In this video I go over another Applied Project and titled “Radiation from the Stars”. This is an interesting project from my calculus book at the end of the section on Infinite Sequences and Series. The project involves blackbody radiation and comparing the classical model with the newer quantum mechanics model.
Blackbody radiation is the heat radiation of a simplified ideal object that absorbs all incoming radiation and emits radiation that is dependent only on temperature of the object and not the frequency of the incoming radiation. Objects such as a furnace blast, matte black, and superheated objects like the Sun behave as blackbody radiators.
In the 19th century, John William Strutt aka “Lord Rayleigh” and James Jeans had derived a theoretical model for the radiation spectrum of a blackbody, but this diverged significantly from known experimental findings, in particular at low wavelengths or high frequency light. This resulted in what is known as the Ultraviolet Catastrophe.
In 1900, Max Planck looked to resolve this by postulating that light can only exist in discrete packets or quanta and not at any arbitrary value. This quantization of light produced experimentally accurate results for blackbody radiation and ushered in the start of “Quantum Mechanics”.
In this particular Applied Project, I go over Planck’s Law, determine its limits, and show that at high wavelengths the law converges to Rayleigh-Jeans Law.
Later in the video I make a note regarding Planck’s Constant and a potentially better interpretation of the quantization of energy from the YouTuber Lori Gardi aka Fractal Woman. I had initially written up a more extensive derivation of Planck’s Law in this video, but I have since removed it to do as a separate video in the future. Nonetheless, I have included the following links for further research:
- Derivation of Planck’s Law by “Physics Explained”: https://youtu.be/rCfPQLVzus4
- Interpretation of Plank’s Constant by “Fractal Woman”: https://peakd.com/hive-128780/@mes/cycles-planck-s-constant-and-the-true-nature-of-light
The topics covered in this video are listed below with their time stamps.
- @ 0:00 – Intro
- @ 1:34 - MES Note: Sharpen Your Mind with Mathematics
- @ 3:31 - Calculus Book Reference
- @ 3:45 - Topics to Cover
- @ 4:16 - Note on Applied Projects
- @ 4:37 - Applied Project: Radiation from the Stars
- @ - 13:23 - 5 Questions
- @ 15:44 - Solution to Question 1
- @ 40:33 - Solution to Question 2
- @ 51:00 - Solution to Question 3
- @ 56:04 - Solution to Question 4
- @ 56:44 - Solution to Question 5
- @ 1:02:08 - Quick Review of Planck's Law
- @ 1:11:28 - MES Note on Planck's Constant
Download Video Notes:
Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
Infinite Sequences and Series: Applications of Taylor Polynomials: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
Applied Projects Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H2EYiMvHro1O0xDDnew5mK .
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