de Broglie Wavelength
The de Broglie hypothesis assigns wavelength lambda = h/p to a particle of momentum p. For non-relativistic motion p = m v; the momentum form remains the safest starting point whenever direction or collisions matter.
Why this shows up in the exam
Estimating matter-wave scales · Comparing microscopic and macroscopic wave behavior · Inferring momentum from measured wavelength
Learn the idea
Every moving particle has a wavelength inversely proportional to its momentum. Matter behaves more wave-like when its momentum is small. Increasing either mass or speed usually shortens the wavelength, which is why wave effects are easy to see for microscopic particles but not everyday objects.
🧠 Memory hook: More momentum means less wavelength.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- lambda = h/p — general de Broglie relation in terms of momentum magnitude
- lambda = h/(m v) — non-relativistic wavelength for a particle of mass m and speed v
How to approach it
- 1Start from lambda = h/p
- 2Choose the correct momentum relation for the given regime
- 3Use ratios before substituting constants
Common slip-ups that cost marks
- •Using velocity with sign instead of momentum magnitude for wavelength
- •Applying p = m v at relativistic speeds
- •Assuming only charged particles have matter waves
🌟 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.