understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence for a wave nature

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Wave‑Particle Duality

Wave‑Particle Duality

The concept of wave‑particle duality states that electromagnetic radiation (and, more generally, all quantum particles) exhibits both wave‑like and particle‑like properties depending on the experimental context. This dual nature is a cornerstone of modern physics and is demonstrated most clearly by the photoelectric effect, interference, and diffraction.

Learning Objective

Understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation, while phenomena such as interference and diffraction provide evidence for a wave nature.

1. Evidence for the Particulate Nature – The Photoelectric Effect

When light shines on a metal surface, electrons are emitted. Key observations:

  • The kinetic energy of emitted electrons depends on the frequency of the incident light, not its intensity.

  • No electrons are emitted below a certain threshold frequency, regardless of light intensity.

Einstein’s explanation (1905) treats light as a stream of photons, each carrying energy \$E = h\nu\$, where \$h\$ is Planck’s constant and \$\nu\$ is the frequency.

Einstein’s photoelectric equation:

\$K_{\max}=h\nu-\phi\$

where \$K_{\max}\$ is the maximum kinetic energy of the emitted electrons and \$\phi\$ is the work function of the metal.

From the equation we see:

  1. Increasing intensity (more photons) increases the number of emitted electrons but not their kinetic energy.

  2. Increasing frequency increases \$K_{\max}\$ linearly, confirming the photon energy \$h\nu\$.

2. Evidence for the Wave Nature – Interference and Diffraction

When coherent light passes through two slits or around an obstacle, a pattern of alternating bright and dark regions is observed. This pattern can only be explained if light behaves as a wave that can superpose.

2.1 Double‑slit Interference

The condition for constructive interference (bright fringes) is

\$d\sin\theta = m\lambda\$

and for destructive interference (dark fringes)

\$d\sin\theta = \left(m+\tfrac12\right)\lambda\$

where \$d\$ is the slit separation, \$\theta\$ the angle to the central axis, \$m\$ an integer (order), and \$\lambda\$ the wavelength.

2.2 Single‑slit Diffraction

The minima in a single‑slit diffraction pattern satisfy

\$a\sin\theta = m\lambda\qquad (m=1,2,3,\dots)\$

where \$a\$ is the slit width.

Both sets of equations predict the observed spacing of bright and dark bands, confirming the wave character of light.

3. Synthesis – Complementarity

Quantum objects cannot be described fully by either a pure wave model or a pure particle model. The principle of complementarity, introduced by Niels Bohr, states that wave and particle aspects are mutually exclusive descriptions that together give a complete picture.

4. Summary Table

PhenomenonKey ObservationInterpretation
Photoelectric EffectElectron kinetic energy \$K_{\max}=h\nu-\phi\$; threshold frequencyLight consists of photons with energy \$E=h\nu\$ (particle nature)
Double‑slit InterferenceBright and dark fringes obey \$d\sin\theta = m\lambda\$Light behaves as a coherent wave that interferes with itself (wave nature)
Single‑slit DiffractionIntensity minima at \$a\sin\theta = m\lambda\$Wave spreading and superposition (wave nature)
Compton Scattering (optional)Shift in wavelength \$\Delta\lambda = \frac{h}{m_ec}(1-\cos\theta)\$Photon momentum \$p = h/\lambda\$ (particle nature)

5. Suggested Classroom Activities

  • Demonstrate the photoelectric effect using a U \cdot lamp and a metal plate connected to a voltmeter; record stopping potential versus frequency.

  • Use a laser pointer and a double‑slit slide to observe interference fringes; measure fringe spacing and calculate \$\lambda\$.

  • Analyse diffraction patterns from a single slit of known width; compare measured minima positions with theory.

Suggested diagram: Sketch of the double‑slit experiment showing incident wavefronts, two coherent sources, and resulting interference pattern on a screen.

Suggested diagram: Energy diagram of the photoelectric effect illustrating photon absorption, work function \$\phi\$, and emitted electron kinetic energy \$K_{\max}\$.

6. Key Equations (for Revision)

  • \$E = h\nu\$ – photon energy

  • \$p = \dfrac{h}{\lambda}\$ – photon momentum

  • \$K_{\max}=h\nu-\phi\$ – photoelectric equation

  • \$\lambda = \dfrac{h}{p}\$ – de Broglie wavelength (general particle‑wave relation)

  • \$d\sin\theta = m\lambda\$ – double‑slit constructive interference

  • \$a\sin\theta = m\lambda\$ – single‑slit diffraction minima

7. Concluding Remarks

The photoelectric effect and interference/diffraction experiments together demonstrate that electromagnetic radiation cannot be classified solely as a wave or a particle. Mastery of these concepts is essential for progressing to quantum mechanics and for solving A‑Level exam questions that require clear, evidence‑based reasoning.