Chapter 4

Introduction

By the time sunlight reaches Earth's surface, it consists of trillions upon trillions of photons travelling at the speed of light.

Although every photon is a particle of light, they do not all carry the same amount of energy. Some photons possess only a tiny amount of energy, while others carry thousands or even millions of times more.

Why?

The answer lies in one of the most important discoveries in modern physics. A photon's energy depends entirely on its frequency, or equivalently, its wavelength.

Understanding this simple relationship helps explain everything from radio communications and medical X-rays to the light that powers life on Earth.

Planck's Revolutionary Idea

For centuries, scientists believed that light could possess any amount of energy. Then, in 1900, German physicist Max Planck proposed something extraordinary.

He suggested that light is not emitted as a continuous stream but in tiny, indivisible packets of energy called quanta. Today, these packets are known as photons.

At first, Planck considered this little more than a mathematical idea to explain his observations. Instead, it became one of the foundations of quantum physics, transforming our understanding of the Universe.

The Planck Equation

Planck discovered that the energy carried by a photon depends directly on its frequency. This relationship is described by one of the most famous equations in physics:

E = hf

where:

• E = the energy of the photon, measured in Joules (J).

• h = Planck's constant, approximately 6.626 × 10⁻³⁴ (J·s).

• f = the frequency, measured in Hertz (Hz)

The equation reveals a remarkably simple rule. The higher the frequency, the greater the energy carried by each photon.

Double the frequency, and every photon carries twice as much energy.

Wavelength and Energy

Earlier, we learned that frequency and wavelength are closely related.

Every electromagnetic wave travels through a vacuum at the speed of light. As a result, shorter wavelengths always have higher frequencies, while longer wavelengths have lower frequencies.

Combining this relationship with Planck's equation gives another useful expression:

E = hc / λ

where:

• E = the energy of the photon, measured in Joules (J).

• h = Planck's constant, approximately 6.626 × 10⁻³⁴ (J·s).

• c = speed of light in a vacuum, approximately 299,792,458 m/s

• λ (lambda) = wavelength, measured in metres (m)

Instead of thinking about frequency, we can now describe photon energy using wavelength alone. The shorter the wavelength, the greater the energy. The longer the wavelength, the lower the energy.

This is why gamma rays are far more energetic than visible light, while radio waves carry comparatively little energy, even though every one of them travels through space at exactly the same speed.

Comparing Photon Energies

The differences in photon energy are far greater than most people imagine. A blue photon carries noticeably more energy than a red photon, even though the two colours appear side by side in a rainbow.

Move further along the electromagnetic spectrum and the differences become enormous. A single ultraviolet photon carries more energy than visible light, while an X-ray photon may carry hundreds or even thousands of times more energy than the light our eyes can detect.

At the opposite end of the spectrum, radio photons carry only tiny amounts of energy.

Yet despite these enormous differences, every photon still travels through space at exactly the same speed: the speed of light. The only thing that changes is the amount of energy each photon carries.

Why Photon Energy Matters

Photon energy determines how light interacts with the world around us.

Low-energy radio photons can travel enormous distances carrying television broadcasts, mobile phone signals and satellite communications. Visible photons stimulate the light-sensitive cells inside our eyes, allowing us to see. Ultraviolet photons possess enough energy to damage DNA, causing sunburn after prolonged exposure. X-rays carry even more energy, allowing them to pass through soft tissue while being absorbed by bone, making medical imaging possible.

Although all of these are forms of light, their behaviour differs dramatically because each photon carries a different amount of energy.

As we will soon discover, this same principle also determines whether a photon can transfer its energy to matter.

Looking Ahead

We now know that every photon carries a precise amount of energy determined by its wavelength.

But carrying energy is only part of the story.

For anything to happen, a photon must first encounter matter.

What happens next depends not only on the photon itself, but also on the material it strikes. Some photons are reflected. Others pass straight through. Others are absorbed completely.

These simple interactions determine everything from why we can see the world around us to how sunlight can eventually be converted into electricity.

In the next chapter, we'll explore what happens when light finally meets matter.