Wien’s Displacement Constant

A black-body spectrum with hidden λ_max. Park a cursor on the B_λ peak at several temperatures and recover b from a fit of λ_max versus 1/T.

School· 24 min·Related simulator: ThermodynamicsBlack Body: Planck Spectrum

Goal

Determine Wien’s constant from λ_max T = b. The slope of λ_max versus 1/T is b.

Equipment

Black-body source
Scanning spectrometer (B_λ vs λ)
Wavelength cursor

Experiment

Live B_λ spectrum. Find the peak with the cursor. The constant b is hidden.

Find the B_λ peak by sweeping the wavelength cursor. The displacement constant is hidden; the bench does not label the peak or place a marker. Record stores your cursor as the peak estimate.

Temperature TT = 5000 K

Cursor λλ = 600 nm

Spectrometer B_λ = 1.276e+13 W·sr⁻¹·m⁻³

Record = “this cursor is my λ_max”. Take at least 6 temperatures (3500–7500 K). The bench does not snap to the peak.

Measurements

№	T K	λ_max nm	λ m	1/T K⁻¹
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Wien’s Displacement Constant

Generated: 24 Aug 2026, 22:30

Goal

Determine Wien’s constant from λ_max T = b. The slope of λ_max versus 1/T is b.

Measurement table

#	T (K)	λ_max (nm)	λ (m)	1/T (K⁻¹)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted Wien constant agrees with b = λ_max T. Main uncertainties: parking the cursor slightly off the B_λ peak and the finite wavelength window.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Planck’s B_λ has a maximum at λ_max = b/T with b ≈ 2.898×10⁻³ m·K. The bench draws the spectrum without a Wien marker and never prints λ_max or b. You place a cursor and record that wavelength as your peak estimate.

Procedure

Set the black-body temperature T. Sweep the cursor until the spectrometer B_λ reading is highest — that is your λ_max.
Record. The row stores T and the cursor wavelength. The bench does not auto-pick the peak and does not show Wien’s b.
The notebook computes 1/T and λ in metres.
Repeat for at least 6 temperatures from about 3500 K to 7500 K.
Fit λ (m) versus 1/T; the slope is b. Compare with the reference.

Conclusion

The fitted Wien constant agrees with b = λ_max T. Main uncertainties: parking the cursor slightly off the B_λ peak and the finite wavelength window.