Photoelectric Effect of hydrogen atom

[tigg3992]

1. The problem statement

A hydrogen atom has an electron in the fundamental state.

a. Show that a radiation with λ = 50 nm will ionize the atom.

b. What will be the excess kinetic energy of the electron in joules?

What is this question asking? Is it asking what wavelength will free an electron? Because if so, it didn't give me the work function for hydrogen. I think I know how to calculate that, but I'm not certain. Or is it asking something else entirely?

Homework Equations

Work function/Planck's constant= threshold frequency

wavelength*threshold frequency=frequency

Energy=Planck's constant*frequency

The Attempt at a Solution

I'm stumped. If I understood what to look for, I'd be able to attempt a solution.

 

[berkeman]

1. The problem statement

A hydrogen atom has an electron in the fundamental state.

a. Show that a radiation with λ = 50 nm will ionize the atom.

b. What will be the excess kinetic energy of the electron in joules?

What is this question asking? Is it asking what wavelength will free an electron? Because if so, it didn't give me the work function for hydrogen. I think I know how to calculate that, but I'm not certain. Or is it asking something else entirely?

Homework Equations

Work function/Planck's constant= threshold frequency

wavelength*threshold frequency=frequency

Energy=Planck's constant*frequency

The Attempt at a Solution

I'm stumped. If I understood what to look for, I'd be able to attempt a solution.

Welcome to the PF.

You should be able to just look up the work function for hydrogen -- is that all you need to finish this problem?

 

[tigg3992]

Welcome to the PF.

You should be able to just look up the work function for hydrogen -- is that all you need to finish this problem?

I would, but I don't even know if that's what it's asking. I think that's not it, because we finished work functions and now we're working on spectroscopy. But none of those concepts work as well for this question as work function does. I don't think it's asking anything about what frequencies of light a hydrogen atom will emit, but I think that's probably related.

 

[cartonn30gel]

a) You need to show that the energy of the radiation with λ = 50 nm. Then you need to show that this is greater than the work function of hydrogen.

b) The excess kinetic energy can be found using conservation of energy. The electron that the question is talking about is the one that is given off by the atom when its ionized by the 50 nm radiation.

Is that clear now?

 

[tigg3992]

But hydrogen doesn't have a work function, because the photoelectric effect only works with metals. So I had it wrong from the beginning.

Maybe the question is asking about orbital levels? Because hydrogen only has one electron, so wouldn't it only have one level? And the energy it would take another electron in a different element to move to a higher level would ionize a hydrogen atom.

 

[tigg3992]

That's wrong too. It has nothing to do with orbitals either.

 

[cartonn30gel]

Work function can be used in multiple contexts. When you're doing solid state physics, it's "the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface". More generally "the work function is the minimum energy that must be given to an electron to liberate it from the surface of a particular substance." This is also the ionization energy. (These are quoted from wikipedia)

So, you need to either calculate or look up that minimum energy needed to remove the only electron that a hydrogen atom has. To calculate it, you will need to look up some constants. Think about the electric potential between the proton and the electron of the hydrogen atom.

 

[cartonn30gel]

Work function can be used in multiple contexts. When you're doing solid state physics, it's "the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface". More generally "the work function is the minimum energy that must be given to an electron to liberate it from the surface of a particular substance." This is also the ionization energy. (These are quoted from wikipedia)

So, you need to either calculate or look up that minimum energy needed to remove the only electron that a hydrogen atom has. To calculate it, you will need to look up some constants. Think about the electric potential between the proton and the electron of the hydrogen atom.