What was de Broglie's central hypothesis (1924)?

Electrons orbit the nucleus in specific circular paths, like planets around the sun All matter — not just light — has wave properties, with wavelength λ = h/p, where p is the particle's momentum Energy is quantised in atoms, so only specific electron energies are allowed Matter can be converted into light when it is accelerated to the speed of light

How does the de Broglie wavelength change as a particle moves faster?

The wavelength increases — faster particles have more energy and longer waves The wavelength decreases — λ = h/p = h/(mv), so higher speed means higher momentum and shorter wavelength The wavelength stays the same — it depends only on the particle's mass, not speed The wavelength becomes zero — classical mechanics applies once the particle is moving

Which particles have the longest de Broglie wavelength at the same speed: electron, proton, or neutron?

The proton — it is positively charged and interacts more strongly with matter The neutron — it has no charge, so nothing slows it down The electron — it is the lightest, so λ = h/mv is largest at any given speed All three have the same wavelength at the same speed

What did the Davisson-Germer experiment (1927) demonstrate?

Electrons are deflected by magnetic fields — confirming they carry charge Electrons scatter off a nickel crystal surface in a diffraction pattern consistent with their de Broglie wavelength — directly confirming matter waves Electrons travel at the speed of light inside metals Electrons are composed of smaller particles called quarks

How did de Broglie's matter waves provide a physical explanation for Bohr's quantised orbits?

The electron wave bounces back and forth between the proton and the edge of the atom The allowed orbits are those where an integer number of electron wavelengths fits exactly around the circumference — forming stable standing waves Electrons in non-allowed orbits emit too much radiation and fall into the nucleus De Broglie showed Bohr's orbits were incorrect — electrons actually have no defined orbit

An electron microscope uses electrons instead of light. What is the key advantage?

Electrons travel faster than light, giving a time advantage in scanning Electrons can be given very short de Broglie wavelengths (much shorter than visible light) by accelerating them to high speeds — enabling imaging of features far too small for optical microscopes Electron microscopes use no lenses — this eliminates all optical aberrations Electrons can penetrate any material, so you can image inside solid objects without cutting them

Why don't humans show wave-like behaviour despite being made of quantum particles?

Humans are too complex for quantum laws to apply — these laws only work for simple particles A person's de Broglie wavelength is astronomically small (far smaller than any atomic spacing) — quantum effects exist in principle but are completely undetectable Quantum mechanics only applies at temperatures near absolute zero Consciousness prevents quantum behaviour in living organisms

Neutron diffraction is used to study the structure of materials. What property makes neutrons useful for this?

Neutrons carry no charge, so they travel faster than electrons and produce sharper images Thermal neutrons have de Broglie wavelengths comparable to atomic spacings and are sensitive to light atoms (like hydrogen) that X-rays often miss Neutrons are heavier than protons, giving them shorter wavelengths and higher resolution than electrons Neutrons glow when near crystal lattices — this makes lattice defects visible

De Broglie's wavelength formula λ = h/p is universal. Calculate the de Broglie wavelength of a 0.1 kg ball travelling at 10 m/s (h = 6.6 × 10⁻³⁴ J·s). Which statement is true?

λ = 6.6 × 10⁻³⁴ m — far too small to ever detect or cause observable quantum effects λ = 6.6 × 10⁻³³ m — still smaller than an atom but potentially detectable λ = 66 nm — in the UV range, enough to cause noticeable diffraction λ = 0 m — classical objects have no wavelength

What is the broader significance of de Broglie's hypothesis for quantum theory?

It resolved the ultraviolet catastrophe that Planck couldn't fully explain It showed wave-particle duality is universal — not just a quirk of light — and directly inspired Schrödinger to develop his wave equation for matter It proved Einstein's special relativity was wrong at atomic scales It showed electrons are made of smaller waves called photons