# Miscellaneous

- Page ID
- 127068

- 459: The Art of Science
- Popular views of science imply that there exists a mechanical and logically certain relationship between scientific facts and their explanations. According to these views scientific knowledge possesses a certainty which is not to be found in other disciplines such as the humanities or the social sciences.

- 460: Mass-Energy Equivalence
- This derivation of the mass-energy equivalence equation is based on the analyses of an elementary photon emission event by two sets of inertial observers .

- 461: Commentary on “Probing the Orbital Energy of an Electron in an Atom”
- Slater was one of the early users of quantum theory in the search for an understanding of atomic and molecular structure, and so we should not be surprised that he attempted to use the classical concepts of kinetic and potential energy as guides for interpretive purposes. However, today we know that this program is not viable; classical concepts cannot provide an acceptable model for the stability and structure of atoms and molecules, nor their interaction with electromagnetic radiation.

- 462: The Use of Models in Introductory Chemistry
- In attempting to reach and educate all of the constituencies of general chemistry, we should not over-simplify the concepts because it makes them easier to teach. Teaching simple models that students can easily digest is tempting, but these easily digestible models are frequently fundamentally incorrect.

- 463: Reaction to Gillespie's Six Great Ideas in Chemistry - Another Great Idea
- We should follow Einstein’s advice in our teaching and “make things as simple as possible, but no simpler.”

- 464: An Alternative Derivation of Gas Pressure Using the Kinetic Theory
- The kinetic theory is used to derive the pressure of an ideal gas assuming that the gas occupies a spherical container of diameter D.

- 465: Examining Fourier Synthesis with Dirac Notation
- The purpose of this tutorial is to use Dirac notation to examine Fourier synthesis.

- 466: Finding Roots of Transcendental Equations
- The attempt to find analytical solutions to Schrödingerʹs equation for some problems yields transcendental equations which must be solved by a combination of graphical and numerical techniques.

- 476: Cosmic Background Radiation
- The cosmic background radiation fills all space and is a relic from the "big bang" that created the universe approximately 18 billion years ago. The data1 shown below, spectral brightness2 as a function of wave number, was recorded recently (1989) by the Cosmic Background Explorer satellite (COBE). Below the data is fit with the Planck blackbody radiation equation to determine the cosmic background temperature.

- 477: Age of the Elements
- Analysis of cosmic microwave background radiation (CMBR) obtained by the Planck satellite telescope has added 80 million years to the age of the universe, making the best estimate of the current age 13.8 billion years. This tutorial deals with the more modest task of estimating the age of the elements found in the earth's crust.

*Thumbnail: The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. (CC BY-SA 3.0; Dhatfield).*