8. In a simple model of the hydrogen atom, an electron of mass m and charge 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 that the kinetic energy of the electron is; e2 where r is the radius of the orbit and ε, is the permittivity of free space. (ii) Find the total energy of the electron. (iii) Given that the angular momentum of the electron nh equal to where 2π n is an integer and h is Plank's constant, show that the total energy of 1 the electron is:En = −() me n²
8. In a simple model of the hydrogen atom, an electron of mass m and charge 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 that the kinetic energy of the electron is; e2 where r is the radius of the orbit and ε, is the permittivity of free space. (ii) Find the total energy of the electron. (iii) Given that the angular momentum of the electron nh equal to where 2π n is an integer and h is Plank's constant, show that the total energy of 1 the electron is:En = −() me n²
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter24: Electric Potential
Section: Chapter Questions
Problem 37AP
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