Dual Nature of Radiation and Matter

Physics · Class 12

Lesson 11 of 11 · 15 min

Chapter review

Watch a class

The whole chapter on YouTube

Arvind AcademyWhole chapter · Hinglish

Photoelectric effect and de Broglie, full chapter

Open on YouTube
Next Toppers - 12th ScienceWhole chapter · Hinglish

Complete chapter revision for boards

Open on YouTube
Loading the full lesson

Must-know facts

20 facts

  1. 01Work function φ₀: least energy for an electron to escape a metal surface; 1 eV = 1.602 × 10⁻¹⁹ J.
  2. 02Three ways out: thermionic (heat), field (about 10⁸ V m⁻¹, spark plug), photoelectric (light of suitable frequency).
  3. 03e/m of the electron = 1.76 × 10¹¹ C/kg; elementary charge 1.602 × 10⁻¹⁹ C (Millikan, 1913).
  4. 04Hertz found photoelectric emission in 1887; Hallwachs and Lenard studied it in 1886–1902.
  5. 05Zinc, cadmium and magnesium need ultraviolet; alkali metals (Li, Na, K, Cs, Rb) respond to visible light.
  6. 06Photocurrent and saturation current are proportional to intensity.
  7. 07Stopping potential V₀ is independent of intensity and rises linearly with frequency; Kmax = eV₀.
  8. 08Changing frequency at fixed intensity changes V₀ but leaves the saturation current the same.
  9. 09Below the threshold frequency ν₀ there is no emission, however intense the light.
  10. 10Emission is instantaneous: delay of about 10⁻⁹ s or less.
  11. 11Einstein (1905): Kmax = hν − φ₀; ν₀ = φ₀/h.
  12. 12V₀ = (h/e)ν − φ₀/e: slope h/e, the same for every metal; intercept on the ν axis is ν₀.
  13. 13Millikan (1906–1916) measured the slope for sodium and confirmed the equation; h = 6.626 × 10⁻³⁴ J s.
  14. 14Photon: E = hν = hc/λ, p = hν/c = h/λ, speed c, no charge.
  15. 15More intensity means more photons per second, not more energy per photon.
  16. 16Example 11.1: 2.0 mW at 6.0 × 10¹⁴ Hz → 3.98 × 10⁻¹⁹ J per photon, 5.0 × 10¹⁵ photons per second.
  17. 17Example 11.2: caesium, 2.14 eV → ν₀ = 5.16 × 10¹⁴ Hz; V₀ = 0.60 V → λ = 454 nm.
  18. 18de Broglie (1924): λ = h/p = h/mv.
  19. 19Electron at 5.4 × 10⁶ m/s: λ = 0.135 nm, comparable with X-rays.
  20. 20Ball of 0.150 kg at 30.0 m/s: λ = 1.47 × 10⁻³⁴ m, far beyond measurement.

Common traps

Where marks are lost

Formulas

8 to know

Stopping potential

Kmax = eV₀

V₀ is the smallest retarding potential that stops the photocurrent.

Einstein's photoelectric equation

Kmax = hν − φ₀

Holds for ν ≥ ν₀.

Threshold frequency

ν₀ = φ₀/h

Threshold wavelength λ₀ = hc/φ₀.

Stopping potential against frequency

V₀ = (h/e)ν − φ₀/e

Straight line of slope h/e; eV₀ = h(ν − ν₀).

Photon energy

E = hν = hc/λ

h = 6.63 × 10⁻³⁴ J s in NCERT's worked examples.

Photon momentum

p = hν/c = h/λ

Same for every photon of a given frequency.

Photons per second

N = P/E

P is the beam's power, E the energy of one photon.

de Broglie relation

λ = h/p = h/mv

Matter wave of a particle of mass m and speed v.

Key terms

16 terms

Work function
The least energy an electron needs to escape from a metal surface, written φ₀.
Electron volt
Energy an electron gains across 1 V: 1.602 × 10⁻¹⁹ J.
Thermionic emission
Electrons escaping from a metal that has been heated strongly.
Field emission
Electrons pulled out of a metal by a very strong electric field.
Photoelectric emission
Electrons ejected from a surface by light of suitable frequency.
Photoelectron
An electron released from a surface by light.
Emitter and collector
The photosensitive plate C that releases electrons, and the plate A that gathers them.
Saturation current
The largest photocurrent, reached when every emitted electron gets to the collector.
Stopping potential
The smallest retarding potential on the collector that brings the photocurrent to zero.
Threshold frequency
The lowest frequency that can eject electrons from a given metal; ν₀ = φ₀/h.
Quantum
A single packet of radiation energy, hν.
Photon
The particle of light: energy hν, momentum h/λ, speed c, no charge.
Planck's constant
h = 6.626 × 10⁻³⁴ J s; links a photon's energy to its frequency.
Dual nature
Radiation and matter each show wave behaviour in some experiments and particle behaviour in others.
Matter wave
The wave associated with a moving material particle.
de Broglie wavelength
λ = h/p, the wavelength of a particle's matter wave.
Question bankTest yourself: 10 questionsExam-style questions on Dual Nature of Radiation and Matter, with full solutions.Start
Dual Nature of Radiation and Matter Revision | Class 12