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AST-06

Wien displacement

λ_max T = 2.897×10⁻³ m·K. Peak of B_λ for a blackbody.

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RadiationWien

Governing equation

λmax⁡T=2.897×10−3 m K\lambda_{\max}T=2.897\times 10^{-3}\,\mathrm{m\,K}

T∈[200,40000]T \in \left[200, 40000\right]

where

T
Temperature (K)
\lambda_{max}
Peak wavelength (nm)

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AST-06 · spectrum
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①

Governing law — red

λmax⁡T=2.897×10−3 m K\lambda_{\max}T=2.897\times 10^{-3}\,\mathrm{m\,K}

T∈[200,40000]T \in \left[200, 40000\right]

T=200T = 200λmax=14488.9\lambda_{max} = 14488.9

②

Domain of the variable — blue

Tmin⁡=200,Tmax⁡=40000T_{\min} = 200,\quad T_{\max} = 40000

T∈[200,40000]T \in \left[200, 40000\right]

T=200T = 200T=200T = 200

③

Response curve — green

λmax⁡T=2.897×10−3 m K\lambda_{\max}T=2.897\times 10^{-3}\,\mathrm{m\,K}

T∈[200,40000]T \in \left[200, 40000\right]

T=200T = 200λmax=14488.9\lambda_{max} = 14488.9

④

Rate of change — amber

dλmaxdT\frac{\mathrm{d}\lambda_{max}}{\mathrm{d}T}

T∈[200,40000]T \in \left[200, 40000\right]

T=450.3T = 450.3λmax′=−20.68\lambda_{max}^{\prime} = -20.68

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-06 — Wien displacement) is the form associated with Wien. Working symbols: TT →\rightarrow λmax\lambda_{max}. The B_ν peak is at a different constant (5.88×10¹⁰ Hz/K). Colour of stars follows Wien.

Purpose

Purpose: compute λmax\lambda_{max} from TT in Astrophysics via λmax⁡T=2.897×10−3 m K\lambda_{\max}T=2.897\times 10^{-3}\,\mathrm{m\,K} λ_max T = 2.897×10⁻³ m·K. Peak of B_λ for a blackbody. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given T=5772.000 KT = 5772.000\,\mathrm{K}, the governing relation λmax⁡T=2.897×10−3 m K\lambda_{\max}T=2.897\times 10^{-3}\,\mathrm{m\,K} yields λmax=502.0 nm\lambda_{max} = 502.0\,\mathrm{nm}. A spectrum, a moving peak. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Peak wavelength \lambda_{max}502.0 nm
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AST-06 · spectrum
00:0 / 00:08

Narration of this film

A spectrum, a moving peak.

The B_ν peak is at a different constant (5.88×10¹⁰ Hz/K). Colour of stars follows Wien.

Reading speed

Watch on YouTube