Potential Energy Between Atoms As A Function Of Nucleic Spacing

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Potential Energy Between Atoms As A Function Of Nucleic Spacing

The bonding force F, between atoms may be expressed approximately as follows:
** F(r) = A/r ^{M} - B/r^{N}** (N > M) -----------(1)

Where r, is the center-to-center spacing between atoms and A, B, M, and N are constants that vary according to the type of bond.

In general, the potential energy, U(r) between atoms is defined as the work capacity of interatomic forces for a given reference frame.

Hence,

(a) Determine the expression for U(r) by integrating equation (2).

(b) Show that the curve U(r) in figure 10.8 has a minimum at equilibrium spacing, r

(c) What is the significance of U(r

(d) Explain the meaning of the area under the curve U(r) from r

**The strings**:

S_{7}P_{3}A_{31} (Force - Pull)
**The math**:

Pj Problem of Interest is of type *force* (electrostatic). Energy is the capacity for work. It is force that is the doer of the work. So energy and work problems are of type *force*.

(a) **U(r) = ∫F(r)dr = ∫(A/r ^{M} - B/r^{N})dr**

= -(A/M-1)(1/r

= -(a/r

Where a, b and C are constants and a = A/M-1, b = b/N-1

If we set our reference spacing, r = ∞ (infinity) then U(∞) = 0

So, C = 0 from equation (3)

So,

Where, m = M -1 and n = N -1.

So, the potential energy between atoms is the sum of the attractive energy, -a/r

(b) U(r) = ∫F(r)dr

So, dU(r)/dr = F(r)

At the equilibrium spacing r

So, dU(r

So, the curve of U(r) is horizontal at the equilibrium spacing, r

Furthermore, a second derivative of U(r) = d

F(r)/dr gives a positive slope at equilibrium spacing,r

So, U(r

So, the curve of U(r) has its minimum at equilibrium spacing, r

(c) U(r

The

(d) The area under the curve U(r) from r

=

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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