Dual Nature of Radiation and Matter

NCERT Class 12 Physics Chapter 11

Dual Nature of Radiation and Matter for Class 12 Physics, JEE and NEET: the photoelectric effect, Einstein’s equation, photons and de Broglie waves.

7 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part II (Class 12), Chapter 11 “Dual Nature of Radiation and Matter”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.8 MB, ncert.nic.in) (opens in a new tab)

Checked on 19 Oct 2026.

Learn in this order

  1. Electron emission and work function

    Work function, electron volt to joule, thermionic, field and photoelectric emission, with solved examples.

    NCERT Sections 11.1–11.2 12 min read 4 solved examples 7 practice questions

  2. Photoelectric effect: Hertz, Hallwachs and Lenard

    Hertz’s discovery, Hallwachs’ and Lenard’s observations, photoelectrons and the threshold frequency.

    NCERT Section 11.3 10 min read 4 solved examples 7 practice questions

  3. Experimental study of the photoelectric effect

    The photoelectric experiment, its four laws, Kmax = eV0 and the graphs.

    NCERT Section 11.4 12 min read 4 solved examples 7 practice questions

  4. Photoelectric effect and the wave theory of light

    Why the wave theory fails to explain the threshold, a fixed Kmax and instant emission.

    NCERT Section 11.5 9 min read 4 solved examples 7 practice questions

  5. Einstein’s photoelectric equation

    Kmax = hν − φ0, threshold frequency and wavelength, the V0–ν graph and solved examples.

    NCERT Section 11.6 13 min read 4 solved examples 7 practice questions

  6. The photon: particle nature of light

    Particle nature of light, energy E = hν = hc/λ, momentum p = h/λ, properties, photons per second and solved examples.

    NCERT Section 11.7 11 min read 4 solved examples 7 practice questions

  7. Wave nature of matter: de Broglie wavelength

    The de Broglie relation λ = h/p, λ = h/√(2mK), electrons through V volts, and why balls show no waves.

    NCERT Section 11.8 13 min read 4 solved examples 8 practice questions

Key formulas in this chapter

Electron emission

  • 1 eV = 1.602 × 10−19 J
  • energy gained = e × V
  • m = e/(e/m)

Photoelectric effect

  • n = I/e (electrons per second)
  • ν = c/λ

Experimental study of the photoelectric effect

  • Kmax = eV0
  • photocurrent ∝ intensity

Photoelectric effect and the wave theory

  • time ≈ energy needed / power per electron
  • E = hν (one quantum)

Einstein’s photoelectric equation

  • E = hν
  • Kmax = hν − φ0
  • ν0 = φ0/h
  • λ0 = hc/φ0
  • Kmax = eV0
  • V0 = (h/e)ν − φ0/e

Photon

  • E = hν = hc/λ
  • p = h/λ
  • N = P/E

Wave nature of matter

  • λ = h/p ≈ h/mv (v ≪ c)
  • λ = c/ν (photon)
  • λ = h/√(2mK)
  • λ = h/√(2mqV)
  • λ ≈ 1.227/√V nm (electron)
  • λrms = h/√(3m kB T)

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