Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 2, Problem 2.25P
To determine

The value of B for an ion pair.

Expert Solution & Answer
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Answer to Problem 2.25P

The value of constant B is 8.3497×10134Jm12.

Explanation of Solution

Given:

The value of m is 12.

The energy required to separate one pair of K+ and Cl ions is 5.0eV.

The equilibrium interionic separation is 0.266nm.

Formula used:

The formula to calculate the inter-ionic potential is given by,

Vpion(r)=( Ze)24πε0r+Brm      ......... (I)

Here, Vpion(r) is the inter-ionic potential, Ze is the electron charge of K+ ion, ε0 is the permittivity of vacuum, r is inter atomic separation and B, and m are constants.

Calculation:

The inter-ionic potential is calculated as,

Substitute 5eV for Vpion(r), 1.602×1019C for Ze, 8.85×1012F/m for ε0, 0.266×109m for r and 12 for m in equation (I).

5eV= ( 1.602× 10 19 C )24π( 8.85× 10 12 F/m )( 0.266× 10 9 m)+B ( 0.266× 10 9 m ) 125eV( 1.60218× 10 19 J 1eV)= ( 1.602× 10 19 C )24π( 8.85× 10 12 F/m )( 0.266× 10 9 m)+B ( 0.266× 10 9 m ) 128.01×1019J=2.307× 10 280.266× 10 9m+B ( 0.266× 10 9 m ) 12B=(6.654× 10 20)(1.2548× 10 115m 12)

Solve further as,

B=8.3497×10134Jm12

Conclusion:

The value of constant B is 8.3497×10134Jm12.

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Chapter 2 Solutions

Materials Science And Engineering Properties

Ch. 2 - Prob. 11CQCh. 2 - Prob. 12CQCh. 2 - Prob. 13CQCh. 2 - Prob. 14CQCh. 2 - Prob. 15CQCh. 2 - Prob. 16CQCh. 2 - Prob. 17CQCh. 2 - Prob. 18CQCh. 2 - Prob. 19CQCh. 2 - Prob. 20CQCh. 2 - Prob. 21CQCh. 2 - Prob. 22CQCh. 2 - Prob. 23CQCh. 2 - Prob. 24CQCh. 2 - Prob. 25CQCh. 2 - Prob. 26CQCh. 2 - Prob. 27CQCh. 2 - Prob. 28CQCh. 2 - Prob. 29CQCh. 2 - Prob. 30CQCh. 2 - Prob. 31CQCh. 2 - Prob. 32CQCh. 2 - Prob. 33CQCh. 2 - Prob. 34CQCh. 2 - Prob. 35CQCh. 2 - Prob. 36CQCh. 2 - Prob. 37CQCh. 2 - Prob. 38CQCh. 2 - Prob. 39CQCh. 2 - Prob. 40CQCh. 2 - Prob. 41CQCh. 2 - Prob. 42CQCh. 2 - Prob. 43CQCh. 2 - Prob. 44CQCh. 2 - Prob. 45CQCh. 2 - Prob. 46CQCh. 2 - Prob. 47CQCh. 2 - Prob. 48CQCh. 2 - Prob. 49CQCh. 2 - Prob. 50CQCh. 2 - Prob. 51CQCh. 2 - Prob. 52CQCh. 2 - Prob. 1ETSQCh. 2 - Prob. 2ETSQCh. 2 - Prob. 3ETSQCh. 2 - Prob. 4ETSQCh. 2 - Prob. 5ETSQCh. 2 - Prob. 6ETSQCh. 2 - Prob. 7ETSQCh. 2 - Prob. 8ETSQCh. 2 - Prob. 9ETSQCh. 2 - Prob. 10ETSQCh. 2 - Prob. 11ETSQCh. 2 - Prob. 12ETSQCh. 2 - Prob. 13ETSQCh. 2 - Prob. 1DRQCh. 2 - Prob. 2DRQCh. 2 - Prob. 3DRQCh. 2 - Prob. 4DRQCh. 2 - Prob. 5DRQCh. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Prob. 2.6PCh. 2 - Prob. 2.7PCh. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10PCh. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Prob. 2.19PCh. 2 - Prob. 2.20PCh. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26P
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