Of course! Here are comprehensive and engaging study notes on the "Structure of the Atom," tailored for HKDSE Physics students and formatted in HTML. These notes are based directly on the provided syllabus, breaking down complex ideas into simple, understandable steps.

Hello Future Physicists! Welcome to the Atomic World!

Ever wondered what you're made of? Not just bones and muscle, but the truly, truly tiny stuff? In this chapter, we're going on an incredible journey inside the atom – the fundamental building block of everything around us! We'll start with the basics and travel through time to see how our understanding of the atom has changed, leading to some of the most mind-bending ideas in all of science.

Why is this important? Understanding the atom is the key to understanding chemistry, how stars shine, nuclear energy, and even the tiny electronics in your phone. It's a wild ride, so let's get started!

Part 1: The Atom's Basic Blueprint

What is an Atom? The 'Lego Bricks' of the Universe

Imagine the universe is made of Lego. The smallest, most basic brick you can get is an atom. Every element on the periodic table, from Hydrogen to Gold, is just a different type of these 'bricks'.

The basic structure of an atom is like a tiny solar system:

  • The Nucleus: This is the dense, heavy centre (like the Sun). It's made of two types of particles:
    • Protons: Positively charged particles (+).
    • Neutrons: Neutral particles with no charge.
  • Electrons: These are tiny, negatively charged particles (-) that orbit the nucleus (like planets).

Analogy: If an atom were the size of a sports stadium, the nucleus would be a tiny marble in the centre! This tells you that an atom is mostly empty space.

An Atom's 'ID Card': Atomic & Mass Numbers

Every atom has a unique ID card that tells us exactly what it is. This is written in a special format called symbolic notation.

$$^A_Z X$$
  • X is the symbol for the element (e.g., C for Carbon, He for Helium).
  • Z is the Atomic Number. This is the number of protons in the nucleus. The atomic number is what defines an element. If an atom has 6 protons, it is ALWAYS Carbon. No exceptions!
  • A is the Mass Number. This is the total number of protons AND neutrons in the nucleus. To find the number of neutrons, you just calculate $$A - Z$$.

Example: Let's look at Carbon-12: $$^{12}_6 C$$
- It's Carbon (C).
- Its Atomic Number (Z) is 6, so it has 6 protons.
- Since atoms are electrically neutral, it must also have 6 electrons to balance the charge.
- Its Mass Number (A) is 12. So, the number of neutrons is $$12 - 6 = 6$$ neutrons.

Quick Review Box

Atomic Number (Z) = Number of protons. Defines the element.
Mass Number (A) = (Number of protons) + (Number of neutrons).
Number of Neutrons = A - Z.
Number of Electrons = Number of protons (in a neutral atom).

Atomic 'Siblings': Isotopes

What if you have two atoms of the same element, but they have different masses? These are called isotopes.

Isotopes are atoms of the same element (same number of protons) but with a different number of neutrons (and therefore a different mass number).

Example: Carbon's Isotopes
- Carbon-12 ($$^{12}_6 C$$) is the most common form. It has 6 protons and 6 neutrons.
- Carbon-14 ($$^{14}_6 C$$) is a less common, radioactive isotope. It has 6 protons but 8 neutrons ($$14 - 6 = 8$$). Because it's radioactive, it's used in "carbon dating" to figure out the age of ancient fossils!

Did you know? Water ($$H_2O$$) is usually made with the most common hydrogen isotope ($$^{1}_1 H$$). But if you use a heavier isotope of hydrogen called deuterium ($$^{2}_1 H$$), you get "heavy water," which is used in nuclear reactors!

Key Takeaway for Part 1

Atoms consist of a central nucleus (protons + neutrons) orbited by electrons. We can describe any atom using its atomic number (Z) and mass number (A). Isotopes are versions of an element with different numbers of neutrons.


Part 2: A New Picture - The Rutherford Model

Rutherford's Famous Gold Foil Experiment

In the early 1900s, scientists thought an atom was like a "plum pudding" - a blob of positive charge with negative electrons stuck in it. Ernest Rutherford decided to test this. The experiment was like firing tiny bullets (called alpha particles, which are positive) at an incredibly thin sheet of gold foil.

  • What they expected: All the 'bullets' should pass straight through the 'pudding'.
  • What they saw (The BIG surprise!):
    1. Most particles went straight through.
    2. Some were deflected by a small angle.
    3. A tiny number (about 1 in 8000) bounced almost straight back!

Rutherford said, "It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

The Nuclear Model is Born

This surprising result completely changed our view of the atom. Rutherford concluded:

  1. Most of the atom is empty space. (This is why most alpha particles passed through).
  2. There must be a tiny, dense, positively charged centre, which he called the nucleus. (This positive nucleus repelled the positive alpha particles, causing the large deflections and bounce-backs).
  3. Electrons must orbit this nucleus from a distance.

This is the Rutherford model, also known as the nuclear model of the atom.

Uh Oh... Problems with the Rutherford Model

Rutherford's model was a huge step forward, but it had two major flaws according to the physics of his time (classical physics):

  1. The Death Spiral: Classical physics says an orbiting charged particle (like an electron) should constantly radiate energy. This means the electron should lose energy and spiral into the nucleus in a fraction of a second. Atoms should collapse! But they don't.
  2. The Barcode Mystery: This model couldn't explain line spectra. When you heat up a gas, it doesn't glow with all the colours of the rainbow. It only emits light at very specific, sharp colours, like a barcode unique to that element. Rutherford's model had no explanation for this.
Key Takeaway for Part 2

Rutherford's Gold Foil experiment proved that atoms have a tiny, dense, positive nucleus and are mostly empty space. However, his model couldn't explain why atoms are stable or why they produce unique line spectra.


