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Dual Nature

The photoelectric equation and the de Broglie wavelength. Short questions, few with numeric answers, and the laws are often asked as statements.

Questions in the bank
131
q/paper in 2025–26
0.90
Numeric answer
6%
Notes pages
5

Tier: Long tail

When you’ll see it

Photons and their energy or momentum, the photoelectric effect and stopping potential, or the de Broglie wavelength of a particle.

How this chapter is tested

The chapter splits between light and matter. On the light side the questions ask what one photon carries and read the photoelectric effect through Einstein's equation. On the matter side most questions compare two particles' wavelengths.

The arithmetic is short if energies stay in electron-volts and hc is taken as 1240 eV nm. Few questions want a typed number; most are options and statements, and the statements about frequency, intensity and graphs repeat.

Marks are lost on what a ratio holds fixed: the same kinetic energy, the same voltage and the same wavelength give three different answers. Brighter light never changes the stopping potential. Photon energies carry straight into the transitions of Atoms, and the momentum of light is the radiation pressure of Electromagnetic Waves.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Photon energy, momentum and threshold

    E = hc/λ and p = h/λ; photons per second = P/E, so at equal power a longer wavelength sends more; a photon frees an electron only above the threshold frequency.

  • Photoelectric laws and graphs

    Frequency decides whether electrons leave and how fast the fastest move, intensity only how many; the V₀–ν line has slope h/e for every metal.

  • Einstein's equation

    hν = φ + eV₀; with two wavelengths on one metal, subtract the equations to remove φ; speeds go as the square root of the leftover energy.

  • de Broglie wavelength

    λ = h/p = h/√(2mK) = h/√(2mqV); an electric field changes λ, a magnetic field never does; electron diffraction shows the wave nature of matter.

  • Comparing wavelengths

    Same kinetic energy: λ ∝ 1/√m. Same voltage: λ ∝ 1/√(mq). Same speed: λ ∝ 1/m. The same wavelength means the same momentum, and a photon uses E = pc.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Brighter light

    More intensity sends more photons of the same energy. The current rises, but the stopping potential stays the same and the threshold does not fall.

  • Doubling the frequency

    K = hν − φ, so at 2ν the energy is 2K + φ, more than twice K. The stopping potential likewise more than doubles.

  • What the ratio holds fixed

    Same energy, same voltage and same speed give 1/√m, 1/√(mq) and 1/m. An alpha through the same voltage gains twice a proton's energy.

  • ω for ν

    A wave written as sin(ωt) gives the angular frequency; the photon energy is hω/2π. Using hω makes it 2π times too large.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Dual Nature notes

Drill every Dual Nature question

131 questions from the bank, across 5 subtopics.

Drill the 131 questions

Drill one subtopic at a time

The 5 subtopics, in teaching order.

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