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+q+qP+4+q

Question

The figure shows eight point charges arranged at the corners of a cube with sides of length d.  The values of the charges are +q and −q, as shown.  This is a model of one cell of a cubic ionic crystal.  In sodium chloride (NaCI), for instance, the positive ions are Na+ and the negative ions are CI.  (a) Calculate the potential energy U of this arrangement.  (Take as zero the potential energy of the eight charges when they are infinitely far apart.)  (b) In part (a), you should have found that U < 0.  Explain the relationship between this result and the observation that such ionic crystals exist in nature.

(HINT:  This is a configuration energy problem.  However, it is lengthy to solve.)

+q
+q
P
+4
+q
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+q +q P +4 +q

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check_circleAnswer
Step 1

a)

The total number of pair is,

п(п- 1)
р-
8(8-1)
2
= 28
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п(п- 1) р- 8(8-1) 2 = 28

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Step 2

In between this 28 pairs, 12 of them with charge q and –q are separated by a distance of d.

12 of them are with charge q and –q separated by a distance of...

12
4
U-ka12
2d 3 d
-(L.46)q
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12 4 U-ka12 2d 3 d -(L.46)q

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