Interatomic Force As A Function Of Nucleic Spacing

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{31} Base Sequence = 12735 String Sequence = 12735 - 3 - 31 **

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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.

(a) Express the equilibrium spacing r

(b) Derive another form for F(r) in which the only constants are r

(c) From the equation for F(r) derived in (b) calculate the following:

(i) The spacing r

(ii) The value of the maximum force F

**The strings**:

(a) S_{7}P_{7}A_{72} (Dynamic - Equilibrium)

(b) S_{7}P_{3}A_{31} (Force - Pull)

(c)(i) S_{7}P_{1}A_{12} (Containership -Length)

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

Pj Problem of Interest is of type *force* (electrostatic). Problem is primarily of type *force* since interatomic force underlies problems (a), (b) and (c).
** F(r) = A/r ^{M} - B/r^{N}** (N > M) -----------(1)

At the equilibrium spacing r

So, F(r

So, A/(r

So,(r

So, equilibrium spacing, r

From equation (2) B = A(r

Let A(r

Then, F(r) = A/r

(c)(i) Let r

Then the derivative of F at r

Using F(r) of equation (4):

dF(r)/dr = -MAr

dF(r

NA(r

So, (N/M)(r

So,(N/M)(r

So, The spacing r

r

(c)(ii) Substitute the expression for r

The attractive forces in interatomic bonds are primarily electrostatic. So, the expression A/r

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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