Comparing Matter Waves of Different Particles
For any two particles, lambda_1/lambda_2 = p_2/p_1. Non-relativistically, use p = mv, p = square root of 2mK, or p = square root of 2m absolute q V according to the data.
Why this shows up in the exam
Comparing proton, electron, deuteron, and alpha-particle waves · Solving equal-energy or equal-momentum questions · Checking accelerator scaling relations
Learn the idea
Matter-wave comparisons become simple when every case is reduced to momentum. Mass, speed, energy, charge, and voltage can all differ, but wavelength cares only about final momentum. Converting each case to momentum prevents memorized ratio rules from being used outside their assumptions.
🧠 Memory hook: Compare momenta first; invert only at the final wavelength step.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- lambda₁/lambda₂ = p₂/p₁ — general wavelength ratio
- lambda proportional to 1/sqrt(mK) — comparison at specified non-relativistic kinetic energies
- lambda proportional to 1/sqrt(m |q| V) — comparison after acceleration from rest
How to approach it
- 1Write lambda₁/lambda₂ = p₂/p₁
- 2Translate the stated equal quantity into a momentum formula
- 3Simplify symbolically before substituting particle data
Common slip-ups that cost marks
- •Assuming equal kinetic energy means equal momentum for different masses
- •Ignoring the alpha particle's charge in equal-voltage problems
- •Inverting the wavelength ratio twice
🌟 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.
Photons of energy 5 eV illuminate a metal of work function 2 eV. Find the stopping potential.
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