Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Advanced Physics Homework Help
Derivation of Wien's+Reyleigh-Jean's Laws from Planck's Law
Reply to thread
Message
[QUOTE="Zacarias Nason, post: 5376375, member: 529063"] [h2]Homework Statement [/h2] After reading the forum stickies I'm not entirely sure where to put this question since it involves using math to solve a question, but is informally stated and isn't a book problem, either-I just started reading Fong's Elementary Quantum Mechanics, and in the first few pages the relationship between the Plank, Wien and Rayleigh-Jean formulas are discussed. I'm assuming that since Rayleigh-Jean and Wien are special cases of Planck's Law that they can be derived from Planck's Law, but I'm having trouble getting from one to the other/proving they are equivalent under some circumstances, assuming only algebra is really necessary for this. [h2]Homework Equations[/h2] [/B] It displays all of the formulas in the form of energy per unit volume. [tex] u(v)dv = \frac{8 \pi v^2 k T}{c^3} dv \ \ \ \text{(Rayleigh-Jean's)} [/tex] [tex] u(v)dv \ \text{~} \ v^3e^{-hv/kT} dv \ \ \ \text{(Wien's)}[/tex] [tex] u(v)dv = \frac{8 \pi h v^3}{c^3} \frac{1}{e^{hv/kT}-1} \ \ \ \text{(Planck's)} [/tex] [h2]The Attempt at a Solution[/h2] I tried to equate the Wien and Planck formula and ran into some trouble, but may very well be doing this wrong from the outset. Also, I'm not really sure how or if the tilde/asymptote approx. symbol may affect this. Here's my work: [tex] v^3 e^{-hv/kT} dv = \frac{8 \pi h v^3}{c^3} \frac{1}{e^{hv/kT}-1} dv[/tex] [tex] e^{-hv/kT} dv = \frac{8 \pi h}{c^3} \frac{1}{e^{hv/kT}-1} dv[/tex] [tex] e^{-hv/kT} = \frac{8 \pi h}{c^3} \frac{1}{e^{hv/kT}-1} [/tex] [tex] e^{-hv/kT} = \bigg(\frac{8 \pi h}{c^3}\bigg) (e^{-hv/kT})\bigg( \frac{1}{1-1/e^{hv/kT}}\bigg) [/tex] [tex] 1 = \bigg(\frac{8 \pi h}{c^3}\bigg) \bigg( \frac{1}{1-1/e^{hv/kT}}\bigg) [/tex] [tex] 1-1/e^{hv/kT} = \frac{8 \pi h}{c^3} [/tex] [tex] e^{hv/kT} = 1 - \frac{c^3}{8 \pi h} [/tex] This...obviously can't be right. Apart from the crazy huge number, I can't take the natural log of a negative number. What am I doing wrong? Does the necessary approach require integral calc or something? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Derivation of Wien's+Reyleigh-Jean's Laws from Planck's Law
Back
Top