Part 3: The Quantum Leap - The Bohr Model

Don't worry if the last part seemed tricky! A Danish physicist named Niels Bohr came along with some radical new ideas to fix Rutherford's model. This is where we enter the weird and wonderful world of quantum mechanics!

Bohr's Bold Ideas (Postulates)

Bohr focused on the simplest atom, Hydrogen. To solve the problems, he proposed two main rules, or postulates:

  1. Special Orbits Only: Electrons can't just orbit anywhere they want. They can only exist in special, fixed orbits called stationary states or energy levels. While in one of these orbits, an electron does not radiate energy. This solved the 'death spiral' problem!
  2. Quantum Jumps: An electron can "jump" from a higher energy level to a lower one by emitting a photon of light. It can jump from a lower level to a higher one by absorbing a photon. The energy of this photon is exactly equal to the energy difference between the two levels.

A photon is a tiny packet, or "quantum," of light energy.

Energy Levels and Line Spectra

Bohr's second idea perfectly explained the mystery of line spectra! Since electrons can only exist in fixed energy levels, they can only emit photons with specific energies corresponding to the gaps between these levels. Each gap corresponds to a specific colour (or wavelength) of light. That's why we see a sharp 'barcode' of colours, not a continuous rainbow!

Line spectra are direct evidence for the existence of discrete energy levels in atoms.

For the hydrogen atom, Bohr calculated the energy of these levels with a famous formula:

$$E_n = -\frac{13.6}{n^2} \text{ eV}$$
  • $$E_n$$ is the energy of the level.
  • n is the principal quantum number (n = 1, 2, 3, ...). `n=1` is the lowest energy level, called the ground state. `n=2, 3, ...` are excited states.
  • eV stands for electron-volt, a tiny unit of energy that's perfect for the atomic scale.
Common Mistake Alert!

The energy levels are negative! This means the electron is bound to the nucleus. A higher energy level (like n=3) is actually less negative (e.g., -1.51 eV) than a lower energy level (like n=1, which is -13.6 eV). Zero energy corresponds to the electron being completely free from the atom.

Excitation and Ionization

  • Excitation: When an electron absorbs energy and jumps from a lower energy level to a higher one (e.g., from n=1 to n=3).
  • Ionization: When an electron absorbs enough energy to be completely removed from the atom. For hydrogen in the ground state, this requires 13.6 eV of energy, which is its ionization energy. This corresponds to a jump from `n=1` to `n=∞`.

Calculating the Light from a Quantum Jump

When an electron drops from a high energy level (let's call it `n=a`) to a low one (`n=b`), it emits a photon. Here's how to calculate its wavelength:

Step 1: Find the energy difference.
$$ \Delta E = E_{high} - E_{low} = E_a - E_b $$

Step 2: Relate energy to wavelength.
The photon's energy is also given by the formula $$E = hf = \frac{hc}{\lambda}$$, where `h` is Planck's constant, `c` is the speed of light, and `λ` is the wavelength.

Step 3: Combine them!
$$ \frac{hc}{\lambda} = E_a - E_b $$
$$ \frac{1}{\lambda} = \frac{E_a - E_b}{hc} $$

Using Bohr's formula for hydrogen, this becomes:

$$ \frac{1}{\lambda_{ab}} = \frac{13.6 \text{ eV}}{hc} \left( \frac{1}{b^2} - \frac{1}{a^2} \right) $$
Key Takeaway for Part 3

Bohr's model introduced quantized energy levels, solving the stability and line spectra problems for hydrogen. Electrons can only exist in these specific levels and can "jump" between them by absorbing or emitting photons of specific energies.


Part 4: The Strangest Idea of All - Wave-Particle Duality

Get ready, because things are about to get even weirder. So far, we've treated electrons as particles and light as waves (except for those photon 'packets'). The truth is much stranger.

Light: A Wave... and a Particle?

We know light behaves like a wave because it shows diffraction and interference. But an experiment called the photoelectric effect (where light shining on a metal can knock electrons out) can only be explained if light acts as a stream of particles – the photons we met earlier, each with energy $$E=hf$$.

So which is it? Light is both! It has a dual nature. This is called wave-particle duality.

Electrons: A Particle... and a Wave?

In 1924, a physicist named Louis de Broglie had a brilliant thought: if waves (light) can act like particles, maybe particles (like electrons) can act like waves?

He proposed that every moving particle has a wavelength associated with it, given by the de Broglie wavelength formula:

$$ \lambda = \frac{h}{p} = \frac{h}{mv} $$
  • λ is the de Broglie wavelength.
  • h is Planck's constant (a very tiny number!).
  • p is the momentum of the particle (mass × velocity).

This was a shocking idea, but it was proven true! Experiments showed that a beam of electrons could be diffracted, just like a wave of light. This is the evidence for the wave nature of electrons.

Did you know? The wave nature of electrons is the principle behind powerful electron microscopes, which can see things much smaller than any normal light microscope!

Key Takeaway for Part 4

Both light and matter (like electrons) exhibit wave-particle duality. They can behave as either a wave or a particle depending on the situation. The de Broglie equation relates a particle's momentum to its wavelength.