Why Does Metal Require More Energy for Electron Emission?

[desmond iking]

Homework Statement

in my book , i was told that for the emission of electron from a metal surface to occur , the photon which incident on the metal must have at least the energy more than the work function of metal , whereas for the emission of electron from H atom, the photon must have exactly the same energy between the energy levels... is there reason for this ?

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

The statement about H atoms is incorrect.

 

[desmond iking]

The statement about H atoms is incorrect.

please refer to the underlined notes.

 

[Simon Bridge]

The notes in the pic talk about the excitation of hydrogen by absorption of an electron.
In post #1 you wrote:

...whereas for the emission of electron from H atom, the photon must...

emission and excitation are different things.
the equivalent to the work function for hydrogen is the ionization energy - 13.6eV

 

[desmond iking]

The notes in the pic talk about the excitation of hydrogen by absorption of an electron.
In post #1 you wrote:

emission and excitation are different things.
the equivalent to the work function for hydrogen is the ionization energy - 13.6eV

sorry. noted my mistake.
now , my question is for excitation for hydrogen atoms , why must the photon energy hf exactly equal to difference between energy level , whereas for emission of electron for metal surface , the incident photon energy can be equal or MORE than the work function of metal?

 

[Simon Bridge]

You are still comparing apples and pears - but I think I can see what you are getting at.
Recap:

When you excite an atom, the electron is still bound to the atom.
If you excite a metal, the electron is still bound to the metal.
In both cases, the incoming energy must be exactly a transition energy between two levels.

For a photon to knock an electron off a metal, it must have energy at least equal to the work function.
If the energy is more than the work function - the difference is the kinetic energy of the electron.
If the energy is exactly the work function, then the electron barely breaks out and it's 50:50 that it will go back in.

For a photon to knock an electron off an atom, it must have energy at least equal to the atom's ionization energy.
If the energy is more than the ionization energy - the difference is the kinetic energy of the electron.
Basically the same as for the metal.

I'm thinking: you may be asking why empty space does not have discrete energy levels like inside an atom - is that the case?
But you may also be asking why you cannot eject an electron from a metal by giving it energy exactly equal to the work function.
Or it may be something else.