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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 22 / Problem 55P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: Thomson’s Model of the Atom, Continued. Using

Chapter 22, Problem 55P

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QUESTION:

Problem 55P

Thomson’s Model of the Atom, Continued. Using Thomson’s (outdated) model of the atom described in Problem 22.54, consider an atom consisting of two electrons, each of charge \(-e\), embedded in a sphere of charge \(+2 e\) and radius R. In equilibrium, each electron is a distance d from the center of the atom (Fig. P22.55). Find the distance d in terms of the other properties of the atom.

Equation Transcription:

$-e$

$+2e$

$+2e$

$-e$

$-e$

Text Transcription:

-e

+2e

+2e

-e

-e

Questions & Answers

QUESTION:

Problem 55P

Thomson’s Model of the Atom, Continued. Using Thomson’s (outdated) model of the atom described in Problem 22.54, consider an atom consisting of two electrons, each of charge \(-e\), embedded in a sphere of charge \(+2 e\) and radius R. In equilibrium, each electron is a distance d from the center of the atom (Fig. P22.55). Find the distance d in terms of the other properties of the atom.

Equation Transcription:

$-e$

$+2e$

$+2e$

$-e$

$-e$

Text Transcription:

-e

+2e

+2e

-e

-e

ANSWER:

Solution 55P

Step 1 of 5:

$The\ electron\ 1\ exerts\ force\ on\ 2\ and\ also\ electron\ 2\ exerts\ force\ on\ electron\ 1.$

$According\ to\ \ Coulomb’s\ law,\ \ the\ \ force\ between\ the\ electrons.\ \$

$\$

$Consider\ the\ forces\ on\ the\ electron\ 2.\ There\ is\ a\ repulsive\ force\ {F}_{1}\ due\ to\ the\ other\ electron\ \$

$because\ both\ are\ same(negative)\ charge.\ where\ 2d\ is\ the\ distance\ between\ the\ electrons\ .R\ is$

$the\ radius\ of\ the\ sphere.$

${F}_{1}=\frac{1}{4\pi{}{\epsilon{}}_{0}}\frac{{e}^{2}}{(2d{)}^{2}}$

$\ \ \ \ =\frac{1}{4\pi{}{\epsilon{}}_{0}}\frac{{e}^{2}}{4d{\ }^{2}}............................(1)$

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