BLACK BODY RADIATION - MAX PLANCK               topics

Continuous spectra

Examples -

Infrared photo of OUR Galaxy!!!



Anything which is "hot" will absorb and emit electromagnetic radiation. That is what we mean when we say a stove element is "red hot" or a light filament is "white hot".

What is "hot"? Any temperature above -2730C or O kelvin.

Radiation coming in will impinge on the material's electrons, some will be reflected, some absorbed. Equally, the material's electrons are accelerating and can emit radiation, not much if cool, lots if warm. ( Whatever cool and warm are! ) Solids have electrons in energy bands rather than in the individual levels of single atoms. Metals are extreme examples of this characteristic. The electrons can therefore behave very freely - just as they do in a plasma - a gas of ionised particles such as the Sun. This allows them to behave as antennae and reflect etc.

All "hot" bodies of the same temperature have the same shape radiation graph with a peak at a characteristic point absolutely dependent on the temperature. However, different materials have different brightnesses of radiation. Tungsten in a filament lamp emits the same shape curve but at a slightly different strength than a ceramic at the same temperature.

We humans are at a temperature of 370C or 310 K. We therefore emit radiation with the peak in the infrared at 9.3 μm. We also emit microwaves and radio waves. A hot plate at 4000C or 673 K will have a peak at 4.3 μm but will also emit a little in the visible red. It will appear red hot!

(Infrared detectors "see" humans extremely well in the dark or cold because humans are brighter than their cooler surroundings. Infrared detectors are therefore common on Search and Rescue and military machines.)

Is there a greatest ( brightest ) curve? YES - that of a PERFECTLY BLACK OBJECT- one which will perfectly absorb every littlest bit of light ( radiation ) landing on it.

Most people know that black objects warm up faster than white objects in the sun. What most do not realise is that black things cool down faster than white ones when out of the sun! ( Chip cooling fins on ICs should be painted black, insulation foil in walls of houses and in vacuum flasks are white - silver ( same thing ) for these reasons. )

PROBLEM - How to make a Black Body ? - Solution - by making a CAVITY RADIATOR.

Imagine you are terrified by your big sister/brother - pretty easy unless you are the eldest.( If you are the eldest - try your little sibling .) You are to go down the corridor past their bedroom door which is slightly ajar on your way bed. IT IS SPOOKY. The gap is BLACK, Fearsome Creatures live in there!!

You can see that light entering the door gets in BUT FINDS IT HARD TO ESCAPE. The gap is a black body!

Further, the interior radiation must be in an equilibrium state - no light can enter, none can escape so the emissions must balance the absorptions, and the light must be as bright as is possible for the temperature of the room.

When, in practice, hollow metals or ceramics are heated, the radiation from a tiny hole is indeed brighter (more energy per second for the volume inside) than the surface and IS Black Body (BB) . You have seen or felt this no doubt when looking into the family fire when the hottest radiation clearly comes from gaps between red hot coals. ( Hottest - read brightest or most intense or most energy per second for the volume. )


How to match the known emitted radiation of a "hot" object with theory - "The Black Body problem".

Situation late C19th.

German Physicist, Max Planck, wrestled with the problem and finally managed to come up with the correct curve by modifying Wien's graphical fit. He realised that inserting "-1" in the denominator gave the right equation. He had no idea at first why it worked.

1900-01 - he found a method of getting the correct graph. How he got there later horrified him. He "incorrectly" used Boltzmann's entropy theory by not completing a limiting process as used in calculus. For those who know calculus, taking limits smooths, makes continuous, processes. As it was, the theory was discontinuous, lumpy. Had he - he would have ended up back at the Rayleigh-Jeans' result, which was wrong. In essence, he had to use LITTLE BITS OF ENERGY IN EMISSION AND ABSORPTION . Each little bit was associated with a frequency.

ΔE = h f

h = constant, Planck's Constant = 6.623 x 10-34 Js

He spent years trying to regularize ( "classicise" ) the maths but failed. Einstein was the one who recognised that a whole new physics was evolving - quantum physics. He used the ideas further in solving the Photoelectric Effect and developing Bose-Einstein statistics.


The Universe is the perfect cavity - it has no leaks and contains all of its radiation. It therefore has a temperature - a Black Body radiation spectrum belonging to a certain temperature. That temperature is 2.728 K. The curve is in the microwave region and is small but real. The radiation curve is near proof that the Universe had a very hot beginning ( the Big Bang - though now replaced by the "Inflation Theory".)

The Universe is now thought to have been "born" about 12-15 billion years ago and occupied no volume at first. It rapidly expanded and some of the radiation condensed into matter. As the Universe has continued to expand, the remnant radiation has stretched with it lengthening the wavelength and so "cooling" it - ie associating it with a lower BB temperature.