Maximum Wavelength of Photon - electron ejection

[max8404]

I have worked on this problem for about an hour, looked through the book lots of times, and honestly just don't know how to get it done. So I am here with all you fellow physicists for help! :)

Homework Statement

X rays bombarding heavy atoms can be used
to eject electrons from the 1s shell in atoms;
indeed, this is the starting point for Moseley’s
experiments.
Estimate the maximum wavelength of pho-
tons required to eject an electron from the 1s
shell of copper, for which Z = 29. Planck’s
constant is 6.63 × 10−34 J · s and the speed of
light is 3 × 108 m/s2. Answer in units of nm.

Homework Equations

here is what I have found:
E=hc/lambda
lambdamin=hc/Ko
E=-(z)^2x13.6eV/n^2

These may seem like random equations, but honestly, these are all the ones I think that may be relevant. I can't figure out a starting point here at all.

The Attempt at a Solution

I tried solving several times. I assume that since we are ejecting the electron from the 1S shell, it has very high energy since it's so close to the nucleus. I tried this

-z^2x13.6eV/n^2=hc/lambda to solve for lambda, but I am stuck with what to do with the quantum number. Does ejecting the electron from 1s change the n from 1 to something else?

Thanks

Edit: What's weird is that the question also asks to "estimate" the max wavelength. Does that in any way change anything?

 

[nickjer]

First, you could ask yourself what is the minimum energy to eject the electron from the 1s shell. Since wavelength is inversely proportional to energy, it is the same as asking the maximum wavelength.

Second, you want to eject the electron from the 1s shell to out of the atom completely. You should remember that the 1s shell is n=1, and escaping the atom is the same as n=infinity.

And third, be careful with the units.

 

[max8404]

First, you could ask yourself what is the minimum energy to eject the electron from the 1s shell. Since wavelength is inversely proportional to energy, it is the same as asking the maximum wavelength.

Second, you want to eject the electron from the 1s shell to out of the atom completely. You should remember that the 1s shell is n=1, and escaping the atom is the same as n=infinity.

And third, be careful with the units.

Thanks for your reply, but I don't really understand what you are trying to say with the first sentence. I think I took everything you said in consideration, but the equation that I wrote is wrong since I am getting a negative number for my wavelength, and the wavelength is too small anyways. Could you give me another hint or re explain the first part?

Thanks!

 

[nickjer]

The core electron is bound to the atom by positively charged nucleus. So you need some energy to dig it out of there (similar to it being stuck in a well). If you give it too little of energy, then it will jump up but not be able to escape. You need to give it just the right amount of energy or more than that for it to escape. So there is a minimum energy needed. Since the energy is inversely proportional to the wavelength, this is the same as saying you need a maximum wavelength.

As for your your negative wavelength, it is because you are not taking into account that the photon is transitioning the electron from one state to another. Initially the electron is in state n=1, but we want the final state to be n=infinity. So your equation should look like:

$$E_f - E_i = hf$$

and becomes...

$$E_{\infty} - E_1 = hf$$

P.S.: They use the word "estimate" because this equation is not exact for real atoms other than the hydrogen atom.

 

[max8404]

The core electron is bound to the atom by positively charged nucleus. So you need some energy to dig it out of there (similar to it being stuck in a well). If you give it too little of energy, then it will jump up but not be able to escape. You need to give it just the right amount of energy or more than that for it to escape. So there is a minimum energy needed. Since the energy is inversely proportional to the wavelength, this is the same as saying you need a maximum wavelength.

As for your your negative wavelength, it is because you are not taking into account that the photon is transitioning the electron from one state to another. Initially the electron is in state n=1, but we want the final state to be n=infinity. So your equation should look like:

$$E_f - E_i = hf$$

and becomes...

$$E_{\infty} - E_1 = hf$$

P.S.: They use the word "estimate" because this equation is not exact for real atoms other than the hydrogen atom.

Hey, thanks a lot for this explanation, I really appreciate it! :)