understanding If Q has a mass of 4.00 g...Ch. 7 - Check Your Understanding What is the potential...Ch. 7 - Check Your Understanding Is the electrical...Ch. 7 - Check Your Understanding How much energy does a...Ch. 7 - Check Your Understanding How many electrons would...Ch. 7 - Check Your Understanding How would this example...Ch. 7 - Check Your Understanding From the examples, how...Ch. 7 - Check Your Understanding What is the potential...Ch. 7 - Check Your Understanding What is the potential on...Ch. 7 - Check Your Understanding What is the potential on...
Ch. 7 - Check Your Understanding Which coordinate system...Ch. 7 - Check Your Understanding What are the...Ch. 7 - Would electric potential energy be meaningful if...Ch. 7 - Why do we need to be careful about work done on...Ch. 7 - Does the order in which we assemble a system of...Ch. 7 - Discuss how potential difference and electric...Ch. 7 - What is die strength of the electric field in a...Ch. 7 - If a proton is released from rest in an electric...Ch. 7 - Voltage is the common word for potential...Ch. 7 - If the voltage between two points is zero can a...Ch. 7 - Wliat is the relationship between voltage and...Ch. 7 - Voltages are always measured between two points...Ch. 7 - How are units of volts and electron-volts related?...Ch. 7 - Can a particle move in a direction of increasing...Ch. 7 - Compare the electric dipole moments of charges +Q...Ch. 7 - Would Gauss’s law be helpful for determining the...Ch. 7 - In what region of space is the potential due to a...Ch. 7 - Can the potential of a nonuniformly charged sphere...Ch. 7 - If the electric field is zero throughout a region,...Ch. 7 - Explain why knowledge of E(x, y, z) is not...Ch. 7 - If two points are at the same potential, are there...Ch. 7 - Suppose you have a map of equipotential surfaces...Ch. 7 - Is the electric potential necessarily constant...Ch. 7 - Linder electrostatic conditions, the excess charge...Ch. 7 - - Can a positively charged conductor be at a...Ch. 7 - Can equipotential surfaces intersect?Ch. 7 - Why are the metal support rods for satellite...Ch. 7 - (a) Why are fish reasonably safe in an electrical...Ch. 7 - What are the similarities and differences between...Ch. 7 - About what magnitude of potential is used to...Ch. 7 - Consider a charge Q1(1+5.0C) fixed at a site with...Ch. 7 - Two charges Q1(1+2.00C) and Q2(+2.00C are placed...Ch. 7 - To form a hydrogen atom, a proton is fixed at a...Ch. 7 - (a) What is the average power output of a heart...Ch. 7 - Find the ratio of speeds of an electron and a...Ch. 7 - An evacuated tube uses an accelerating voltage of...Ch. 7 - Show that units of V/m and N/C for electric field...Ch. 7 - What is the strength of the electric field between...Ch. 7 - The electric field strength between two parallel...Ch. 7 - The voltage across a membrane forming a cell wall...Ch. 7 - Two parallel conducting plates are separated by...Ch. 7 - Find the maximum potential difference between two...Ch. 7 - An electron is to be accelerated in a uniform...Ch. 7 - Use die definition of potential difference in...Ch. 7 - The electric field in a region is pointed away...Ch. 7 - Singly charged gas ions are accelerated from rest...Ch. 7 - A 0.500-cm-diameter plastic sphere, used in a...Ch. 7 - How far from a 1.00C point charge is the potential...Ch. 7 - If the potential due to a point charge is 5.00102...Ch. 7 - In nuclear fission, a nucleus splits roughly in...Ch. 7 - A research Vail de Graaff generator has a 2.00-m-...Ch. 7 - An electrostatic paint sprayer has a...Ch. 7 - (a) What is the potential between two points...Ch. 7 - Find the potential at points P1,P2,andP4 in the...Ch. 7 - Two charges 20Cand+2.0C are separated by 4.0 cm on...Ch. 7 - (a) Plot the potential of a uniformly charged 1-m...Ch. 7 - Throughout a region, equipotential surfaces are...Ch. 7 - In a particular region, the electric potential is...Ch. 7 - Calculate the electric field of an infinite line...Ch. 7 - Two very large metal plates are placed 2.0 cm...Ch. 7 - A very large sheet of insulating material has had...Ch. 7 - A metallic sphere of radius 2.0 cm is charged with...Ch. 7 - Two large charged plates of charge density 30C/m2...Ch. 7 - A long cylinder of aluminum of radius R meters is...Ch. 7 - Two parallel plates 10 cm on a side are given...Ch. 7 - The surface charge density on a long straight...Ch. 7 - Concentric conducting spherical shells carry...Ch. 7 - Shown below are two concentric spherical shells of...Ch. 7 - A solid cylindrical conductor of radius a is...Ch. 7 - (a) What is the electric field 5.00 m from die...Ch. 7 - (a) What is the direction and magnitude of an...Ch. 7 - A simple and common technique for accelerating...Ch. 7 - In a Geiger counter, a thin metallic wire at the...Ch. 7 - The practical limit to all electric field in air...Ch. 7 - To form a helium atom, an alpha particle that...Ch. 7 - Find the electrostatic energy of eight equal...Ch. 7 - The probability of fusion occurring is greatly...Ch. 7 - A bare helium nucleus has two positive charges and...Ch. 7 - An election enters a region between two large...Ch. 7 - How far apart are two conducting plates that have...Ch. 7 - (a) Will the electric field strength between two...Ch. 7 - Membrane walls of living cells have surprisingly...Ch. 7 - A double charged ion is accelerated to an energy...Ch. 7 - The temperature near the center of the Sun is...Ch. 7 - A lightning bolt strikes a tree, moving 20.0 C of...Ch. 7 - What is the potential 0.5301010 m from a proton...Ch. 7 - (a) A sphere has a surface uniformly charged with...Ch. 7 - What are the sign and magnitude of a point charge...Ch. 7 - In one of the classic nuclear physics experiments...Ch. 7 - A 12.0-V