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Collisions of Electrons with Atoms

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Collisions of Electrons with Atoms

Atom and electron collisions are processes in which electrons can ionise an atom, removing electrons from its structure or excite electrons, thus moving them from one place to another in the areas in which they occur inside the atom. The initial state of the electrons, if they are stable, is named the ground state.

Electron collision with atoms and ionisation

Electrons can also initiate a beta decay to ionise or excite the electrons, a process that depends on:

  1. The energy of the incident electron, which is given by its kinetic energy.
  2. The energy of the electrons moving around the atom.

Collisions of Electrons with Atom ionization electron collision StudySmarterFigure 1. When an electron or a photon impacts an atom, part of their kinetic injects energy into the electrons orbiting around the atom. This moves them to another orbit. If the energy is high enough, it ejects the electrons from the atom. Source: Manuel R. Camacho, StudySmarter.

What happens when an atom and electrons collide?

Electrons can be released by the atom when a photon impacts it or when an unstable isotope breaks into pieces. Electrons that fly free with larger kinetic energies can impact another atom, leading to three possible interactions after this impact:

  1. Excited level states: the electron colliding with the atom gives its kinetic energy to another electron already present in the atom. The electron receiving the energy moves into an excited state and thus to a new orbit.
  2. Atom ionisation by knocking out other electrons. If the atom already has a negative charge, this increases its positive charge even more.
  3. Proton–neutron conversion, i.e., the conversion of a proton into a neutron, which can occur if the nucleus captures an electron. This process is named beta plus decay, as it releases a positron (positive electrons).

What happens when an electron collision excites another electron?

The first type of interaction between an electron colliding with an atom is the excitation of another electron. When the electron impacting the atom gives its kinetic energy to another electron that is orbiting within the atom, you can assume the electron was in the ground state.

Collisions of Electrons with Atoms. Ionisation. Energy exchange. StudySmarterFigure 2. Electron or photon impacting and exchanging energy with an electron in a ground state. Source: Manuel R. Camacho, StudySmarter.

As the electron that lives in the atom is bound to its location with some fixed energy, the energy excess given by the other electron makes it jump to another energy level.

Collisions of Electrons with Atoms. Ionisation process. StudySmarterFigure 3. Electron jumping to an excited state after absorbing energy from the incident electron or photon. Source: Manuel R. Camacho, StudySmarter.

The electron will stay in an excited state for some time. However, as the atom seeks to be stable, the electron eventually releases its excess energy as a photon. After releasing the excess energy, the electron reverts to the ground state and its initial energy level.

Collisions of Electrons with Atoms. Excited state. Stability. Photon release. StudySmarterFigure 4. Electron jumping back from an excited state and releasing energy as a photon. Source: Manuel R. Camacho, StudySmarter.

Calculating the energy levels after electron collisions

You need to use the energy conservation law to calculate the energy of an electron that jumps energy levels inside an atom after a collision with an electron. The new energy level is equal to that given by the incoming electron.

An electron flying with a kinetic energy of 10.2 electron volts collides with a hydrogen atom. What happens to the electron of the hydrogen after the collision?

First, we need to realise that the electron colliding with the atom will inject some energy into the electron inside the atom, making it jump to a new energy level. Its energy will be equal to that provided by the electron colliding with the atom.

The energy level is calculated as the difference in the atom’s energy levels. See the following table for the first three energy levels for hydrogen:

Energy levelNameEnergy level ‘n’Energy
1stGround staten = 1-13.6 [eV]
2nd1st excited staten = 2-3.4 [eV]
3rd2nd excited staten = 3-1.5 [eV]

The energy of the incoming electron is used to move the electron up. Its energy will be equal to the difference between the two levels.

In this case, we subtract E2 from E1.

The electron in the atom will move to the energy level n = 2, which is the first excited state or the first energy level.

But what if you want to know what happens to the electron later?

The first excited state is unstable, as the atom, seeking stability, will release the excess energy in the form of a photon. The released energy of the photon will be equal to the energy gained by the electron. To calculate this, we need to use the photon’s energy equation as below.

Here, f is the photon’s frequency, while h is the Planck constant: h = 6.62 ⋅ 10 ^ −34 [j] per hertz. The frequency of the photon released after the electron goes back to its ground state is calculated as follows:

As one electron volt is equal to 1.6 ⋅ 10 ^ -19 [j], 10.2 [eV] are equal to 1.63 ⋅ 10 ^ -18 [j].

And what if you want to know whether the released photon belongs to the visible light, the x-ray spectrum, UV light, radio waves, or some other form of radiation?

