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Blackbody Radiation Question 2: Planck's Law Approximates Rayleigh-Jeans Law at Large Wavelengths

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First published at 15:29 UTC on May 29th, 2024.

#math
#science
#physics

Math Easy Solutions

MES

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In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law, it becomes Rayleigh-Jeans Law. This results in a good approximation for Rayleigh-Jeans Law at large wavelengths sin…

Timestamps:

- Question 2: Using Taylor polynomials, Planck's Law approximates Rayleigh-Jeans Law at large wavelengths: 0:00
- Solution: Approximating exponential function using Taylor series: 0:28
- Recap on Taylor series: 0:56
- Exponential function as a Taylor series: 2:40
- Approximating Planck's Law using Taylor series for Exponential function: 4:03
- Approximating Taylor series for large wavelengths: 5:58
- Large wavelength approximation for Planck's Law: 6:40
- Canceling out terms of Planck's Law to get Rayleigh-Jeans Law: 8:36
- Summary: Using the first non-zero term of Taylor series only approximates Rayleigh-Jeans Law: 9:44

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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