SME
Climatology · Problem type
Peak wavelength of the Sun’s and Earth’s light
Use this for “At what wavelength does the Sun, at 5,772 K, shine brightest, and Earth, at 288 K?”
Diagram
λₘₐₓ = 0.5021 μm: visible light (green).
This is an example. Type your own values to start a new problem.
λₘₐₓ (μm)
=
2,898
μm·K
T (K)
Formulas
λₘₐₓ
=
2,898
T
0.5021
=
2,898
5,772
Assumptions
•
Both glow as black bodies; λₘₐₓ is only the brightest wavelength of a broad spectrum.
•
Wien’s constant b = 2,898 μm·K, so λₘₐₓ in μm is 2,898 over T in kelvins.
•
The Sun peaks in visible light and Earth near 10 μm, so greenhouse gases act on the outgoing infrared.
Step-by-step
WE KNOW
T = 5,772 K
FIND
peak wavelength (λₘₐₓ)
Step 1 · Find peak wavelength (λₘₐₓ)
Use λₘₐₓ = 2,898 ÷ T
Wien’s law: the hotter the body, the shorter its brightest wavelength.
λₘₐₓ
=
2,898
5,772
λₘₐₓ = 0.5021 μm
Check
Put the numbers back in. Both sides should match.
0.5021
=
2,898
5,772
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.