8. In a simple model of the hydrogen atom, an electron of mass m andcharge e is considered to move in a nearly circular orbit about a proton.(i) Write down the expression for the force on the electron, and show thatthe kinetic energy of the electron is where r is the radius of thee2περιorbit and ε, is the permittivity of free space.(ii) Find the total energy of the electron.nh(iii) Given that the angular momentum of the electron equal to wheren is an integer and h is Plank's constant, show that the total energy ofthe electron is: En=- -me8ɛh²/ n²

Answered: Image /qna-images/answer/21ea80a7-58e0-4497-968d-786167ed04fa.jpg

Answered: 8. In a simple model of the hydrogen…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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13. The electron in a CRT are accelerated through a potential difference of 30 kV. (a) Do the electrons move from a region of high potential to a region of low potential, or vice versa? (b) What is the change in kinetic energy of one of the electrons? (c) If the initial speed is very small, what is the final speed of the electron?
2. Charged particle interactions and energy conservation A stationary charge, Q =+ 31.0µC, remains fixed in position. A moving charge, q =+7.70µC, with mass, m = 1.18 x 10 kg, heads toward this stationary charge along the x axis. The moving charge starts at position A with an initial speed of 892 m/s. Point A is 1.64 m from the fixed charge. Point B is 0.550 m from the fixed charge. a. Use energy conservation principles to set up an energy conservation equation for this system. b. Solve the energy conservation equation for the speed of the moving charge, Vx, when it reaches point B. %3D q, m Q >+x axis A Fixed stationary charge
2. In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The KE of the protons is used to kill cells in the tumor. For one patient, it is desired to deposit 0.1 J of proton energy into a tumor. To create the beam, proton at rest are accelerated through a potential difference of 10 MV (megavolts). a) What is the KE of a single proton fired at the tumor? b) How many protons must be fired at the tumor? ans. 6.25×1010 protons
5) Consider a set of individual point charges arranged along the x-axis with 9₁=2q x₁=b 9₂=9 x₂=3b q3=-2q x=4b where q is some base amount of charge and b is some distance unit. Calculate the total energy of the system (hint use equation 2.41).
3a. What is the potential energy U of this lightning bolt? U = 310 Joules of the square? Find 30 (1.0x10) 3b. If all this energy where to be converted to kinetic energy, what would be the speed of a m = 1000 kg car. Vf = r16 = 34 = m/s 16. These charges are numbered as: raw the re Redraw the rectangle with the actual charges (evaluate 2q1, 492, etc.) 16a. What is the distance between the indicated pairs of charges. Find these in meters. r24 = r26 = 15 = 35 = P278Volt Volts 1 2 3 MI 4 5 6 16b. Starting with all the charges at ∞, what is the potential at the upper left corner, and how much work is done to put the charge at the upper left corner? V₁ = 05 W₁ = Joules ainT V3 = V13 + V23 = srpC = 10-12 Cond m 16c. What is the potential at the location of 2, due to the previous charges? How much work is done to bring in the 2nd charge? Make sure you use the correct distance. V₂ = V12 = Volts W₂ = 16d. What is the potential at the location of 3, due to the previous charges? How much work is…
To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of 0.529 × 10-10m, the average distance between proton and electron in a hydrogen atom. How much work is done? O a. 4.36 × 10-20 J O b. 4.36 × 10-18 J O c. 4.36 x 10-16 J O d. 4.36 x 10-¹² J
The distance, r, between the proton and electron in the hydrogen atom is about 1010 m. Determine the value of the kinetic energy of the electron. Provide your answer in electron-volts (eV).
One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r) = U0 [(r0 / r)16 - (r0 / r)9] where r0 = 0.70 nm and U0 = 7.0 eV. Note: 1 eV = 1.6*10-19 J. You can use SI units, but CAPA will also accept these units that will simplify your calculations: [Force] = eV/nm[Energy] = eV[distance] = nm r_eq = 7.6 *10^-1 nm If the distance between the atoms increases from equilibrium by r1 = 0.20 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract). F_r (r_eq +r_1) = ? The atoms are oscillating back and forth. The maximum separation of the atoms is r2 = 2.2 nm. What is the kinetic energy of the atoms when they are separated by the equilibrium distance? K(r_eq) = ?
In the Bohr model of the hydrogen (H) atom, the electron moves on a circular path (orbit) around the nucleus,which consists of a single proton. In the ground state of H (the lowest energy level of H), the electron orbitsthe proton at a distance of 0.529 A (or 5.29 × 10^−11 m; 1 A˚ = 10^−10 m) with a linear speed of 2.19 × 10^6 m/s.(a) What is the angular speed of the electron?(b) How many orbits around the proton does the electron make each second?(c) What is the electron’s centripetal acceleration?
1)What is the electric potential due to the nucleus of hydrogen at a distance of 6.50×10-11 m? Assume the potential is equal to zero as r→∞. (Express your answer to three significant figures.)

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