Wien Displacement and Blackbody Spectra
Wien's displacement law states lambda_max T=b for an ideal blackbody, relating absolute temperature to the wavelength of maximum spectral radiance while the complete curve is governed by Planck's distribution.
Why this shows up in the exam
Comparing star colours · Interpreting furnace and filament spectra · Ordering temperatures from radiation curves
Learn the idea
A hotter blackbody spectrum peaks at a shorter wavelength while its total emitted area rises. As temperature rises, the spectral hump moves left and grows; the peak position gives temperature, but power at one wavelength is not the same as total power.
🧠 Memory hook: Hotter peaks move left to shorter wavelength.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- lambda_max T = b — Wien displacement law for the spectral peak
- b approximately 2.898 x 10⁻³ m K — Wien displacement constant in wavelength form
How to approach it
- 1Locate each spectral peak on the wavelength axis
- 2Use lambda_max T=b with kelvin
- 3Use Stefan-Boltzmann separately if total power is also needed
Common slip-ups that cost marks
- •Reading curve height alone as peak wavelength
- •Using total-power ratios in place of Wien's law
- •Applying wavelength-form Wien law to a frequency-spectrum peak
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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