Matter Wavelength in Electric and Magnetic Fields
Under a force, momentum evolves according to dp vector by dt = F vector, and the instantaneous wavelength is h divided by the momentum magnitude. A purely magnetic Lorentz force does no work, whereas an electric field can change kinetic energy.
Why this shows up in the exam
Charged-particle beam steering · Time-dependent matter-wave calculations · Separating electric and magnetic effects on wavelength
Learn the idea
Fields change de Broglie wavelength only by changing the particle's momentum magnitude. The wavelength tracks momentum, not merely the presence of a field. A magnetic field can bend a trajectory without changing speed, while an electric field can change both direction and speed.
🧠 Memory hook: Direction can bend while wavelength stays fixed; watch momentum magnitude.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- d p_vector/dt = q(E_vector + v_vector x B_vector) — momentum evolution of a charged particle
- lambda(t) = h / |p_vector(t)| — instantaneous de Broglie wavelength
- dK/dt = q E_vector dot v_vector — magnetic force alone does not change kinetic energy
How to approach it
- 1Find the momentum vector as a function of time
- 2Take its magnitude before computing wavelength
- 3Use work-energy as a shortcut when only kinetic energy is needed
Common slip-ups that cost marks
- •Assuming every magnetic field changes particle speed
- •Adding velocity components as scalars instead of vectors
- •Using lambda = h/(mv) after relativistic acceleration
🌟 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.