Background
Classical particle view: A long time ago, scientists believed that light was made up of very small particles, kind of like tiny balls, that travel through empty space. They thought these particles could explain how light moved and how we could see things.
Wave behavior observed: Later, scientists did many experiments and noticed that light could do things like bounce off surfaces (which is called reflection), bend when it enters a new material like water or glass (refraction), form colorful patterns when it overlaps (interference), and spread out when it goes through small holes (diffraction). All of these are behaviors that are usually seen in waves, like sound or water waves.
Wave theory dominance: Because of those experiments, most scientists started to agree that light must be a wave. The wave model explained many things that the particle model could not.
Birth of quantum physics: But not everything fit the wave theory either. Some experiments showed light acting like particles again. Since neither wave nor particle theory alone could explain all the observations, scientists developed a new kind of science—quantum physics—which could explain how light sometimes behaves like a wave and sometimes like a particle.
Planck's Quantum Theory
Black body study: Max Planck, a scientist from Germany, studied an interesting kind of object called a black body. A black body is a perfect absorber and emitter of heat and light—it doesn’t reflect anything. Planck wanted to understand how these black bodies give off radiation (heat energy).
Black body definition: A black body is a special object that absorbs all the light and heat that hits it and also gives off radiation. It doesn’t let any energy pass through it and doesn’t bounce any back, which makes it perfect for studying how objects emit energy.
Classical theory failure: Old physics theories said black bodies should release more and more energy as the wavelength got shorter. But this didn’t match what was actually observed. Instead, at very short wavelengths, the energy should have become infinite, which was impossible. This problem was called the “ultraviolet catastrophe.”
Energy quantisation: To fix the problem, Planck had a new idea. He said that energy wasn’t given out in a smooth, continuous way. Instead, it was released in small, fixed amounts. These little chunks of energy were called “quanta.”
Photon energy formula: Planck discovered that the amount of energy in each quantum (which we now call a photon) depends on its frequency. He wrote a formula to show this: E = hf, where E is energy, h is a very tiny number called Planck’s constant, and f is the frequency of the light.
Frequency-energy relation: This means that the higher the frequency of the light wave, the more energy it has. For example, ultraviolet light has more energy than infrared light because it has a higher frequency.
Relationship between Energy, Frequency, and Wavelength
Light speed relation: Light always moves at a constant speed in empty space, and we call that speed “c.” Scientists found that light’s speed depends on two things: its frequency (f) and its wavelength (λ). The formula that connects them is c = fλ.
Photon energy formula: We can also find out how much energy a light wave has by using another formula: E = hc/λ. In this case, h is Planck’s constant, c is the speed of light, and λ is the wavelength. This formula shows that if the wavelength gets shorter, the energy gets higher.
Wavelength-energy link: So, when the wavelength is small (like in ultraviolet light), the energy is big. And when the wavelength is long (like in red light), the energy is small. That’s why blue or violet light has more energy than red light.
Wave-Particle Duality
Dual behavior of light: Light is very strange—it doesn’t just act like a wave or a particle. In some tests, like when it passes through slits and makes a pattern, it behaves like a wave. In others, like when it knocks electrons off metal in the photoelectric effect, it acts like a particle. So, it has two personalities!
Quantum concept: The idea that light can act like both a wave and a particle is called wave-particle duality. It’s a key part of quantum physics and helps us understand the behavior of very tiny things.
de Broglie's Hypothesis
Wave-like matter: A French scientist named Louis de Broglie asked an important question: If light can act like a wave and a particle, could matter—like electrons and atoms—also act like waves?
Matter waves: He said yes! Electrons, even though they are particles, also have wave-like properties. This idea helped explain things about atoms that didn’t make sense before.
Wavelength formula: De Broglie gave us a formula to calculate the wavelength of any particle. It is λ = h/p, where λ is the wavelength, h is Planck’s constant, and p is momentum (how much motion the particle has).
Momentum relation: Momentum (p) means mass multiplied by velocity, or p = mv. So you can also write de Broglie’s formula as λ = h/mv.
Mass effect on wavelength: If something has a small mass, like an electron, its wavelength is bigger, and we can actually detect its wave behavior.
Large object limitation: But big things like people or soccer balls have really tiny wavelengths—too small to notice. So we don’t see them behaving like waves in real life.
Electron diffraction: Scientists tested de Broglie’s idea and found that electrons could make wave-like patterns when passed through a crystal. This proved that electrons really do behave like waves.
Applications of Wave-Particle Duality
Electron microscopes: We use special tools called electron microscopes to look at really small things. These microscopes use electron waves instead of light waves, and because electrons have much shorter wavelengths, they can show much more detail.
Wavelength advantage: The small wavelengths of electrons mean they can show us things that are too tiny for normal light microscopes, like viruses and the parts inside cells.
Key Concepts and Relationships
Energy quantisation: In quantum physics, energy is given or taken in small, fixed packets called quanta. The amount of energy depends on the frequency of the light or radiation.
Photon energy: Every little packet of light, called a photon, has energy that depends only on how often the light wave vibrates (its frequency). This is shown with E = hf.
Photon momentum: Even though photons have no mass, they still have something called momentum, which helps us understand their movement. We can find it using the formula p = h/λ.
Energy-momentum link: There’s another way to figure out momentum, using the energy of the photon and the speed of light: p = E/c.
Dual nature principle: Both light and matter can behave like waves and like particles. This is one of the most important ideas in quantum science.
Summary
Quantum revolution: The discovery that energy is released in small bits, that light can act like both a wave and a particle, and that even things like electrons have wave properties, changed the way scientists understood nature. These discoveries gave rise to quantum mechanics, the science that explains how tiny particles behave.