Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

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Sound

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Language

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States Of Matter

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Nuclear Reactions

Molecular Shapes

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Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

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Photosynthesis

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Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Electron Behaviors

(a) Table 22.1 highlights important concepts associated with an electron. Associate each concept with a behavior of an electron.

(b) Derive the equation for the De Broglie wavelength.

**The strings**:
S_{7}P_{2}A_{21} (Identity - Physical Property)
**The math**:

Pj Problem of Interest is of type *identity* (physical property). *Identity* of electron behaviors

(a)i Niels Bohr is credited with the postulation of *energy levels* in an atom. The *Bohr Model* of the atom assumes that electrons move in *orbits* around the nucleus of the atom and that each orbit has an energy associated with it. Modern quantum mechanics no longer accept this view of the motion of electrons in orbits around the nucleus. However, it retains the concept of *electron transitions* from one energy level to another energy level. *The absorption and emission of energy is an electron behavior associated with an electron's energy level*.

(ii) Louis De Broglie is credited with the discovery of the De Broglie wavelength of the electron. It established the *wave behavior* of the electron.

(iii) Werner Heisenberg is credited with the discovery of the Heisenberg Uncertainty Principle. The electron moves in a manner that makes it impossible to accurately know simultaneously, its momentum and position. However, the probability of its being in a given position can be calculated.

(iv) Wolfgang Pauli is credited with the discovery of the Pauli Exclusion Principle. An electron prefers to live with no more than one other electron in an *orbital* (their residence). The electrons must not be exactly the same. In technical terms, *an orbital can hold a maximum of two electrons and they must have opposite spins*.

(v) Hund is credited with the discovery of Hund's Rule. An electron prefers an empty orbital that has not been occupied by an electron like itself so it will reside in an empty orbital before pairing up with another electron with the same spin in another orbital. In technical terms, *for degenerate orbitals (subshells), the lowest energy is attained when the number of electrons with the same spin is maximized*

(b) De Broglie used three equations to derive the De Broglie wavelength:
**E = mc ^{2}** ---------(1) Einstein' energy equation

E is Energy; m is mass; where ν is frequency of light, c is velocity of light; λ is wavelength of light, and h is Planck's constant.

From equation (2) λ = c/ν ---------(4)

Substituting the expression for ν in (3), in (4) we have:

λ = ch/E -----------(5)

Substituting the expression for E in (1), in (5) we have:

&lamda; = ch/mc

De Broglie replaced velocity of light c, with velocity of the electron, v

So, the De Broglie wavelength =

where m is the mass of the electron, λ the wavelength of the electron and v the velocity of the electron.

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

Real Numbers

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

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

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

More Pj Problem Strings