Modern Physics
Electron KE: classical vs relativistic
400 keV electron — compare matter-wave K with relativity K_class vs K_rel chart; readouts should agree on β.
Electron KE: classical vs relativistic — interactive Modern Physics simulation. 400 keV electron — compare matter-wave K with relativity K_class vs K_rel chart; readouts should agree on β.
Relativistic KE
400 keV electron — compare matter-wave K with relativity K_class vs K_rel chart; readouts should agree on β.
A 400 keV electron has β from relativistic kinematics. Compare the matter-wave panel (highlighted) with the relativity chart: de Broglie λ = h/p uses relativistic p = γmₑv, while K_class = ½mₑv² lags K_rel = (γ−1)mₑc² at the same β. Readouts for β, K, and λ should be mutually consistent across both panels.
- K_rel vs K_class
- β from KE
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A 400 keV electron moves fast enough that relativistic effects matter (β ≈ 0.83). Does using the simple non-relativistic de Broglie formula λ = h/√(2mK) still give an accurate wavelength at this energy?
Predictions to weigh
- Yes — the non-relativistic formula still works fine at any electron energy.
- No — at this energy the electron's momentum must be computed relativistically; the non-relativistic formula would be noticeably wrong.
- Wavelength calculations don't depend on relativistic effects at all.
Variable roles
What you set:
- Kinetic energy K (eV)
What you measure:
- De Broglie wavelength λ (pm)
How the investigation runs
- Open the electron-ke-comparison preset and press Reset. This preset's default kinetic energy is 400 keV, giving β ≈ 0.83.
- Enable the de Broglie wavelength readout.
- Set the electron's kinetic energy for each trial (all in the relativistic regime) and record its de Broglie wavelength using the relativistic momentum formula.
Governing equation
Relativistic Momentum-Energy Relation — K = (γ − 1) m₀ c²
For a relativistic particle, momentum and kinetic energy relate through (pc)² = K(K + 2mc²), derived from the full relativistic energy-momentum relation E² = (pc)² + (mc²)². This reduces to the familiar non-relativistic p = √(2mK) only when K ≪ mc².
What the printable worksheet asks students to work out
- For one trial, compute the relativistic momentum via pc = √(K(K + 2m_ec²)) (with m_ec² ≈ 511 keV, the electron's rest energy), then λ = hc/(pc) — converting units carefully. Compare to the table.
- Explain why the relativistic momentum formula pc = √(K(K + 2mc²)) reduces to the familiar non-relativistic p = √(2mK) when K is much smaller than the rest energy mc² — and why that approximation breaks down once K becomes comparable to or larger than mc².
Where this shows up beyond the lab
- An electron's rest energy m_ec² ≈ 511 keV. At 400 keV kinetic energy, the electron's total energy is already about 78% more than its rest energy — solidly in the relativistic regime. Explain why physicists have a rule of thumb that relativistic corrections become important once kinetic energy approaches roughly 10% of rest energy.
- Particle accelerators routinely reach kinetic energies enormously larger than a particle's rest energy (ultra-relativistic). Explain why, in that extreme limit, pc ≈ K (momentum-energy and kinetic energy become nearly equal) even though that's clearly not true at everyday, non-relativistic speeds.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — A.5 Galilean and special relativity
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Electron Ke Comparison
- Select the electron
- Press Play
- Relativistic vs classical KE
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
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