Collisions of electrons with atoms

Welcome to the World of Atomic Collisions!

In this chapter, we are going to dive inside the atom to see what happens when fast-moving electrons crash into them. Why does this matter? Because these tiny collisions are responsible for everything from the glowing lights in your classroom to the X-rays used in hospitals. Don't worry if it sounds a bit "hidden" at first—we'll break it down into simple steps!

1. The Electron Volt (eV)

Before we look at collisions, we need a better ruler for energy. Using Joules (J) to measure the energy of a single electron is like using a massive truck scale to weigh a single grain of sugar—the numbers are just too small and awkward!

Physicists use the electron volt (eV) instead. One electron volt is the work done (energy gained) when a single electron is accelerated through a potential difference of 1 Volt.

The Golden Conversion:
\(1\text{ eV} = 1.60 \times 10^{-19}\text{ J}\)

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

Key Takeaway:

The eV is a tiny unit of energy used for subatomic particles. Always check which unit the exam question is asking for!

2. Excitation and Ionisation

Imagine an atom like a hotel. The nucleus is the ground floor, and the electrons live in rooms on the higher floors called energy levels. Usually, electrons like to stay in the lowest possible level, called the ground state.

When a moving "incident" electron hits an atom, it can transfer its energy to one of the atom's electrons. Two main things can happen:

A. Excitation

The atom’s electron absorbs just enough energy to jump to a higher energy level. It’s still in the "hotel" (the atom), but it’s on a higher floor.
Important: The incident electron must have energy equal to or greater than the difference between the two levels to make this happen.

B. Ionisation

The incident electron hits the atom's electron so hard that it is knocked completely out of the atom. The atom is now "ionised" (it has a positive charge).
Ionisation energy is the minimum energy required to remove an electron from an atom in its ground state.

Did you know?

If the incident electron has more energy than needed for ionisation, the leftover energy simply stays with the electrons as kinetic energy. It’s like buying a $10 ticket with a $20 bill—you get change back!

3. Energy Levels and Line Spectra

Electrons don't stay in high energy levels for long. They quickly fall back down to lower levels. When they do, they must "pay back" the energy they borrowed by releasing a photon (a packet of light).

The energy of this photon is exactly equal to the difference between the two levels:
\(hf = E_1 - E_2\)

Where:
- \(h\) is the Planck constant.
- \(f\) is the frequency of the light.
- \(E_1\) is the higher energy level.
- \(E_2\) is the lower energy level.

Evidence for Discrete Levels

Because these energy levels are discrete (specific, fixed steps), atoms can only emit specific frequencies of light. This creates a line spectrum—a series of bright lines against a dark background. Think of it like a "barcode" that is unique to every element!

Quick Review Box:

- Excitation: Electron moves to a higher shell.
- De-excitation: Electron moves to a lower shell and releases a photon.
- Line Spectrum: Proof that energy levels are fixed, not a continuous ramp.

4. How a Fluorescent Tube Works

This is a classic exam topic! A fluorescent tube uses everything we've just learned in a four-step process:

1. Ionisation & Acceleration: High voltage accelerates free electrons through the tube. These electrons collide with mercury vapor atoms.
2. Excitation: The collisions excite the electrons in the mercury atoms to higher levels.
3. UV Emission: As the mercury electrons fall back to the ground state, they emit ultraviolet (UV) photons. (We can't see these, and they are harmful!)
4. Fluorescence: The phosphor coating on the inside of the glass absorbs the UV photons. This excites the phosphor's electrons, which then fall down in smaller steps, emitting visible light photons.

Common Mistake to Avoid:

Many students think the mercury emits visible light. Actually, the mercury emits UV, and the phosphor coating converts that UV into visible light.

5. X-Rays: High-Energy Collisions

X-rays are produced when very high-speed electrons hit a metal target (usually tungsten) inside an X-ray tube.

The X-ray Tube Structure

- Cathode: A heated filament that releases electrons (thermionic emission).
- Anode: A metal target that the electrons smash into.
- Vacuum: So electrons don't hit air molecules on the way.
- High Voltage: To give the electrons massive amounts of kinetic energy.

The X-ray Spectrum

When you look at an X-ray spectrum, you see two parts:
1. Continuous Spectrum: A broad "hump" caused by electrons slowing down as they pass near nuclei (braking radiation).
2. Characteristic Peaks: Sharp vertical lines. These are caused by incident electrons knocking out inner-shell electrons of the target metal, causing outer electrons to drop down and release high-energy X-ray photons. These peaks are "characteristic" of the metal used for the anode.

Real-World Application:

X-rays are used in medicine because they pass through soft tissue but are absorbed by dense materials like bone, creating a shadow image.

Summary and Tips for Success

- Remember the difference: In a collision with an electron, the atom can take *part* of the kinetic energy. In a collision with a photon, the atom must take *all* of the energy or none at all (unless it's ionisation).
- Calculations: Always check if your energy is in Joules before using \(E = hf\). If the question gives you eV, convert it first!
- The "Why": Why do we see lines? Because energy levels are discrete. This is a very common one-mark answer!

Don't worry if the math for photons feels heavy; just keep practicing the conversions between eV and Joules, and the rest will fall into place!