You will need to use the photon-wavelength-frequency relationship to work this out. This relationship relates the photon’s energy to its frequency and the Planck constant.

We also know that the energy of a wave is inversely proportional to its wavelength, and the photon is a type of wave.

The photon’s energy is equal to the electron’s energy when the electron jumps back to n = 1. The energy to jump back is also equal to the energy used to move up 1.63 ⋅ 10 ^ -18 [j] or 10.2 [eV].

This is equal to the wavelength-energy relationship.

As the light velocity (c) is 3 ⋅ 10 ^ 8 [m / s] and the Plank constant is h = 6.62 ⋅ 10 ^ −34 [Joules / Hertz], we can calculate the wavelength λ as follows:

The length of this wavelength is around 0.12 micrometres. Looking at the electromagnetic spectrum, you find that the range for UV light is from around 0.01 [micrometres] to 0.38 [micrometres]. The released photon is within this range, which tells us that the photon released after the electron reverts to its ground state is ultraviolet light.

What happens to the electron that caused the other electron to jump? The electron that gave the energy ends up with a velocity of 0.

Wavelengths and frequencies for common types of photons

Photons can be classified according to their frequency ‘f’ (energy) and their respective wavelength ‘λ. See the following table, which displays the values for a range of photons.

PhotonWavelength ()Frequency (hertz)
Gamma rays0.001
X-rays1
UV light100
Dark blue (visible)442-663
Infrared1000

A good way to convert between the photon frequency and wavelength is the equation below, where c is the speed of light in a vacuum.

Collisions of Electrons with Atoms - Key takeaways

  • Electrons and photons can impact atoms.
  • The impact of electrons and photons injects energy into the electrons orbiting the atom.
  • The energy of the electrons changes, exciting them and making them jump to another orbit or even ejecting them.
  • Electrons that are not excited are said to be in their ground state.
  • When the electrons go back to their ground state, they release energy in the form of a photon.

Frequently Asked Questions about Collisions of Electrons with Atoms

Electrons can collide with many other particles. These interactions can cause a range of processes. If the collision is with an atom, the electron’s kinetic energy can be transferred to an electron inside the atom and excite or eject it from the atom. If the electron is captured by the nucleus, a proton will combine with it, causing a beta plus decay.

Neutrons can impact an atomic nucleus. When this happens, the neutron imparts energy, which, if large enough, will break the atom in a process that produces radiation and lighter elements.

When an electron collides with an atom, there is the probability that the electron will push out an electron orbiting the atom. This happens because the electrostatic force repels both, and the one orbiting feels enough force to be kicked out of the atom. This, in turn, makes the atom a positive ion.

Another possibility is that the atom is positively charged (by lacking electrons) and captures an electron. In this case, the electron will remain in the atom, and the atom will release the electron’s excess kinetic energy in the form of a photon.

Final Collisions of Electrons with Atoms Quiz

Question

Name the three processes that can occur when an electron impacts an atom.

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Answer

Ionisation, excitation, and beta decay.

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Question

What is ionisation?

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Answer

Ionisation occurs when an electron or a photon impacting an atom have enough energy to remove an electron from the atom. This process also happens when the atom gains an electron.

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Question

What happens during the excitation process?

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Answer

The electron or photon injects energy into an electron in the atom, making it jump to a new orbit with higher energy.

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Question

What happens during the beta plus decay?

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Answer

A proton converts into a neutron.

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Question

What is the ground state?

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Answer

It is the energy state of an electron that is not excited.

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Question

How can an electron move to an upper, excited level?

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Answer

By gaining energy.

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Question

From where does an electron gain the energy to move to a new orbit?

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Answer

From an electron or a photon impacting the atom.

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Question

Does the electron stay at the excited level after gaining energy?

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Answer

No, the atom will look for a stable state, releasing the excess energy and moving the electron back to its original position.

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Question

What happens when the electron moves back to its ground level?

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Answer

It releases excess energy in the form of a photon.

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Question

Without making any calculations, if an electron injects energy to a hydrogen atom, making the electron jump from E0 to E3, how much energy does the electron in the atom gain?

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Answer

It gains energy equal to the difference between both energy levels.

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Question

If a photon impacts a hydrogen electron on its ground state and moves it to n=2 or the first excited state, how much energy was gained? To answer this, you should consult the table in the explanation.

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Answer

It gains 13.6-3.4[eV] or 10.2[eV].

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Question

If a hydrogen electron moves from an excited state n=3 to the ground state n=1, how much energy is emitted in the photon? To answer this, you should consult the table in the explanation.

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Answer

12.1 [eV].

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