# Kinetic energy of recoil atom in the photoelectric effect

• thatguy145
In summary, the conversation discusses the photoelectric effect and the calculation of kinetic energy for the photoelectron and ionized atom. The author skips some steps in the solution, causing the person to question their approach. Conservation of momentum and energy are necessary, and angles for momentum are not needed. The initial energy of the atom and photon system should be considered.
thatguy145

## Homework Statement

In the photoelectric effect it is generalley assumed that all the energy is given as kinetic energy to the electron while the atom is neglected. Do not neglect the recoil kinetic energy of the atom and calculate the kinetic energy of the photoelectron and the ionized atom and determine their ratio

Note: Etr (Energy transferred) = hf - EB = EKe- + EKM+

## Homework Equations

The above equation is relevant. I am not sure which other ones are relevant otherwise. most likely a few relativistic equations Ek = E-E0

## The Attempt at a Solution

I already know the solution as it is given in the textbook except the author skipped quite a few steps.

The author gives Eke- = m(ionized atom)/M(total) * Etr and Ek(atom ionized) = me/M(total) * Etr
where m is the mass and Etr is defined above

I don't know how he gets this. I started off doing conservation of momentum:

xdir: h*nu/c = pecos(theta) + pacos(phi)
ydir: 0 = pesin(theta) + pasin(phi)

and it was suggested to me to use the relation p^2/2m and solve for the kinetic energy. I don't think that's correct. I also think solving the above equation won't yield the correct answer since it doesn't incorporate the binding energy and will require conservation of energy. At this point though I am wondering if I am going down the wrong rabbit hole since the author of the textbook just sort of wrote the equation down (when usually there is very strict derivation).

Any help would be appreciated. If clarifications are needed I will do that

Ok, so you have the right idea. You need to apply conservation of momentum and energy to the system before and after the absorption and emission. You don't need to concern yourself with any angles for the momentum.

What do you think the initial energy of the atom and photon system is?

## 1. What is kinetic energy of recoil atom in the photoelectric effect?

The kinetic energy of the recoil atom in the photoelectric effect refers to the energy that is transferred to the atom when an electron is ejected from a material due to the absorption of a photon. This energy is equal to the difference between the energy of the photon and the work function of the material.

## 2. How is the kinetic energy of the recoil atom measured in the photoelectric effect?

The kinetic energy of the recoil atom can be measured by detecting the energy of the ejected electron using a detector such as a Faraday cup. The maximum kinetic energy of the electron is equal to the energy of the incident photon minus the work function of the material.

## 3. What factors affect the kinetic energy of the recoil atom in the photoelectric effect?

The kinetic energy of the recoil atom is affected by the energy of the incident photon, the work function of the material, and the angle of emission of the ejected electron. It is also influenced by the properties of the material, such as its atomic structure and electronic configuration.

## 4. How does the kinetic energy of the recoil atom relate to the threshold frequency in the photoelectric effect?

In the photoelectric effect, the threshold frequency is the minimum frequency of light required to eject an electron from a material. The kinetic energy of the recoil atom is directly related to the threshold frequency, as it is essentially the energy required to overcome the work function of the material and eject an electron.

## 5. Can the kinetic energy of the recoil atom be manipulated in the photoelectric effect?

Yes, the kinetic energy of the recoil atom can be manipulated by changing the energy of the incident photon or the properties of the material. For example, increasing the energy of the incident photon or using a material with a lower work function can result in a higher kinetic energy of the recoil atom.

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