Electron emits a photon that emits an electron

[skate_nerd]

Homework Statement

This problem has a photon that was emitted by an electron orbiting a hydrogen atom that dropped from n=5 orbit to n=2. I need to find out, if this photon emitted an electron from the n=4 orbit of another hydrogen atom, what the k.e. of this electron would be.

Homework Equations

1/λ=R(1/n_f^2-1/n_i^2)
E=hc/λ
not sure of what else i need

The Attempt at a Solution

So far I found the wavelength using the first equation I listed, and then from this found the energy of the first emitted photon. I got 2.856 eV. I'm pretty sure I am supposed to use this information to find out what the k.e. of the electron that this photon emits is, but I am unsure of how to do that.
At first I thought maybe the energy of the photon was equal to the total energy of the electron, and so 2.856 eV=k.e.+rest energy of the electron, but this obviously didnt work (got a negative number for k.e.).
Im sure there's just some equation I am missing. If someone would fill me in that would be appreciated.

 

[voko]

I think your are getting confused by the terminology. The photon does not emit an electron. Rather, it strikes another atom and the atom emits the electron.

 

[gneill]

You want to know if a photon, with an energy of 2.856 eV, is capable of kicking out an electron from the n=4 orbit of a hydrogen atom. How will you calculate the energy required?

 

[skate_nerd]

Would the energy required be E=-13.6 eV * 1^2 / 4^2?

 

[skate_nerd]

What do i do with that energy required though?

 

[mukundpa]

How this electron (n=4) is getting this amount of energy to be kicked out?

 

[gneill]

Would the energy required be E=-13.6 eV * 1^2 / 4^2?

That's the negative of the energy required... emitting a negative amount of energy is equivalent to absorbing the same amount.

What do i do with that energy required though?

Compare the amount of energy required to what is available in the incoming photon.

 

[skate_nerd]

So I am pretty sure that by compare it you mean the total energy of the electron is the difference between the energy required to kick it out and the total energy of the photon.
However, i am still somewhat stuck on finding out how to get the kinetic energy out of this. If i use the total E of the electron=the k.e. + the rest E, ill get a negative number when i solve for the kinetic energy

 

[gneill]

So I am pretty sure that by compare it you mean the total energy of the electron is the difference between the energy required to kick it out and the total energy of the photon.
However, i am still somewhat stuck on finding out how to get the kinetic energy out of this. If i use the total E of the electron=the k.e. + the rest E, ill get a negative number when i solve for the kinetic energy

You're not creating an electron, just moving one. So the rest mass doesn't enter the picture (unless there's so much energy involved that the electron's speed will be a substantial fraction of c, and that won't be the case for a photon that originated in a small transition in a hydrogen atom).

Once enough energy has been supplied to remove the electron ("escape"), whatever is left over will end up as remaining KE for the electron.

 

[skate_nerd]

Oh okay i think i understand now. Thanks guys