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

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Energy Of An Electron In A Quantum Energy Level

Figure 22.12 presents four quantum energy levels of an arbitrary quantum mechanical system:

(a) Indicate the quantum energy levels associated with the *transition* that requires the most energy.

(b) Indicate the quantum energy levels associated with the *transition* that requires the least energy.

(c) Which *transition* will absorb or emit light with the longest wavelength?

(d) Which *transition* will absorb or emit light with the shortest wavelength?

(e) Suppose the electron of this quantum system is from a nucleus with atomic number 3. Compare the energy of its n = 4 to n = 3 transition with the energy of a n = 2 to n = 1 transition of an electron from a nucleus with atomic number 2.

**The strings**:
S_{7}P_{3}A_{32} (Force - Push)
**The math**:

Pj Problem of Interest is of type *force* (push). Electron is pushed to higher energy level when it absorbs energy and pushed back to the lower energy when it emits energy.

(a) The energy required for the transition from one quantum energy level to another is the difference in energy between the energy levels. The farther the energy level is from the nucleus the greater its energy.

So, in general, the vertical distance between energy levels can be used to rank transition energy.

So, the transitions between n =1 and n = 4 requires the most energy

(b) The transitions between n = 1 and n =2 requires the least energy.

(c) A quantum of energy E = νh = ch/λ is absorbed or emitted when an electron transits from one energy level to another.

So, light with the least energy will have the longest wavelength while light with the most energy will have the shortest wavelength.

So, light absorbed or emitted in transition associated with n =1 and n = 4 will have the shortest wavelength.

(d) Light absorbed or emitted in transition associated with n =1 and n =2 will have the longest wavelength.

(e) The energy E, at quantum energy level n is:

E = -(Z^{2}e^{2})/(2a_{o}n^{2}) ----------(1)

Where Z is atomic number; e is electron charge; a_{o} is Bohr radius; n is quantum energy level.

For Z = 3, and transition from n = 4 to n = 3:

Substituting in equation (1), we have:

E_{4} - E_{3} = 9e^{2}/[2a_{o}(1/9 - 1/16)]

For Z = 2, and transition from n = 2 to n = 1:

Substituting in equation (1), we have:

E_{2} - E_{1} = 4e^{2}/[2a_{o}(1/1 - 1/4)]

Comparing the transition energies:

9e^{2}/2a_{o}[1/9 - 1/16] : 4e^{2}/2a_{o}[1/1 - 1/4]

= 3(1/9 -1/16) = 7/48 = 14.58%.

So, the energy emitted in the n = 4 to n = 3 transition by an electron from a nucleus with atomic number 3 is 14.58% more than the energy emitted in the n = 2 to n = 1 transition by an electron from a nucleus with atomic number 2.

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