# Quantum Physics: Electron Microscope

• 10104863
In summary, the conversation discussed the use of an electron microscope with an accelerating voltage of 15 kV and a lens diameter of 0.5 cm and focal length of 50 cm. The resolution requirement for this microscope is one-tenth of the size of the object being studied. The smallest object that can be studied at this resolution is determined by the equation 1.22 (fλ/D). The energy of photons with the same wavelength as the electrons in the microscope is compared to the energy of the electrons, which can be calculated using the equation E = h2/(2mλe2). The momentum of photons with the same wavelength as the electrons is given by p = h/λγ. The energy and momentum of
10104863
Quantum Physics: Electron Microscope

## Homework Statement

Consider electrons in the accelerating voltage of 15 kV used in an electron microscope with a 'lens' diameter D = 0.5 cm and focal length f= 50 cm.
a) We require that the resolution is a tenth of the size of the object we want to study. What is the size of the smallest object that we can study with this electron microscope ?

b) Electrons in this microscope have wavelength λe. If we had photons with the same wavelength, λγ = λe, how would their energy compare to the energy of the electrons in the microscope ?

c) What is the momentum of photons with λγ = λe ?

## Homework Equations

E = hc/λ
p = h/λ
There are definitely others that are needed but I don't know which ones.

3. Attempt
I don't even know how to begin with part a, so if anyone can give me some advice that would be great. You don't have to do the work for me, just tell me what to do and why.
For part b, I think the energy of the photon is hc/λγ, while the energy of the electron can be found through the equation E = h2/(2mλe2) so the result will depend on the wavelength, which I don't know.
Finally, for part c, I know that the momentum is p = h/λγ.

Last edited:
The smallest object you can study focal distance away is given by $$1.22 \frac{f \lambda}{D}$$ where D is the diameter of the lens

the energy of the electron is given by $$qV$$ and you should be able to work out the wavelength from that and consequently the rest of the question

## 1. What is a quantum physics electron microscope?

A quantum physics electron microscope is a powerful tool used by scientists to study the atomic and subatomic structures of materials. It uses a beam of electrons to create high-resolution images, allowing researchers to see objects at a much smaller scale than traditional light microscopes.

## 2. How does a quantum physics electron microscope work?

A quantum physics electron microscope works by firing a beam of electrons at a sample, which then interacts with the atoms in the sample. This interaction produces signals that are collected and translated into an image by a computer. The electrons used in this microscope have extremely short wavelengths, allowing for a higher resolution image compared to traditional light microscopes.

## 3. What are the advantages of using a quantum physics electron microscope?

One of the main advantages of a quantum physics electron microscope is its ability to produce high-resolution images at a much smaller scale than traditional microscopes. This makes it a valuable tool for studying the atomic and subatomic structures of materials. Additionally, this type of microscope can also provide information about the chemical composition and electronic properties of a sample.

## 4. What are the limitations of a quantum physics electron microscope?

One limitation of a quantum physics electron microscope is that it can only be used in a vacuum, as the electrons can easily be scattered by air molecules. This means that samples must be prepared and placed in a vacuum chamber before imaging. Additionally, the high energy electrons used in this microscope can also damage sensitive samples.

## 5. What are some real-world applications of quantum physics electron microscopes?

Quantum physics electron microscopes have a wide range of applications in various fields such as materials science, biology, and nanotechnology. They are used to study the structure and composition of materials, analyze biological samples at a cellular level, and aid in the development of new technologies such as semiconductors and computer chips.

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