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

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Sound

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Nuclear Reactions

Molecular Shapes

Electron Configurations

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Human-cells

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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

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Painting

Molecular Orbital Theory

1. Why Is there molecular orbital theory given that there exist valence bond theory?

2. What is the Difference between *atomic orbitals* and *molecular orbitals*?

3. (a) Use the *atomic orbitals* of the hydrogen atom (H), to obtain the *molecular orbitals* for the hydrogen molecule (H_{2}). Hints: *whenever two atomic orbitals overlap, two molecular orbitals form*.

(b) Draw the Energy-Level Diagram representing the atomic orbitals -molecular orbitals interaction of problem 3(a).

4. Write the general representative string for the excitation of one of the electrons of the hydrogen molecule by light from the *bonding MO* (σ_{1s}) to the *antibonding MO ^{*}* (σ

5. Use the respective

1. Valence bond theory and hybrid orbitals does not explain all aspects of bonding. For example, it does not successfully describe the excited states of molecules. A scenario involved in molecular light absorption and the resultant color emission.

2. Atomic orbitals are the wave functions that describe the probable location of electrons in atoms. Molecular orbitals are the wave functions that describe the proble locations of the electrons in the context of molecules. Most of the concepts in atomic orbitals theory carry-over to molecular orbital theory (abbreviated as MO). The primary difference is that MOs are associated with the entire molecule instead of a single atom.

3(a) The 1s atomic orbitals of the two hydrogen atoms overlap to form two molecular orbitals (figure 1). One of the molecular orbitals has its wave function concentrated between the nuclei of the atoms, that is, the electrons are more likely to be found in this region and thus more likelely to bond. This molecular orbital is called the *bonding molecular orbital*. The strong mutual nucleic pull on the electrons in the bonding molecular orbital establishes a strong covalent bond (σ1s bond) between the electrons and thus a stable hydrogen molecule. In other words, the electron is more stable in the *bonding molecular orbital* than it is in its 1s atomic orbital. This stability is associated with lower energy state (figure 1b). The wave function in the other molecular orbital is scantily distributed in the region between the nuclei and highly distributed on opposite sides of the nuclei. As a result, there is little electron density in the region between the nuclei and a low likelihood of electron bonding. This molecular orbital is called the *antibonding molecular orbital*. In the *antibonding molecular orbital* atomic orbitals cancel each other instead of enhancing each other. The electron is repelled from the bonding region and as a result it is less stable (i.e, it has higher energy) than it is in the 1s atomic orbital.

(b) Atomic - molecular orbitals interaction is often represented by the *energy-level diagram* (also called *molecular orbital diagram*). Figure 2 is the *energy-level diagram* for the hydrogen molecule (H_{2}).

4. The excited electron is pushed away from its bonding molecular orbital and further repelled in the antibonding molecular orbital. Thus the general representative string is S_{7}P_{3}A_{32} (*force-push in a multi-matter multi-dynamic space*).

5. The *bond order* is defined in molecular orbital theory as follows:

(1/2)[number of *bonding electrons* - *antibonding electrons*].

A *bond order of 1 represents a single bond; a bond order of 2 represents a double bond; and a bond order of 3 represents a triple bond*.

Hydrogen (H_{2}) has 2 bonding electrons and 0 antibonding electrons.

So its *bond order* = (1/2)[2 - 0] = 1. Therefore, H_{2} is stable.

Helium (He_{2}) has 2 bonding electrons and 2 antibonding electrons.

So its *bond order* = (1/2)[2 - 2] = 0.

A bond order of 0 implies no bond exists. Therefore, He_{2} is not stable

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.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

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

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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