Physics (9630) | Collisions of electrons with atoms

Studying Electron-Atom Collisions: Unlocking the Atomic "Barcodes"

Welcome to one of the most fascinating topics in Physics! This chapter, "Collisions of electrons with atoms", takes us deep inside the atom to explore how energy is stored and transferred in the quantum world. Don't worry if this feels different from studying waves and mechanics—it's the stepping stone to modern physics, proving that energy isn't continuous, but comes in specific, countable packets.

Understanding these collisions explains everything from how a household light bulb works to how doctors use X-rays. Let's break down how electrons interact with atoms!

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1. Excitation vs. Ionisation: Two Ways to Hit an Atom

When a free electron collides with an atom, it transfers some or all of its kinetic energy to the atom. What happens next depends entirely on the amount of energy transferred.

1.1 Excitation: The Temporary Boost

Excitation occurs when an electron inside an atom absorbs energy and jumps from its original low-energy state (often called the ground state) to a higher, discrete energy level. The key term here is discrete—the electron can only jump if the incoming energy exactly matches the difference between two allowed energy levels.

• The Process: A colliding electron transfers energy \(E\) to an atomic electron.
• The Result: If \(E = E_{\text{higher}} - E_{\text{lower}}\), the atomic electron moves up to the higher level.
• Analogy: Imagine energy levels are like steps on a staircase. To get from step 1 to step 3, you need exactly enough energy to cover those two steps. If you have slightly too much or too little energy, the jump cannot happen, and the atom typically remains unexcited (the collision is elastic).

1.2 Ionisation: Kicking the Electron Out

Ionisation is a more drastic event. It occurs when the colliding electron provides enough energy to completely remove an electron from the atom, making the atom a positively charged ion.

• The Process: The colliding electron must transfer energy greater than or equal to the Ionisation Energy (or ionisation potential) of the atom.
• The Result: The atomic electron escapes the atom. Any excess energy transferred by the colliding electron becomes the kinetic energy of the now-free electron.
• Analogy: You have enough energy not just to reach the top step of the staircase, but to launch yourself out of the building entirely!

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2. The Electron Volt (eV): A Convenient Unit of Energy

When dealing with atomic and subatomic particles, the Joule (J) is often an inconveniently large unit. We use the electron volt (\(eV\)) instead.

2.1 Defining the Electron Volt

The electron volt (eV) is defined as the kinetic energy gained by a single electron when it is accelerated from rest through a potential difference of 1 Volt.

• We know that the work done (energy transferred) when charge \(Q\) moves through potential difference \(V\) is \(W = QV\).
• For one electron (\(Q = e\)) moving through \(V=1 \, \text{Volt}\):
  $$W = (1.60 \times 10^{-19} \, \text{C}) \times (1 \, \text{V}) = 1.60 \times 10^{-19} \, \text{J}$$

Therefore, the conversion factor is:

$$1 \, \text{eV} = 1.60 \times 10^{-19} \, \text{J}$$

Memory Aid: To convert from eV to J, you multiply by the charge of the electron (\(e\)). To convert from J to eV, you divide by \(e\).

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3. Line Spectra: The Barcodes of the Atom

When an electron in an excited atom drops back down to a lower energy level (de-excitation), it must release the energy difference between the two levels. Since the energy levels are discrete (specific values), the released energy also comes in specific, discrete amounts, packaged as photons.

3.1 The Energy Transition Equation

The energy of the emitted photon (\(E_{\text{photon}}\)) is exactly equal to the difference between the initial higher energy level (\(E_1\)) and the final lower energy level (\(E_2\)).

We use the relationship \(E = hf\), where \(h\) is the Planck constant and \(f\) is the frequency of the photon.

$$hf = E_1 - E_2$$

Since \(E_1\) and \(E_2\) are fixed values for a given atom, the frequency \(f\) (and therefore the wavelength \(\lambda\), since \(c = f\lambda\)) of the emitted photon is also fixed.

3.2 Evidence for Discrete Levels

If we pass the light emitted from excited atoms (like hydrogen) through a prism or diffraction grating, we don't see a continuous rainbow spectrum (like from a normal lamp). Instead, we see only a few bright, distinct lines—a line spectrum.

• What this proves: The existence of line spectra is direct evidence that atoms can only absorb or emit energy in specific quantities, confirming that the electrons within the atom occupy discrete (quantised) energy levels.
• Did you know? Each element has a unique line spectrum, acting like a chemical "fingerprint" or barcode, allowing scientists to identify elements present in stars millions of light-years away.

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4. Application 1: The Fluorescent Tube

The fluorescent tube is a perfect real-world example of controlled excitation and de-excitation.

Step-by-Step Operation:

1. Electron Acceleration: Electrons are accelerated through a potential difference (voltage) inside the tube.
2. Excitation: These high-speed electrons collide with mercury vapour atoms inside the tube. This transfers energy, causing the mercury atoms to become excited.
3. De-excitation (UV Emission): The excited electrons in the mercury atoms quickly fall back down to lower energy levels, releasing photons. The energy levels in mercury are such that these photons are predominantly in the ultraviolet (UV) range (which is invisible).
4. Visible Light Conversion: The inside of the glass tube is coated with a powder called phosphor. When the invisible UV photons hit the phosphor coating, the atoms in the phosphor are excited. When they de-excite, they release energy in the form of visible light.

The initial electron collisions result in excitation, which then leads to emission of visible light via an intermediate conversion step.

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5. Application 2: X-Rays

X-rays are high-energy electromagnetic waves used widely in medicine and industry. They are produced using electron collisions in a specialised device called an X-ray tube.

5.1 Basic Structure and Operation of an X-Ray Tube

An X-ray tube uses a high voltage (typically 10 kV to 100 kV) to accelerate electrons towards a dense metal target (the anode).

The process is:

1. A heated filament (cathode) releases electrons via thermionic emission.
2. A massive potential difference (the accelerating voltage) accelerates these electrons across a vacuum gap towards the target (anode), giving them very high kinetic energy.
3. The high-energy electrons strike the target metal. Only about 1% of the energy produces X-rays; the rest is dissipated as heat.

5.2 The X-Ray Spectrum

When the electrons hit the target, two types of X-rays are produced, resulting in a spectrum with both continuous and sharp line features:

1. The Continuous Spectrum (Bremsstrahlung):
   • This means "braking radiation."
   • It is produced when the high-speed electrons pass close to the nuclei of the target atoms and are decelerated (slowed down) by the electric field of the nucleus.
   • Since electrons lose energy randomly, they produce photons with a continuous range of frequencies (and thus wavelengths).
   • The minimum wavelength (\(\lambda_{\text{min}}\)) of this spectrum is determined by the accelerating voltage, as the highest energy photon occurs when an electron loses *all* its kinetic energy in one go.
2. The Characteristic Spectrum (Line Spectrum):
   • If the colliding electron has enough energy, it can ionise an inner-shell electron (e.g., K-shell) of a target atom.
   • An electron from an outer shell (L, M, etc.) drops into the vacant inner shell, releasing a very high-energy photon specific to that element.
   • These emissions produce sharp, bright peaks (lines) on the spectrum—the characteristic X-rays. This confirms the discrete energy levels of the target material itself.

5.3 X-Rays in Medical Applications

X-rays are critical for medical imaging because different materials absorb X-rays to different extents:

• Dense materials (like bone) absorb X-rays strongly.
• Less dense materials (like soft tissue) absorb X-rays weakly.

When an X-ray beam passes through the body onto a detector, areas blocked by bone appear white, while areas that let the X-rays pass through appear black, creating a high-contrast image.