battery-operated bottle warmer heats 50.0...Ch. 7 - A battery-operated car uses a 12.0-V system. Find...Ch. 7 - (a) Find the voltage near a 10.0 cm diameter metal...Ch. 7 - A uniformly charged ring of radius 10 cm is placed...Ch. 7 - A glass ring of radius 5.0 cm is painted with a...Ch. 7 - A CD disk of radius (R = 3.0 cm) is sprayed with a...Ch. 7 - (a) What is the final speed of an electron...Ch. 7 - A large metal plate is charged uniformly to a...Ch. 7 - Your friend gets really excited by the idea of...Ch. 7 - (a) Find x L limit of the potential of a finite...Ch. 7 - A small spherical pith ball of radius 0.50 cm is...Ch. 7 - Two parallel conducting plates, each of...Ch. 7 - A point charge of q=50108 C is placed at the...Ch. 7 - Earth has a net charge that produces an electric...Ch. 7 - Point charges of 25.0/ C and 45. C are placed...Ch. 7 - What can you say about two charges q1and q2 if the...Ch. 7 - Calculate the angular velocity of an electron...Ch. 7 - An electron has an initial velocity of 5.00106m/s...Ch. 7 - Three Na+ and three Cl ions are placed alternately...Ch. 7 - Look up (presumably online, or by dismantling an...Ch. 7 - Use the electric field of a finite sphere with...Ch. 7 - Calculate the electric field of a dipole...
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- A uniformly charged ring of radius R = 25.0 cm carrying a total charge of 15.0 C is placed at the origin and oriented in the yz plane (Fig. P24.54). A 2.00-g particle with charge q = 1.25 C, initially at the origin, is nudged a small distance x along the x axis and released from rest. The particle is confined to move only in the x direction. a. Show that the particle executes simple harmonic motion about the origin. b. What is the frequency of oscillation for the particle? Figure P24.54arrow_forward(a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if tlie proton had the same speed as the election? (c) What would the radius be if the proton had tlie same kinetic energy' as die electron? (d) The same momentum?arrow_forwardIn the classic model of the hydrogen atom proposed by Niels Bohr, the electron rotates around a stationary proton in a circular orbit with an approximate radius r = 0.053 nm, see the figure below. (a) Find the magnitude of the electrostatic force of attraction, Fe, between the electron and the proton. (b) Find the magnitude of the gravitational force of attraction, Fg, between the electron and the proton, and then find the Fe / Fg ratio.arrow_forward
- In the early 1900s, scientists modelled the hydrogen atom as an electron orbiting a proton. Like when we look at the Earth and Sun, we can consider the proton to be stationary, and the electron to be in orbit around the proton in a perfect circle. Unlike the Earth and Sun, the force responsible for the circular motion of the electron is the attractive electric force between the proton and electron. All other forces can be ignored. Experiments showed that the electron's orbital radius was 5.29x10^-11m. a) Calculate the speed of the electron in its orbit. b) Show that the circumference of the electron's orbit (2 times pi times radius) is about equal to the electron's De Broglie wavelength at that speed. Electron: mass = 9.11x10^-31kg, charge = -1.60x10^-19C. Proton: mass = 1.67x10^-27kg, charge = +1.60x10^-19C. Coulomb's constant: k = 9.00x10^9 Nm^2/C^2 Planck's constant: h = 6.63x10^-34 Jsarrow_forwardA particle has a mass of 1.2 × 10-5 kg and a charge of 4 × 10-5 C. It is released from rest at point Y and accelerates until it reaches a point Z. The particle moves on a horizontal straight line and does not rotate. The only forces acting on the particle are the gravitational force and the electrostatic force. If the translational speed of the particle at point Z is 10 m/s what is VY – VZ ?arrow_forwardIn the early 1900s, scientists modelled the hydrogen atom as an electron orbiting a proton. Like when we look at the Earth and Sun, we can consider the proton to be stationary, and the electron to be in orbit around the proton in a perfect circle. Unlike the Earth and Sun, the force responsible for the circular motion of the electron is the attractive electric force between the proton and electron. All other forces can be ignored. Experiments showed that the electron's orbital radius was 5.29x10^-11m. a) Calculate the speed of the electron in its orbit. b) At what radius must the electron orbit such that the circumference is twice the De Broglie wavelength? Remember that at a different value of radius, the speed changes as seen in part (a). Explain your calculations. Electron: mass = 9.11x10^-31kg, charge = -1.60x10^-19C. Proton: mass = 1.67x10^-27kg, charge = +1.60x10^-19C. Coulomb's constant: k = 9.00x10^9 Nm^2/C^2 Planck's constant: h = 6.63x10^-34 Jsarrow_forward
- provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 3.09 × 10-11 m. Determine the magnitude of the electron's centripetal acceleration.arrow_forwardIn 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_forwardIn 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.arrow_forward
- A particle of charge Q is fixed at the origin of an xy coordinatesystem. At t = 0 a particle (m = 0.800 g, q = 4.00 mC) is locatedon the x axis at x = 20.0 cm, moving with a speed of 50.0 m/sin the positive y direction. For what value of Q will the moving particleexecute circular motion? (Neglect the gravitational force onthe particle.)arrow_forwardAn 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.arrow_forwardMultiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 3.58 x 10 11 m. Determine the magnitude of the electron's centripetal acceleration. 台灣彩彩彩 Number Units 彩arrow_forward
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