Welcome to the Quantum World!

In our everyday lives, things seem predictable. A ball thrown into the air follows a clear path, and waves in the sea spread out smoothly. However, when we look at the universe on a tiny scale—the scale of atoms and light—the "old rules" of physics start to break down. In this chapter, we explore quantum behaviour, where light acts like particles and particles act like waves. Don't worry if this seems a bit strange at first; even Einstein found it "spooky"! We will break it down into simple, manageable steps.

1. Light as "Packets": Photons

For a long time, scientists thought light was only a wave. But then they discovered that light exchanges energy in discrete "lumps" called photons. Think of a photon as a tiny, weightless "packet" of energy.

The Energy of a Photon

The energy of a single photon depends entirely on the frequency of the light. The higher the frequency (the "bluer" the light), the more energy the photon carries.

We use the formula: \(E = hf\)

  • \(E\) is the energy of the photon (in Joules, \(J\)).
  • \(h\) is the Planck constant (\(6.63 \times 10^{-34} J s\)). This is a fundamental constant of the universe.
  • \(f\) is the frequency of the light (in Hertz, \(Hz\)).

Since we know from waves that \(v = f\lambda\), and the speed of light is \(c\), we can also write: \(E = \frac{hc}{\lambda}\)

Memory Tip: High frequency means high energy. Low wavelength means high energy. Blue photons are "stronger" than red ones!

The Electronvolt (\(eV\))

Photon energies are tiny—often something like \(10^{-19} J\). To make numbers easier to work with, physicists use the electronvolt (\(eV\)). One \(eV\) is the energy gained by an electron moving through a potential difference of 1 Volt.

\(1 eV = 1.60 \times 10^{-19} J\)

Quick Conversion:
To go from \(eV\) to \(J\): Multiply by \(1.60 \times 10^{-19}\).
To go from \(J\) to \(eV\): Divide by \(1.60 \times 10^{-19}\).

Key Takeaway: Light is "quantised" into photons. You can have one photon or two, but never half a photon!

2. Evidence for Photons

How do we know light isn't just a continuous wave? There are three main pieces of evidence you need to know:

A. Coloured LEDs

An LED (Light Emitting Diode) only starts to glow when the voltage across it is high enough to give an electron enough energy to create a photon. By measuring the "striking voltage" (\(V\)) where the LED just starts to light up, we can estimate the Planck constant.

Equation: \(eV \approx hf\)

B. The Photoelectric Effect

When you shine UV light on a metal (like a zinc plate), it can knock electrons off the surface. If light were a wave, any light should eventually knock an electron off if you wait long enough. But in reality:

  • If the light frequency is below a certain threshold frequency (\(f_0\)), nothing happens, no matter how bright the light is.
  • This is because one single photon must have enough energy to "punch" the electron out.
  • The minimum energy needed to escape the metal surface is called the work function (\(\Phi\)).

C. Line Spectra

When gas atoms are excited, they don't glow in a rainbow. They emit very specific colours of light (lines). This shows that electrons in atoms move between fixed energy levels, emitting a single photon of a specific energy (\(E = hf\)) when they "drop" down.

3. The Quantum Model: "All Possible Paths"

Wait—if light is made of particles (photons), how does it still show wave-like behaviour like interference and diffraction? The "Advancing Physics" way to understand this is through probability and phasors.

Phasors and Probability

Quantum mechanics tells us we cannot predict exactly where a single photon will land. We can only predict the probability of it arriving at a certain point.

  1. Imagine a photon travels from A to B. It doesn't just take one straight line; it "explores" every possible path.
  2. For every path, we imagine a little rotating arrow called a phasor.
  3. As the photon travels, the phasor rotates (like the hand of a clock). The speed of rotation depends on the frequency of the light.
  4. When the photon reaches the destination, we "add up" all the phasors from all the possible paths (tip-to-tail).
  5. The length of the final "resultant" phasor tells us the amplitude.

The Golden Rule: The probability of a photon arriving is proportional to the square of the resultant phasor amplitude.

  • If the phasors from different paths point in the same direction, they add up to a long arrow (High probability = Bright spot).
  • If the phasors point in opposite directions, they cancel out (Zero probability = Dark spot).

4. Matter Waves: Electrons as Waves

If light (a wave) can act like a particle, can matter (a particle) act like a wave? Yes!

Evidence for this comes from electron diffraction. When a beam of electrons is fired through a thin layer of graphite, they form a diffraction pattern of rings—just like light passing through a tiny hole. Only waves can diffract!

The De Broglie Wavelength

Every moving object has a wavelength, but it's only noticeable for tiny things like electrons. We calculate it using the De Broglie relationship:

\(\lambda = \frac{h}{p}\)

Where:

  • \(\lambda\) is the wavelength (in metres, \(m\)).
  • \(h\) is the Planck constant.
  • \(p\) is the momentum of the particle (\(p = mass \times velocity\)).

Note: Because \(h\) is so small, your "wavelength" when walking is far too small to ever be detected!

5. Required Practical: Measuring the Planck Constant

In your exam, you might be asked about the practical involving coloured LEDs. Here is a quick summary:

  1. Set up a circuit with a variable power supply, an LED, and a voltmeter in parallel with the LED.
  2. Use a variety of LEDs (e.g., Red, Orange, Green, Blue).
  3. For each LED, slowly increase the voltage until it just starts to glow. Record this "threshold voltage" (\(V\)).
  4. The energy of the electron is \(V \times e\). This energy is converted into one photon of energy \(hf\).
  5. Plot a graph of \(V\) (y-axis) against \(f\) (x-axis).
  6. Since \(V = (\frac{h}{e})f\), the gradient of your graph will be \(\frac{h}{e}\).
  7. Multiply the gradient by the charge of an electron (\(1.6 \times 10^{-19} C\)) to find \(h\).

Quick Summary Table

Term Definition / Key Idea
Photon A quantum (packet) of electromagnetic energy.
Work Function (\(\Phi\)) The minimum energy needed to remove an electron from a metal surface.
Threshold Frequency (\(f_0\)) The minimum frequency of light needed to cause the photoelectric effect.
Phasor A rotating arrow representing the phase and amplitude of a quantum "wave".
Probability Equal to the square of the amplitude of the resultant phasor.

Common Mistakes to Avoid

  • Confusing Energy and Intensity: In the quantum world, intensity (brightness) tells you the number of photons, but the energy of each photon depends only on the frequency.
  • Units: Always check if you need to convert \(eV\) to Joules before using them in the \(E = hf\) formula.
  • Calculators: When using \(h = 6.63 \times 10^{-34}\), make sure you use brackets in your calculator so you don't make an order-of-magnitude error!

You've reached the end of this chapter! You now know that the universe isn't just "waves" or "particles"—it's a quantum mix of both, governed by the rules of probability.