Dual Nature of Radiation and Matter

Physics · Class 12

Lesson 11 of 11 · 15 min

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Must-know facts

20 facts

  1. 1Work function φ₀: least energy for an electron to escape a metal surface; 1 eV = 1.602 × 10⁻¹⁹ J.
  2. 2Three ways out: thermionic (heat), field (about 10⁸ V m⁻¹, spark plug), photoelectric (light of suitable frequency).
  3. 3e/m of the electron = 1.76 × 10¹¹ C/kg; elementary charge 1.602 × 10⁻¹⁹ C (Millikan, 1913).
  4. 4Hertz found photoelectric emission in 1887; Hallwachs and Lenard studied it in 1886–1902.
  5. 5Zinc, cadmium and magnesium need ultraviolet; alkali metals (Li, Na, K, Cs, Rb) respond to visible light.
  6. 6Photocurrent and saturation current are proportional to intensity.
  7. 7Stopping potential V₀ is independent of intensity and rises linearly with frequency; Kmax = eV₀.
  8. 8Changing frequency at fixed intensity changes V₀ but leaves the saturation current the same.
  9. 9Below 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

Saying brighter light raises the stopping potential.

Intensity raises only the saturation current. V₀ depends on frequency and the metal.

Expecting very intense red light to eject electrons from a metal whose threshold is in the ultraviolet.

Below ν₀ there is no emission at all; one photon must carry at least φ₀.

Using Kmax = hν − φ₀ with hν in joules and φ₀ in electron volts.

Convert first: 1 eV = 1.6 × 10⁻¹⁹ J (1.602 × 10⁻¹⁹ J exactly as NCERT states).

Thinking the slope of the V₀–ν line depends on the metal.

The slope is h/e for every metal; only the intercept ν₀ = φ₀/h changes.

Believing all photoelectrons leave with Kmax.

Kmax belongs to the least tightly bound electrons; others come out slower.

Expecting a delay before emission in dim light.

Each absorption is one instantaneous event; dim light only means fewer electrons.

Saying the stopping potential is positive on the collector.

It is a retarding potential: the collector is made negative with respect to the emitter.

Thinking a heavier or faster particle has a longer de Broglie wavelength.

λ = h/mv: larger m or v gives a shorter wavelength.

Assuming the de Broglie wavelength depends on the particle's charge.

Only momentum matters; charge and material do not enter λ = h/p.

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.
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