Figure 3 shows the main parts of a transmission electron microscope (TEM) - AQA - A-Level Physics - Question 3 - 2017 - Paper 7

To determine whether individual atoms can be resolved, we can use the formula for resolution in a TEM: $d = \frac{\lambda}{2 \sin \theta}$ where:

• $d$ is the minimum resolvable distance
• $\lambda$ is the wavelength of the electrons

Using the de Broglie wavelength, we find: $\lambda = \frac{h}{\sqrt{2 m E}}$ where:

• $h = 6.626 \times 10^{-34} \, \text{Js}$ (Planck's constant)
• $m = 9.109 \times 10^{-31} \, \text{kg}$ (mass of an electron)
• $E = 4.1 \times 10^{-16} \, \text{J}$ (kinetic energy of the electron)

Calculating $\lambda$ gives: $\lambda = \frac{6.626 \times 10^{-34}}{\sqrt{2 \times 9.109 \times 10^{-31} \times 4.1 \times 10^{-16}}} \approx 2.4 \times 10^{-10} \, \text{m}$

Since this value is less than 0.1 nm (1 × 10^{-10} m), it indicates that individual atoms can indeed be resolved with this TEM setup.

The process of image formation in a TEM begins with the electron gun, which generates a beam of electrons through thermionic emission. The electrons are accelerated and focused by condenser lenses onto the thin specimen. As the electrons interact with the specimen, some are transmitted through while others are scattered.

The transmitted electrons are then focused by the objective lens to form an image, which is further projected by the projector lens onto a fluorescent screen or photographic film, thereby creating a high-resolution image of the internal structure of the specimen.

Several factors influence the quality and level of detail in TEM images:

1. Electron Beam Quality: A coherent beam with minimal chromatic aberration ensures sharp images.
2. Sample Thickness: Thinner samples allow more electrons to pass through without scattering, improving image quality.
3. Lens System: Accurate alignment and calibration of the lenses reduce distortions and improve resolution.
4. Vacuum Conditions: A high vacuum minimizes electron scattering by air and contaminants, promoting clearer images.
5. Post-Processing: Techniques such as digital enhancements can improve the perceived detail in the final images.