Matter Waves in Collisions and Decays
Total vector momentum is conserved for an isolated collision or decay. After solving for each relevant momentum magnitude, the associated wavelength is h divided by that magnitude.
Why this shows up in the exam
Two-body decay wavelength ratios · Elastic-collision matter-wave questions · Completely inelastic collision wavelength calculations
Learn the idea
Use momentum conservation first, then convert each final momentum magnitude into wavelength. A collision or decay redistributes momentum before it determines wavelengths. The de Broglie formula does not replace mechanics; it translates the mechanical momentum result into wave language.
🧠 Memory hook: Conserve momentum first; attach wavelengths second.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum p_vector_initial = sum p_vector_final — momentum conservation for an isolated process
- lambda_i = h/|p_i| — wavelength assigned after the momentum solution
How to approach it
- 1Draw momentum directions and choose a sign convention
- 2Apply the correct collision or decay conservation laws
- 3Convert final momentum magnitudes to wavelengths
Common slip-ups that cost marks
- •Conserving wavelength instead of momentum
- •Ignoring opposite momentum directions
- •Assuming kinetic energy is conserved in an inelastic collision
🌟 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.
More from Dual Nature of Matter and Radiation
Photoelectric Effect
The photoelectric effect describes the emission of electrons from a material when it is exposed to light of sufficient frequency, governed by concepts such as threshold frequency, work function, stopping potential, and the Einstein photoelectric equation.
de Broglie Wavelength and Matter Waves
All matter exhibits wave-like properties, with the de Broglie wavelength inversely proportional to momentum and dependent on factors like velocity, temperature, and particle type.
Photon Properties and Energy-Momentum Relations
Photons are massless particles of light characterized by their energy, frequency, momentum, and charge neutrality, and their interactions obey conservation laws.
Photon Energy and Momentum
For a photon in vacuum, energy is proportional to frequency and momentum is energy divided by c. Frequency and wavelength obey c = nu lambda, so shorter-wavelength photons have larger energy and momentum.
Photon Rate, Power, and Energy Density
For monochromatic radiation, total energy is the number of photons times h nu. Power is energy per unit time, so the photon emission rate equals power divided by single-photon energy.
Radiation Pressure and Photon Momentum Transfer
Radiation force is the rate of photon momentum transfer. For normal incidence on an ideal absorber the pressure is intensity divided by c; for an ideal reflector it is twice that value.