Photoelectric Effect - Energy Level (hydrogen)

In summary, the problem involves finding the minimum energy level n for a hydrogen atom that can be ionized by a photon with a work function of 2.55eV. The term "ionize" refers to removing an electron from an atom. The correct pair of energy levels to consider is (Ef - Ei) where Ef = 0eV, and the excess energy appears as kinetic energy of the released electron. The minimum energy level n in this case is n=3.

Homework Statement

Consider a photon that is barely capable of causing a photoelectric effect when it strikes a sodium plate having a work function of 2.55eV.

Homework Equations

Find the minimum energy level n for a hydrogen atom that can be ionized by such a photon, and the speed of the released electron far from the nucleus.

Can someone explain to me what is this "ionize" term used in this question mean, because I don't know how to proceed?

The Attempt at a Solution

I'm thinking "ionize" here means "exciting the atom" and if that is so, Ef - Ei = 2.55eV.
Also I first found out the energy levels for hydrogen : -13.6eV, -3.4eV, -1.51eV, -0.85eV...

So I'm thinking that I need to find the correct pair of Ef - Ei that will give 2.55eV so that I can determine the minimum energy level n for the hydrogen atom.

Please correct me where I'm wrong.

'excite an atom'....giving energy to an atom so that an electron makes a transition from one level to a higher level;

'ionise an atom'....giving energy to an atom to REMOVE an electron from an atom;

grzz said:
'excite an atom'....giving energy to an atom so that an electron makes a transition from one level to a higher level;

'ionise an atom'....giving energy to an atom to REMOVE an electron from an atom;

Yea, but even then, I'm still not sure how to approach this question. Any hint?

... Find the minimum energy level n for a hydrogen atom that can be ionized by such a photon, and the speed of the released electron far from the nucleus...

...The attempt at a solution[/b]
... Ef - Ei = 2.55eV.
Also I first found out the energy levels for hydrogen : -13.6eV, -3.4eV, -1.51eV, -0.85eV...

So I'm thinking that I need to find the correct pair of Ef - Ei that will give 2.55eV so that I can determine the minimum energy level n for the hydrogen atom...

You are on the right track except that you need to consider (Ef - Ei) where Ef = 0eV.
That is you have to find the lowest energy level so that an electron from that energy level, once it gains the 2.55eV, is REMOVED from the atom. Any excess energy appears as KE of this electron.

Last edited:
grzz said:
You are on the right track except that you need to consider (Ef - Ei) where Ef = 0eV.
That is you have to find the lowest energy level so that an electron from that energy level, once it gains the 2.55eV, is REMOVED from the atom. Any excess energy appears as KE of this electron.

Oh, so am I right to say that at the energy level, 0eV, the electron will be removed from the atom?

If this is so, then I understand it as that, the minimum energy level n in this case would be n=3.

Oh, so am I right to say that at the energy level, 0eV, the electron will be removed from the atom?

If this is so, then I understand it as that, the minimum energy level n in this case would be n=3.

'Yes' to both quesions.

grzz said:
'Yes' to both quesions.

Thank you so much for the explanations!

1. What is the photoelectric effect?

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to light of a certain frequency. This effect was first observed by Heinrich Hertz in 1887 and later explained by Albert Einstein in 1905.

2. How does the photoelectric effect work?

When light of a certain frequency, called the threshold frequency, is shone on a material, it can transfer energy to electrons in the material. If the energy of the light is greater than the binding energy of the electrons, the electrons will be emitted from the material, creating a current.

3. What is the energy level of hydrogen in the photoelectric effect?

The energy level of hydrogen in the photoelectric effect refers to the different energy states that electrons can occupy in a hydrogen atom. These energy levels are determined by the distance of the electron from the nucleus and are represented by the quantum number n. In the photoelectric effect, the energy level of the electron determines the amount of energy needed for it to be emitted from the material.

4. How does the energy level of hydrogen affect the photoelectric effect?

The energy level of hydrogen plays a crucial role in the photoelectric effect. The higher the energy level of the electron, the more energy it will require to be emitted from the material. This means that electrons in higher energy levels will only be emitted by light of higher frequencies, while electrons in lower energy levels can be emitted by lower frequencies.

5. What is the significance of the photoelectric effect in modern technology?

The photoelectric effect has many important applications in modern technology. It is the basis for solar panels, which convert light energy into electricity, and for photocells, which are used in light sensors and detectors. The understanding of the photoelectric effect also led to the development of quantum mechanics, which has revolutionized our understanding of the behavior of matter and energy at a microscopic level.