[KanaLS]

Titanium (Work Function = 6.94 X 10^-19 J) and silicon (Work function = 7.24 X 10^-19 J) surfaces are irradiated with UV radiation with a wavelength of 250 nm. Which surface emits electrons with the longer wavelength? What is the wavelength of the electrons emitted by the titanium surface?

For the first question, I got Silicon emits longer wavelengths, since it has a higher work function.

The 2nd problem, I have no clue how to approach it...

[Borek]

What is dependence between wavelength and energy?

What is formula describing energy of emitted electrons?

[opti384]

Well if you get the first question right, there won't be any problem with the second one. First you should try to find the energy of the electron emitted by the titanium surface.

[squealer]

Actually for silicon you don't need the work function but the electron affinity. The work function is relevant for metals and silicon is a semiconductor.

to find the electron wavelength find the electron energy first which is equal to : E =  photon energy - electron affinity (or work function if it is a metal).  Then E = p^2 / 2m, where p = h / lamda.

[Borek]

Actually for silicon you don't need the work function but the electron affinity. The work function is relevant for metals and silicon is a semiconductor.

I believe you must be confusing something. Affinity energy would make sense if you were trying to remove electron from negatively charged Si ion. Work function is nothing else but ionization energy (just not for a single atom, but for atom that is on the solid surface), and it doesn't matter if you are dealing with metal or semiconductor, formula for the electron energy is identical.

[squealer]

Actually for silicon you don't need the work function but the electron affinity. The work function is relevant for metals and silicon is a semiconductor.

I believe you must be confusing something. Affinity energy would make sense if you were trying to remove electron from negatively charged Si ion. Work function is nothing else but ionization energy (just not for a single atom, but for atom that is on the solid surface), and it doesn't matter if you are dealing with metal or semiconductor, formula for the electron energy is identical.

No confusion. Work function is the energy of the Fermi level from the vaccuum state (free electron of 0 momentum). Check wikipedia.

http://en.wikipedia.org/wiki/Work_function

[DrCMS]

Actually for silicon you don't need the work function but the electron affinity. The work function is relevant for metals and silicon is a semiconductor.

I believe you must be confusing something. Affinity energy would make sense if you were trying to remove electron from negatively charged Si ion. Work function is nothing else but ionization energy (just not for a single atom, but for atom that is on the solid surface), and it doesn't matter if you are dealing with metal or semiconductor, formula for the electron energy is identical.

No confusion. Work function is the energy of the Fermi level from the vaccuum state (free electron of 0 momentum). Check wikipedia.

http://en.wikipedia.org/wiki/Work_function

squealer I think you need to read your own references before you criticise others.

From http://en.wikipedia.org/wiki/Work_function
"In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface."

From http://en.wikipedia.org/wiki/Electron_affinity
"The Electron affinity of a molecule or atom  is the energy change when an electron is added to the neutral species to form a negative ion. This property can only be measured in an atom in gaseous state."

So for this question about removing an electron from a solid surface work function is the relevant term and mention of electron affinity is complete nonsense. 

It is very annoying trying to help people on this forum when ill informed fools jump into the middle of a thread throwing about terms they do not understand and giving useless advice.

[squealer]

Actually for silicon you don't need the work function but the electron affinity. The work function is relevant for metals and silicon is a semiconductor.

I believe you must be confusing something. Affinity energy would make sense if you were trying to remove electron from negatively charged Si ion. Work function is nothing else but ionization energy (just not for a single atom, but for atom that is on the solid surface), and it doesn't matter if you are dealing with metal or semiconductor, formula for the electron energy is identical.

No confusion. Work function is the energy of the Fermi level from the vaccuum state (free electron of 0 momentum). Check wikipedia.

http://en.wikipedia.org/wiki/Work_function

squealer I think you need to read your own references before you criticise others.

From http://en.wikipedia.org/wiki/Work_function
"In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface."

From http://en.wikipedia.org/wiki/Electron_affinity
"The Electron affinity of a molecule or atom  is the energy change when an electron is added to the neutral species to form a negative ion. This property can only be measured in an atom in gaseous state."

So for this question about removing an electron from a solid surface work function is the relevant term and mention of electron affinity is complete nonsense. 

It is very annoying trying to help people on this forum when ill informed fools jump into the middle of a thread throwing about terms they do not understand and giving useless advice.

Quoting from wikipedia: ""In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is a characteristic property for any solid face[1] of a substance with a conduction band (whether empty or partly filled). For a metal, the Fermi level is inside the conduction band, indicating that the band is partly filled. For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the work function."

Check out the last sentence.

[Borek]

Quoting from wikipedia: ""In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is a characteristic property for any solid face[1] of a substance with a conduction band (whether empty or partly filled). For a metal, the Fermi level is inside the conduction band, indicating that the band is partly filled. For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the work function."

In this particular case wikipedia states "work function is about the sum of half the band gap and the work function". Kind of a recursive definition.

Unfortunately, wikipedia occasionally fails.

Besides, work function is defined for a solid surface, while affinity is defined for an isolated atom. These are completely different things.

[squealer]

Quoting from wikipedia: ""In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is a characteristic property for any solid face[1] of a substance with a conduction band (whether empty or partly filled). For a metal, the Fermi level is inside the conduction band, indicating that the band is partly filled. For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the work function."

In this particular case wikipedia states "work function is about the sum of half the band gap and the work function". Kind of a recursive definition.

Unfortunately, wikipedia occasionally fails.

Besides, work function is defined for a solid surface, while affinity is defined for an isolated atom. These are completely different things.

Ok, to settle this once and for all.

Work function = Vaccuum energy level - Fermi energy level

As you know the Fermi level is an "average energy of electrons in the solid". If the Fermi level is 3eV below vacuum level it doesn't mean that an electron state exists that is 3eV below the vacuum level.

This means that if the material is an insulator there will not be any energy states that have energy equal to the Fermi level. Therefore to extract an electron you need to supply energy
= (vacuum energy level) - (valence electron energy)
~= (vacuum energy level) - (Fermi energy) - (1/2) x (energy bandgap)

because usually the Fermi level is approximately in (1/2) x (energy gap) above the top of the valence energy band.

In a metal there are always electrons with energy equal to the Fermi level (actually the highest available energy for electrons . Therefore to extract an electron you need energy
= (vacuum energy level) - (conduction electron energy)
= (Vaccuum energy level) - (Fermi energy level)

[Borek]

And? Where is the electron affinity of a single atom?

[squealer]

And? Where is the electron affinity of a single atom?

The electron affinity of a single atom is meaningless in the bulk, so strictly speaking the relevant quantity in an insulator is the Valence band energy relative to the vacuum level (but not the Fermi level aka work function).

Is this a lingo issue ?

[Borek]

find the electron energy first which is equal to : E =  photon energy - electron affinity (or work function if it is a metal).

The electron affinity of a single atom is meaningless in the bulk

Is this a lingo issue ?

Call it as you wish, it was you who stated that electron affinity is relevant, when it is not.

[squealer]

find the electron energy first which is equal to : E =  photon energy - electron affinity (or work function if it is a metal).

The electron affinity of a single atom is meaningless in the bulk

Is this a lingo issue ?

Call it as you wish, it was you who stated that electron affinity is relevant, when it is not.

In standard semiconductor references (eg Physics of semiconductor devices,  Sze) the term "electron affinity" is systematically used for solids.

You should be in patent law ...

[Borek]

It would be funny if not for the fact that we are mostly dealing here with HS and undergraduate students that have no idea about other uses of the term. Your approach is confusing for them.

Assuming electron affinity is used the way you say it does.