A star’s colour isn’t just decoration β it’s a thermometer. Wien’s law is what lets astronomers read a star’s surface temperature straight off its spectrum.
π What you need to know
Wien’s law relates the wavelength of peak emission from an object to its surface temperature
It states that Ξ»max β 1βT
Written as an equation: Ξ»maxT = 2.9 Γ 10β»Β³ m K
A hotter object peaks at a shorter wavelength β and emits more intensely at every wavelength
As an object heats up, its peak emission colour shifts: infrared β red β white β blue β ultraviolet
Wien’s Displacement Law
Wien’s lawΞ»max β 1βT
As an equationΞ»maxT = 2.9 Γ 10β»Β³ m K
Where Ξ»max is the wavelength at which radiation is emitted most intensely, in metres, and T is absolute temperature in kelvin. As temperature rises, the intensity increases at every wavelength, but the peak of the curve also shifts toward shorter wavelengths.
Reading the Black-Body Curve
Plotting intensity against wavelength for objects at different temperatures produces a family of curves. Each one rises steeply, peaks, then tails off gradually toward longer wavelengths β and as temperature increases, that peak both grows taller and moves to the left.
Hotter objects peak at shorter wavelengths and higher intensities β the 6000 K curve peaks furthest left and reaches the greatest height
Colour and Temperature
Because Wien’s law shifts the peak wavelength toward shorter wavelengths as temperature rises, an object’s dominant visible colour shifts too. Cooler stars appear reddish or orange, mid-range stars appear yellow-white, and the hottest stars appear blue.
Red β below about 3500 K
Orange β roughly 3500β5000 K
Yellow β roughly 5000β6000 K
Yellow-white β roughly 6000β7500 K
White β roughly 7500β10 000 K
Blue-white β roughly 10 000β30 000 K
Blue β above about 33 000 K
Quick recap: Ξ»_max T = 2.9 Γ 10β»Β³ m K. Hotter objects peak at shorter wavelengths β cooler stars glow red, hotter stars glow blue.
WE 1
A star’s spectrum peaks at a wavelength of 350 nm. Calculate its surface temperature.
Step 1 β Convert wavelength to metres
Ξ»_max = 350 nm = 350 Γ 10β»βΉ m
Step 2 β Rearrange Wien’s law for TT = (2.9 Γ 10β»Β³) Γ· Ξ»_max = (2.9 Γ 10β»Β³) Γ· (350 Γ 10β»βΉ)β 8290 K
WE 2
Star A has a spectrum that peaks at 620 nm; Star B peaks at 410 nm. Calculate the surface temperature of each star, and state which is hotter.
Step 1 β Calculate T for Star AT_A = (2.9 Γ 10β»Β³) Γ· (620 Γ 10β»βΉ) β 4680 KStep 2 β Calculate T for Star BT_B = (2.9 Γ 10β»Β³) Γ· (410 Γ 10β»βΉ) β 7070 KStar B is hotterStar A’s longer peak wavelength gives it an orange appearance; Star B’s shorter peak wavelength gives it a white appearance.
π‘ Top tips
Always convert wavelength to metres before substituting β spectra are usually quoted in nm
Temperature in Wien’s law must be in kelvin
A shorter peak wavelength always means a hotter object β it’s easy to get this backwards
Use the colour ranges as a sanity check on a calculated temperature β a “cool” answer paired with a blue star should raise a flag
β Common mistakes
Forgetting to convert nanometres to metres before substituting into the equation
Assuming a longer peak wavelength corresponds to a hotter object, when it’s actually the opposite
Mixing up which star is hotter when comparing two peak wavelengths
Reading the peak of a black-body curve off the wrong axis
That covers the radiation and star-related ideas in this section β let us know what you’d like to build next.
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