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

To determine the resolving power, we can use the formula:

$d = \frac{\lambda}{2 \sin(\theta)}$

Where:

• ( d ) is the minimum distance that can be resolved,
• ( \lambda ) is the wavelength of the electrons,
• ( \theta ) is the angle of the aperture.

Using de Broglie's equation, the wavelength ( \lambda ) is given by:

$\lambda = \frac{h}{p}$

• Where ( h = 6.626 \times 10^{-34} , Js )
• The momentum ( p = mv )

Calculating the wavelength for the electrons with ( K.E. = 4.1 \times 10^{-16} , J ):

1. First, we use ( K.E. = \frac{1}{2}mv^2 ) to find ( v ). Assuming an electron mass ( m = 9.11 \times 10^{-31} , kg ):
   ( 4.1 \times 10^{-16} = \frac{1}{2}(9.11 \times 10^{-31})v^2 ) Solving for ( v ) gives: ( v \approx 1.0 \times 10^7 , m/s )

2. Now calculate ( p = mv = (9.11 \times 10^{-31})(1.0 \times 10^7) \approx 9.11 \times 10^{-24} , kg , m/s )

3. Plugging this into the de Broglie equation: ( \lambda = \frac{6.626 \times 10^{-34}}{9.11 \times 10^{-24}} \approx 7.27 \times 10^{-11} , m \approx 0.0727 \ nm )

Given that most individual atoms measure approximately 0.1 nm, yes, the images of individual atoms can be resolved.

Process of Image Formation

The transmission electron microscope uses a focused beam of high-energy electrons to illuminate the thin sample. As electrons pass through the specimen, they interact with the atoms, resulting in scattering. The transmitted electrons are then focused by a series of electromagnetic lenses onto a fluorescent screen, where an image of the specimen is formed. The bright and dark areas of the image correspond to areas of high and low electron density, respectively, thus providing contrast and details of the internal structure of the specimen.

Factors Affecting Quality and Level of Detail

1. Electron Source: The quality and stability of the electron gun impact the resolution. A stable source ensures a consistent beam of electrons.
2. Lens Aberrations: Imperfections in the electromagnetic lenses can cause distortions in the image, leading to loss of detail.
3. Sample Thickness: The thickness of the specimen affects the scattering of electrons. Thinner samples allow for better resolution.
4. Vacuum Quality: A high-quality vacuum environment is necessary to prevent electron scattering by air molecules.
5. Defocusing: Correct focusing of the lenses is critical, as any defocus can degrade image quality.