You intend to use an electron microscope to study the...

You intend to use an electron microscope to study the structure of some crystals. For accurate resolution, you want the electron wavelength to be 1.00 $\mathrm{nm}$ . (a) Are these electrons relativistic? How do you know? (b) What accelerating potential is needed? (c) What is the kinetic energy of the electrons you are using? To see if it is great enough to damage the crystals you are studying, compare it to the potential energy of a typical NaCl molecule, which is about 6.0 eV.(d) If you decided to use electromagnetic waves as your probe, what energy should their photons have to provide the same resolution as the electrons? Would this energy damage the crystal?

Key Concepts

Relativistic Effects in Electron Dynamics

Relativistic effects become important in electron microscopy when the electrons’ kinetic energy is a significant fraction of their rest energy. This necessitates using relativistic formulas to accurately determine quantities like momentum and wavelength, ensuring that calculations remain valid at high speeds.

De Broglie Wavelength

The de Broglie wavelength describes the wave-like nature of particles. In the context of electron microscopy, it is crucial because it determines the resolution; a shorter wavelength allows the microscope to resolve finer details of a structure.

Accelerating Potential and Electron Kinetic Energy

To achieve a desired de Broglie wavelength, electrons are accelerated through a potential difference that imparts kinetic energy to them. Understanding the relationship between the accelerating voltage and the resulting electron kinetic energy is key for setting up an electron microscope with the required resolution.

Photon Energy in Electromagnetic Probes

When using electromagnetic waves for probing, the energy of the photons is directly related to their wavelength. To match the resolution capabilities of electrons, the photons must have sufficiently high energy, which also raises concerns about potential damage to the specimen being studied.

Energy Scales and Sample Damage

Comparing the energy imparted to electrons or photons with the intrinsic bond or potential energies within the sample (for instance, in a molecule or crystal lattice) is essential to determine whether the imaging process might cause damage to the specimen.

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