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Blackbody Radiation Questions 3,4: Comparing Planck's Law to Rayleigh-Jeans Law for the Sun

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First published at 17:03 UTC on May 30th, 2024.

#math
#science
#physics

Math Easy Solutions

MES

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In this video I graph out the blackbody radiation energy density for the Sun using both Planck's Law and the classical Rayleigh-Jeans Law. At high wavelengths, both models are similar but at low wavelengths the classical theory diverges wildly to infinity. This was the cause of the Ultraviolet Catastrophe. Planck's Law accurately models experiment data which shows a peak energy density at the 0.5 um wavelength for the Sun, whose temperature is 5700 Kelvin.

Timestamps:

- Question 3: Graphing Planck's Law and Rayleigh-Jeans Law for the Sun (5700 K): 0:00
- Solution to Question 3: Converting meters to micrometers for wavelength: 0:52
- Graphing in Excel: Energy Density (energy volume per each wavelength) vs wavelength: 1:33
- Planck's Law and Rayleigh-Jeans Law are similar at large wavelengths: 2:22
- Planck's Law and Rayleigh-Jeans Law are very different at small wavelengths: 2:51
- Comparison Summary: Ultraviolet Catastrophe: 3:12
- Planck's Law give a maximum at a wavelength of 0.5 um, Rayleigh-Jeans Law has no maximum or minimum: 4:20
- Question 4: Planck's Law for the Sun gives a maximum at a wavelength of 0.5 um: 5:01

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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