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A hydrogen atom (with the Bohr radius of half an angstrom)

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 1P Chapter 4

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 1P

A hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage you would need with this apparatus to ionize the atom. [Use the value of α in Table 4.1. Moral: The displacements we’re talking about are minute, even on an atomic scale.]

Step-by-Step Solution:

Solution 1P

Step 1 of 4:

Consider a hydrogen atom with the Bohr radius of one angstrom, which is situated in between two metal plates, which are connected to the opposite terminals of a  battery. We need to find out what fraction of the atomic radius does the separation distance  amount to and the voltage need with this apparatus to ionize the atom.

The electric field between the plates,

Where  is the electric field potential, .

 is the separation between the plates,

So                         

Step 2 of 4

Chapter 4, Problem 1P is Solved
Step 3 of 4

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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A hydrogen atom (with the Bohr radius of half an angstrom)