Matter waves: wave nature of particles
If light waves can act as particles, moving particles can act as waves. de Broglie called these matter waves; they show up only for tiny particles like electrons.
de Broglie's idea
Light shows both wave and particle nature. In 1924, the French physicist Louis de Broglie argued that nature should be symmetrical. If radiation has a dual nature, then moving material particles (electrons, protons, even a ball) should also show wave nature. He called these waves matter waves. Their wavelength is λ = h/p, where p = mv is the momentum of the particle. This de Broglie relation links a wave property (λ) with a particle property (p).
Worked example: a cricket ball and an electron
Compare the de Broglie wavelengths of (a) a cricket ball of mass 0.15 kg moving at 20 m/s, and (b) an electron moving at 7.28 × 10⁶ m/s. (h = 6.63 × 10⁻³⁴ J s, mₑ = 9.11 × 10⁻³¹ kg)
- (a) p = mv = 0.15 kg × 20 m/s = 3.0 kg m/s.
- λ = h/p = (6.63 × 10⁻³⁴ J s) ÷ (3.0 kg m/s) = 2.21 × 10⁻³⁴ m.
- (b) p = 9.11 × 10⁻³¹ kg × 7.28 × 10⁶ m/s ≈ 6.63 × 10⁻²⁴ kg m/s.
- λ = (6.63 × 10⁻³⁴) ÷ (6.63 × 10⁻²⁴) m = 1.0 × 10⁻¹⁰ m = 0.1 nm.
- The ball's wavelength is about 4.5 × 10²³ times shorter, and far smaller than even a nucleus.
Ball: about 2.2 × 10⁻³⁴ m (impossible to detect); electron: about 0.1 nm (about the spacing of atoms in a crystal, so measurable)
Key points about matter waves
- Wave nature is noticed only when λ is comparable to the size of the slit or obstacle.
- λ ∝ 1/p: the heavier or faster the particle, the shorter its wavelength.
- Matter waves are not electromagnetic waves. Any moving particle has them, charged or neutral, such as a neutron.
- The same relation holds for photons: p = h/λ.
- For an electron, λ is about the spacing between atoms in a crystal, close to X-ray wavelengths, so it can be measured.
- Extra reading, not in your textbook: the electron microscope uses the very short wavelength of fast electrons to show far finer detail than a light microscope.
Dual nature of radiation vs dual nature of matter
Electron microscopes in Indian research laboratories and hospitals use the wave nature of electrons. Their wavelength is thousands of times shorter than that of light, so they can show viruses and the fine parts of cells.
2 marks: “Why is the wave nature of matter not observed in daily life? Support your answer with an estimate.” λ = h/mv is tiny for large m. A 0.15 kg ball at 20 m/s has λ ≈ 2 × 10⁻³⁴ m, far smaller than any slit, so no diffraction can be seen.
1 marks: “Who proposed matter waves, and what is the expression for their wavelength?” Louis de Broglie (1924); λ = h/p = h/mv.
2 marks: “An electron and a proton move with the same speed. Which has the longer de Broglie wavelength, and why?” The electron. λ = h/mv, and the electron's mass is about 1/1836 of the proton's, so its λ is about 1836 times longer.
Light can be lumpy; matter can be wavy. λ = h/p, so heavy or fast means a tiny λ.