Electron Diffraction Virtual Lab: de Broglie Wavelength

Q: Can the class link open on the diffraction tube?

Yes, it opens there by default. To be sure, set Screen to Electron diffraction tube in the link's starting values. You can also pin Accelerating voltage V (diffraction tube) at 2.0 kV so everyone starts from the same reading.

Updated 2026-10-07

This electron diffraction virtual lab turns the classic electron diffraction tube into a practical students can run themselves. Electrons accelerated through 2–5 kV pass a thin graphite film and make two bright rings on a fluorescent screen. Students measure the ring diameters with a ring gauge, calculate the de Broglie wavelength λ = h/√(2meV), plot D against 1/√V and find the spacing of the planes of carbon atoms. Most schools only have one tube, and it needs a high-voltage supply, so this lets every student take their own readings. Every value below was read from the simulation.

Electron diffraction and the de Broglie wavelength – diffraction tube, double slit, electron microscope

Curriculum links

AQA A-level Physics 7408, 3.2.2.4 (wave–particle duality): electron diffraction as evidence for the wave nature of particles, λ = h/mv, and how the pattern changes with electron speed.
IB Physics (first assessment 2025), E.2 (quantum physics): matter waves and electron diffraction.
NSW HSC Physics Module 8 and VCE Physics Unit 4: de Broglie's matter waves and the evidence from electron diffraction.

Simulic is not affiliated with or endorsed by AQA, the International Baccalaureate, NESA or the VCAA.

Before the lab (5 min)

Ask students to commit to a prediction, on paper or as question 1 of the class link:

"The accelerating voltage is raised from 2 kV to 4 kV. What happens to the rings on the screen?"

Many students expect bigger rings, because the electrons have more energy.

Method in the simulation

On the Diffraction tube tab, set Voltage V to 2.0 kV. Leave Bring a magnet near and Compare with X-rays unticked.
Drag on the screen, or use the Ring gauge D slider, until the dashed circle lies along the middle of the inner ring. Set Ring measured to inner ring and press Record.
Fit the gauge to the outer ring, set Ring measured to outer ring and press Record.
Repeat at 3.0, 4.0 and 5.0 kV.
Read the two fitted lines under the graph. Calculate λ for one voltage yourself and check it against the line above the graph.

V (kV)	1/√V	λ (pm)	D inner (mm)	D outer (mm)
2.0
3.0
4.0
5.0

$a freshly opened simulation on the Diffraction tube tab with Voltage V 3.0 kV and the ring gauge at D = 28.5 mm on the inner ring, after recording the inner ring at 35.0, 28.5, 24.5 and 22.0 mm and the outer ring at 61.5, 50.0, 43.0 and 38.5 mm for 2.0, 3.0, 4.0 and 5.0 kV: the screen with the dashed gauge on the inner ring and two straight lines through the origin on the graph of D against 1/√V$

Expected results

Best gauge fits, to the nearest 0.5 mm:

V (kV)	1/√V	λ (pm)	D inner (mm)	D outer (mm)
2.0	0.707	27.42	35.0	61.5
3.0	0.577	22.39	28.5	50.0
4.0	0.500	19.39	24.5	43.0
5.0	0.447	17.34	22.0	38.5

Wavelength at 3.0 kV: λ = 6.63 × 10⁻³⁴ ÷ √(2 × 9.11 × 10⁻³¹ × 1.60 × 10⁻¹⁹ × 3000) = 2.24 × 10⁻¹¹ m, matching the simulation's 22.39 pm.
Graph: both rings give straight lines through the origin. The fits read D = 49.3·(1/√V), so d = 212 pm for the inner ring (accepted 213 pm), and D = 86.5·(1/√V), so d = 121 pm for the outer ring (accepted 123 pm).
One reading: at 3.0 kV, d = 2Lλ/D = 2 × 0.135 m × 22.39 pm ÷ 0.0285 m = 212 pm.
Doubling V from 2 to 4 kV shrinks the inner ring from 35.0 to 24.5 mm, a factor of about 1.4 (√2), not 2.

Questions for students

(Prediction, asked again after the lab) What happens to the rings when V rises from 2 kV to 4 kV?
Which is the dependent variable?
At 3.0 kV, what is the diameter of the inner ring?
What spacing d does your fitted line give for the inner ring?
What do the X-ray comparison and the magnet show about electrons?

Answers for teachers: (1) They get smaller. (2) The ring diameter D. (3) 28.5 mm (accept 27.5–29.5). (4) 212 pm (accept 203–223). (5) X-ray photons of the same wavelength (55.5 keV at 3.0 kV) make the same rings, so electrons diffract like waves with λ = h/p. Only the electron rings move when the magnet is near, so the rings are made by charged particles.

Common misconceptions

"More energy spreads the electrons out more." Faster electrons have more momentum and a shorter wavelength, so they are diffracted through smaller angles.
"λ is proportional to 1/V." It is proportional to 1/√V: from 2 to 4 kV, λ falls from 27.42 to 19.39 pm.
"The rings are a picture of the atoms." They come from waves reflected at two sets of planes, 213 pm and 123 pm apart. Tick Graphite lattice to see them.

Extension

On the Double slit tab, set Emission rate to Slow (one at a time): single dots build up interference fringes.
On the Microscope tab, raise the TEM voltage and explain why shorter wavelengths resolve smaller details.

FAQ

Why does the outer ring give 121 pm instead of 123 pm?

The formula d = 2Lλ/D assumes small angles. The outer ring is deflected by about 13°, where that approximation is about 2% out. The inner ring is close to 213 pm.

How precisely can students fit the gauge?

The gauge moves in 0.5 mm steps and the rings have a visible width. Careful students land within 0.5 mm of the values above; questions 3 and 4 accept about 1 mm either way.

Can the class link open on the diffraction tube?

Yes, it opens there by default. To be sure, set Screen to Electron diffraction tube in the link's starting values. You can also pin Accelerating voltage V (diffraction tube) at 2.0 kV so everyone starts from the same reading.