Final answer:
The effective wavelength of electrons used in electron microscopy typically ranges from about 0.005 nm to 1.00 pm. These short wavelengths allow electron microscopes to magnify and resolve structures with exceedingly fine detail, far beyond the capabilities of normal light microscopes.
Step-by-step explanation:
To resolve an object in an electron microscope, the wavelength of the electrons is significant. As with any form of microscopy, the resolution is fundamentally limited by the wavelength of the probe used to examine the specimen. In the case of electron microscopes, electrons display both particle and wave characteristics, but it is their wave nature that makes them useful for microscopy. Due to their relatively small mass, electrons can be accelerated to high velocities, giving them very short wavelengths. A potential difference of just 54 V is enough to produce electrons with wavelengths smaller than those of visible light, enabling electron microscopes to visualize much tinier structures than traditional optical microscopes can.
Electron microscopes can produce sharp images with magnifications up to 1,000,000 times, considerably higher than the approximately 1,500 times magnification possible with light microscopes. This is primarily because the wavelength of an electron beam is typically around 0.005 nm to 1.00 pm, which is significantly shorter than that of visible light, ranging from about 700 nm to about 400 nm. The shorter the wavelength, the higher the resolution potential, allowing electron microscopes to resolve subcellular as well as certain molecular structures, such as single strands of DNA. However, it should be noted that these microscopes are not suitable for studying live material due to the specimen preparation process.
For example, if electrons with a 2.00-pm wavelength are passed through a single slit, you can calculate the angle for the first diffraction minimum using principles from wave optics. According to the information given, electron microscopes can use wavelengths as short as 1.00 pm to visualize details at the sub-nanometer level, achieving incredibly high-resolution capabilities unmatched by light microscopes.