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The net potential energy between two adjacent ions, EN, may be represented by EN = -A/r + B/rn Where A, B, and n are constants whose values depend on the particular ionic system. Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following procedure: 1. Differentiate EN with respect to r, and then set the resulting expression equal to zero, since the curve of EN versus r is a minimum at E0. 2. Solve for r in terms of A, B, and n, which yields r0, the equilibrium interionic spacing. 3. Determine the expression for E0 by substitution of r0 into the above equation for EN. What is the equation that represents the expression for E0?

Respuesta :

okpalawalter8

We have that the

  • EN with respect to r, is mathematically given as
  • r in terms of A, B, and n,
  • The equation that represents the expression for E0 are given as
  • [tex]EN(r)=\frac{A}{r}+\frac{B}{r^n}[/tex]
  • [tex]r=\frac{A}{nB}^{1/(1-n)}[/tex]
  • [tex]E_0=\frac{-A}{A/nB}1/1-n+\frac{B}{\frac{A}{nB}^{n/{1-n}}}[/tex]

From the question we are told

  • The net potential energy between two adjacent ions, EN, may be represented by EN = -A/r + B/rn
  • Where A, B, and n are constants whose values depend on the particular ionic system.
  • Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following procedure:

Energy

Generally the equation for the EN(r)   is mathematically given as

a)[tex]EN(r)=\frac{A}{r}+\frac{B}{r^n}\\\\dE/dr=\frac{A}{r^2}-\frac{nB}{r^{n+1}}=0\\\\\frac{A}{r^2}=\frac{nB}{r^{2-n-1}}[/tex]

Therefore

b)[tex]r=\frac{A}{nB}^{1/(1-n)}[/tex]

c) [tex]E_0=\frac{-A}{A/nB}1/1-n+\frac{B}{\frac{A}{nB}^{n/{1-n}}}[/tex]

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