Expressions Of Pj Problems

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Inter Atomic Force 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.

(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

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.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

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Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

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Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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