Chapter 3

Introduction

In the previous chapter, we discovered that the Sun emits most of its energy as visible and infrared light because of its surface temperature. But that raises a much deeper question. Why should temperature determine the colour of light at all?

The answer lies in one of the most important ideas in physics: black-body radiation.

Black-body radiation explains why every hot object, from a glowing piece of metal to the surface of the Sun, produces its own unique pattern of electromagnetic radiation. It explains why stars have different colours, why hotter objects shine more brightly, and ultimately why the Sun produces exactly the kind of light that powers solar panels.

Everything Glows

At first glance, the idea of black-body radiation sounds impossible. Surely objects only emit light when they become extremely hot?

In reality, everything glows.

Every object with a temperature above absolute zero contains atoms and molecules that are constantly moving. As these tiny charged particles vibrate and collide, they continually emit electromagnetic radiation.

Your body glows. A cup of tea glows. A block of ice glows. Even the Earth itself glows.

Most of this radiation is emitted as infrared light, making it invisible to our eyes. Only when an object becomes hot enough does a significant amount of its radiation shift into the visible part of the spectrum, allowing it to glow.

What is a Black Body?

To understand this behaviour, physicists imagined a perfect object. Imagine a material that absorbs every single photon that strikes it. None are reflected and none pass through. Every bit of incoming radiation is absorbed. 

This ideal object is known as a black body.

Because it absorbs energy perfectly, it must also emit energy perfectly. A black body is therefore the most efficient possible emitter of thermal radiation.

No perfectly black body exists in nature. However, many real objects behave remarkably similarly. The Sun, stars, planets and even the human body all emit radiation that closely follows black-body theory.

For this reason, black-body radiation provides an excellent model for understanding sunlight.

Temperature Changes Colour

Imagine placing a steel bar inside a furnace. At first, nothing appears to happen. Although the bar is emitting electromagnetic radiation, almost all of it is infrared, which is invisible to your eyes. As the temperature continues to rise, something remarkable happens.

The bar begins to glow a dull red. Heat it further and the glow becomes orange. Then yellow. Eventually it becomes almost white.

The metal hasn't changed. The only thing that has changed is its temperature.

As the metal becomes hotter, its brightest emitted wavelength gradually shifts from the infrared towards the visible part of the spectrum. More and more visible light is produced, causing its colour to change.

Stars behave in exactly the same way. Cool stars appear reddish because they emit more long-wavelength light, while hotter stars appear white or blue because they emit proportionally more short-wavelength light. A star's colour therefore provides astronomers with an immediate clue to its surface temperature.

The Black-Body Spectrum

It might be tempting to think that a hot object emits just one colour of light. In reality, every object emits many wavelengths at the same time.

If we plotted the amount of energy emitted against wavelength, we would obtain a smooth curve known as a black-body spectrum. Rather than producing a single wavelength, the object emits radiation across a continuous range of wavelengths, with some emitted more strongly than others.

As the temperature increases, two important things happen. The entire curve rises, meaning the object emits much more energy overall. At the same time, the peak of the curve shifts towards shorter wavelengths.

This explains why hotter objects appear bluer while cooler objects appear redder. It also explains why the Sun emits visible light alongside infrared and ultraviolet radiation. Visible light is simply the brightest part of a much broader spectrum.

Wien's Displacement Law

As scientists studied glowing objects, they noticed a remarkable pattern. No matter whether they were heating metal in a laboratory or observing distant stars, hotter objects always reached their maximum brightness at shorter wavelengths.

This relationship became known as Wien's Displacement Law:

λmax = b / T

where:

• λmax = the wavelength at which the object emits most strongly.

• T = the object's absolute temperature in kelvin (K).

• b = Wien's constant (approximately 2.9 × 10⁻³ m·K).

The equation reveals a beautifully simple relationship. As temperature increases, the peak wavelength decreases.

For the Sun, whose surface temperature is approximately 5,800 K, the peak wavelength is around 500 nanometres, placing it almost exactly in the middle of the visible spectrum.

This simple relationship allows astronomers to estimate the surface temperatures of distant stars simply by measuring the colour of the light they emit.

The Stefan-Boltzmann Law

Temperature changes more than colour. It also changes brightness.

As an object becomes hotter, it doesn't simply shift towards shorter wavelengths. It also emits dramatically more energy. This relationship is described by the Stefan-Boltzmann Law.

P = σAT⁴

where:

• P = the total power emitted (watts).

• σ = the Stefan-Boltzmann constant.

• A = the surface area of the object.

• T = the object's absolute temperature in kelvin (K).

The most important feature of this equation is the fourth power of temperature. Double an object's temperature and it emits sixteen times more energy.

This explains why stars are such extraordinarily powerful sources of radiation despite having surface temperatures of "only" a few thousand degrees.

Why Black-Body Radiation Matters

We can now answer the question we asked at the beginning of this chapter. Why does the Sun produce mostly visible light?

Because an object with a surface temperature of around 5,800 K naturally produces a black-body spectrum that peaks in the visible part of the electromagnetic spectrum.

The Sun isn't designed to emit visible light. It couldn't emit anything else.

Its spectrum is simply the inevitable consequence of the laws of physics. This turns out to be remarkably fortunate. Silicon solar cells are particularly effective at converting visible and near-infrared photons into electricity, meaning the Sun naturally produces exactly the wavelengths that make solar power possible.

Without black-body radiation, there would be no sunlight as we know it, and without sunlight, there would be no solar energy.

Looking Ahead 

Black-body radiation tells us how the temperature of an object determines the wavelengths of light it emits But another important question remains.

Although the Sun produces light across a broad range of wavelengths, do all of those photons carry the same amount of energy?

The answer is no.

Some photons carry only tiny amounts of energy, while others carry thousands or even millions of times more.

In the next chapter, we'll discover the simple relationship between wavelength, frequency and photon energy, one of the fundamental ideas at the heart of quantum physics.