What was the 'ultraviolet catastrophe'?

The discovery that ultraviolet light destroys all materials it touches The prediction by classical physics that a hot object should emit infinite energy in the ultraviolet and beyond — a prediction that completely contradicted experiment An accidental explosion caused by focusing ultraviolet light in a laboratory The failure of early UV lamps to produce enough light for experiments

How did Max Planck solve the ultraviolet catastrophe in 1900?

He proposed that ultraviolet light travels more slowly, reducing its energy He showed that classical electrodynamics was perfectly correct and the experiments were wrong He proposed that energy is not emitted continuously but in discrete packets (quanta) with energy E = hf — this mathematical assumption matched experiment perfectly He added a friction term to Maxwell's equations that absorbed excess high-frequency energy

What is Planck's constant (h), and what are its units?

h ≈ 3 × 10⁸ m/s — the speed of light in a vacuum h ≈ 6.626 × 10⁻³⁴ J·s — it sets the scale of quantum effects and relates a photon's energy to its frequency h = 1 J — a convenient unit for measuring quantum energies h ≈ 9.11 × 10⁻³¹ kg — the mass of an electron

Using E = hf, which photon has more energy — red light (f ≈ 4.3 × 10¹⁴ Hz) or violet light (f ≈ 7.5 × 10¹⁴ Hz)?

Red light — it has a longer wavelength, so each photon is larger They have the same energy — all visible photons carry the same energy Violet light — higher frequency means higher energy per photon Red light — it travels further, accumulating more energy along the way

What is a 'quantum' of energy?

Any large amount of energy, much greater than the electron's energy The minimum discrete unit of energy that can be emitted or absorbed at a given frequency — E = hf The energy of a single electron in the hydrogen ground state A unit of measurement equal to one joule divided by Planck's constant

Why did Planck's quantisation assumption explain why UV emission drops off at high frequencies?

High-frequency radiation travels too fast to be emitted by ordinary atoms At high frequencies, each quantum E = hf requires so much energy that thermally excited atoms rarely have enough to emit one — drastically reducing high-frequency emission High-frequency radiation is absorbed by the surrounding air before leaving the object Planck added a cut-off frequency above which no radiation could exist

What is a blackbody, and why is this concept important for understanding Planck's work?

An object that appears black in colour and reflects no visible light An idealised object that absorbs all radiation incident on it and emits radiation purely as a function of its temperature — the standard reference for studying thermal emission A black hole — a region where radiation is completely trapped by gravity A material that emits only black (invisible) radiation

As a blackbody gets hotter, what happens to the peak wavelength of its emission?

The peak wavelength increases — hotter objects emit redder light The peak wavelength decreases (shifts to shorter wavelengths, higher frequencies) — Wien's Displacement Law: λ_max = b/T The peak wavelength stays the same — only the intensity changes with temperature Peak wavelength is unrelated to temperature — it depends only on the material

Why is Planck's quantisation described as revolutionary even though Planck himself was uncomfortable with it?

It was not revolutionary — Planck just added a correction term to make the math work It showed that energy is fundamentally discrete at the microscopic level — contradicting the assumption of continuity that underpinned all of classical physics Planck discovered the electron using blackbody radiation experiments It unified electromagnetism and gravity for the first time

If Planck's constant were much larger — say 1 J·s instead of 6.626 × 10⁻³⁴ J·s — how would the world be different?

Nothing — Planck's constant has no effect on the everyday world Quantum effects would be apparent at human scales — throwing a ball would require discrete energy jumps and everyday objects would show wave-like diffraction Light would travel slower, making sunsets longer Atoms would be larger, making all matter less dense