# Why did they use these formulas for energy of electron.

• cloudage
In summary, the conversation discusses the use of an electron microscope and the energy required for each electron of a beam to obtain a specific wavelength. The correct equations for finding this energy are presented, and it is noted that these equations should only be used for massive particles, not photons. Thinking of electrons as photons can lead to incorrect answers.
cloudage

## Homework Statement

An electron microscope employs a beam of electrons to obtain an image of an object. What energy must be imparted to each electron of the beam to obtain a wavelength of 10.0pm?

## Homework Equations

1. E = hv=hc/lambda
2. lambda = h/(mv)
3. KE = .5mv^2

## The Attempt at a Solution

In this problem I thought you could use the first equation to find the energy with the specific wavelength of 10pm. However, the workbook goes through equations 2 and 3 to first find the velocity and then find the kinetic energy. The answers come out very different, so I must be thinking wrong. Can anyone help me understand this?
Since I am solving for energy, why do I need to go through equations 2 and 3?

cloudage said:
1. E = hv=hc/lambda
This only applies to photons.
2. lambda = h/(mv)
3. KE = .5mv^2
For an electron, you'll need these two equations.

So whenever they say "electrons" I need to use them? That makes sense, I figured the electrons were being emitted as photons so I thought of them as photons.

Thank you for your help, I see why I got the wrong answer on a couple of other problems now too

cloudage said:
So whenever they say "electrons" I need to use them?
For any kind of massive particle. (A photon has no mass.)
That makes sense, I figured the electrons were being emitted as photons so I thought of them as photons.
Yikes, don't do that.

## 1. Why was the formula E=mc^2 used to calculate the energy of an electron?

The formula E=mc^2 was initially proposed by Albert Einstein in his theory of special relativity. It states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light (c) squared. This formula was later applied to electrons to calculate their energy due to their small mass and high speeds.

## 2. How is the formula E=hf used to determine the energy of an electron?

The formula E=hf, also known as Planck's equation, relates the energy (E) of a photon to its frequency (f). This formula was used to explain the emission and absorption of light by electrons, as electrons can only absorb or emit energy in discrete packets, or quanta, which are related to their frequency.

## 3. Why do we use the formula E=-13.6/n^2 to calculate the energy levels of electrons in an atom?

The formula E=-13.6/n^2 is derived from the Bohr model of the atom, which states that electrons exist in discrete energy levels around the nucleus. The number 'n' represents the principal quantum number, which indicates the energy level of the electron. This formula was used to explain the spectral lines observed in the emission spectra of atoms.

## 4. What is the significance of the formula E=mv^2/2 in calculating the kinetic energy of an electron?

The formula E=mv^2/2 is the classical equation for kinetic energy, where 'm' represents the mass of the object and 'v' represents its velocity. This formula is used to calculate the kinetic energy of electrons, which is important in understanding their behavior in various physical processes, such as in electrical circuits or in particle accelerators.

## 5. How does the formula E=U+KE relate to the energy of an electron in an electric field?

The formula E=U+KE is the equation for conservation of energy, where 'U' represents the potential energy and 'KE' represents the kinetic energy. In an electric field, an electron experiences a change in potential energy, which is converted into kinetic energy. This formula is used to calculate the total energy of an electron in an electric field.

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