Bragg’s Law: Plane Spacing d

Known X-ray λ. For orders n = 1, 2, 3 find the grazing angle of the intensity peak and recover d from a fit of sin θ versus n.

University / research· 24 min·Related simulator: Optics & LightBragg’s Law (X-ray)

Goal

Determine d from 2 d sin θ = n λ. A plot of sin θ versus n has slope λ/(2d), so d = λ / (2 · slope).

Equipment

X-ray line (known λ)
Unknown crystal
Goniometer
Intensity detector

Experiment

X-ray goniometer. Crystal planes; incident and reflected rays at θ. Live detector intensity I.

Known wavelength λ = 0.154 nm (Cu Kα). Plane spacing is hidden. You set the order n and the grazing angle θ; read intensity I on the detector.

Order nn = 1

Grazing angle θθ = 12.0°

Detector I = 0.000

For n = 1, 2 and 3 hunt the I peak, then record. At least 6 rows (two per order is fine). Angle is not auto-parked at the peak.

Measurements

№	n	θ deg	sin θ
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”.

Bragg’s Law: Plane Spacing d

Generated: 24 Aug 2026, 22:29

Goal

Determine d from 2 d sin θ = n λ. A plot of sin θ versus n has slope λ/(2d), so d = λ / (2 · slope).

Measurement table

#	n	θ (deg)	sin θ
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted d agrees with the hidden plane spacing. Main uncertainties: goniometer steps and judging the intensity peak by eye.

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

Theory

Constructive interference from crystal planes obeys Bragg’s law. The bench hides d, 2d sin θ and any “match” flag. λ is known (Cu Kα). A live detector intensity is the instrument — you hunt the peak for each order.

Procedure

Wavelength λ is fixed and known. d is hidden. Set the order n, then sweep the grazing angle θ.
Watch the live detector. Park at the intensity peak. The bench does not print “Bragg matched”.
Record. The row stores n and θ. The notebook computes sin θ.
Repeat for n = 1, 2 and 3 (two records per order is fine). At least 6 rows.
Fit sin θ versus n; d = λ / (2 · slope). Compare with the reference.

Conclusion

The fitted d agrees with the hidden plane spacing. Main uncertainties: goniometer steps and judging the intensity peak by eye.