# Minumum electron energy and microscopes

• Firecloak
In summary, the highest achievable resolving power of a microscope is limited by the wavelength used. To "see" inside an atom with a diameter of 100 pm, a width of 10 pm must be resolved. To determine the minimum electron energy required for an electron microscope, the equation p = sqrt(2mK) can be used in conjunction with DeBroglie's equation λ = h/p.
Firecloak

## Homework Statement

The highest achievable resolving power of a microscope is limited only by the wavelength used; that is, the smallest item that can be distinguished has dimensions about equal to the wavelength. Suppose one wishes to "see" inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of, say, 10 pm.

(a) If an electron microscope is used, what minimum electron energy is required?

## Homework Equations

E = hc/λ
λ = h/p (DeBroglie wavelength)
p=sqrt(2mK) Momentum
Δλ = (h(1-cos θ))/mc Compton Shift

## The Attempt at a Solution

I tried the equation E = hc/λ = (6.63e-34)(3e8)/(1e-12) = 1.24e6 eV, but that isn't the answer.

E = hc/λ is for photons, not for electrons. What's the equation that gives an object's kinetic energy in terms of its momentum?

p=sqrt(2mK)

So, do I use that equation in conjunction with DeBroglie's? λ = h/p This one is used for electrons, right?

## 1. What is minimum electron energy and how does it affect microscopy?

Minimum electron energy refers to the minimum amount of energy required for an electron to be able to pass through a sample in a microscope. This energy is necessary for the electrons to interact with the atoms in the sample and create an image. If the minimum electron energy is not met, the electrons will be unable to penetrate the sample and no image can be produced.

## 2. How is minimum electron energy determined in a microscope?

The minimum electron energy in a microscope is determined by the voltage applied to the electron gun. This voltage is typically controlled by the user and can be adjusted to meet the specific requirements of the sample being studied. Higher voltages will result in higher electron energies and therefore allow for the visualization of thicker or denser samples.

## 3. Can minimum electron energy be too high for microscopy?

Yes, in some cases, the minimum electron energy can be too high for microscopy. This is because high-energy electrons can cause damage to the sample, leading to distortion or destruction of the image. Additionally, higher electron energies can also result in increased background noise, making it difficult to distinguish the features of interest in the sample.

## 4. How does minimum electron energy impact the resolution of a microscope?

The minimum electron energy has a direct impact on the resolution of a microscope. Higher electron energies can result in better resolution, as the electrons are able to interact with the sample more effectively and create a clearer image. However, if the electron energy is too high, it can also lead to a decrease in resolution due to sample damage.

## 5. Are there any techniques to reduce the minimum electron energy in microscopy?

Yes, there are several techniques that can be used to reduce the minimum electron energy in microscopy. One method is to use a lower voltage in the electron gun, which will result in lower-energy electrons. Another technique is to use a thinner sample or a sample with a lower density, which requires less electron energy for imaging. Additionally, using a special type of microscope called a low-energy electron microscope (LEEM) can also help reduce the minimum electron energy needed for imaging.

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