SolutionsHW1

# SolutionsHW1 - HW A Problem 2.14 a To Find The bond energy...

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HW A Problem 2.14 a. To Find: The bond energy between two ions (E O ) expressed as a function of three parameters A, B and n. b. Given: The equation representing variation of the net potential energy between two adjacent ions (E N ) with inter-ionic spacing (r) : E N = + (±1) c. Assumptions: None Obvious d. Solution: (1) Differentiating the given equation, we get: dr r B d dr r A d dr dE n + = (±2) b dr dE = 1) + ( 1) + (1 n r nB r A (±3) The minimum in the E vs r curve occurs when dr dE = 0 b 1) + ( (2) n r nB r A = 0 b 1) + ( (2) n r nB r A = (±4)

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(2) This minimum in the E vs r curve occurs when r=r o . Solving for r o : 1) + ( (2) ro n ro nB A = (In the above equation ro = r o ) (3) E N = E o when r = r o . n o r B r A E + = o 0 From equation (±5) ) - /(1 ) - 1/(1 + = Eo n n n nB A B nB A A (±6) b r o = (±5)
Problem 2.15 a. To Find: Whether graphically obtained and mathematically calculated values of E o are equal. Also, whether graphically obtained and mathematically calculated values of r o are equal. b. Given:

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SolutionsHW1 - HW A Problem 2.14 a To Find The bond energy...

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