Electron collison with an atom

[mentaaal]

Hi guys, I am new to this forum and decided to join when i stubled upon a similar thread to the one i am about to post.

The question i am pondering is this:

In the question, the three lowest energy levels of an atom of the target material in the xray tube are shown and the question is: "What is the minimum Potential Difference at which the tube can operate if the transition from n=3 to n=1 is possible? Straight away i figured you just subtract n = 1 from n=3 and hey presto but my friend said he recalls the teacher saying something about you have to use the PD relating to the maximum transition, i.e. to allow the atom to be ionised entirely: 0 - (n=3). My thoughts on this is that the PD needed here is only enough to give the elctron enough energy to allow the electron to jump from n = 1 to n = 3.
The atom's model is:

n = 3 ----------------------- -11 x 10^3
n=2 ------------------------- -26 x 10^3
n=1 -------------------------- -98 X 10^3

Could anyone tell me if i am wrong and why?

This question lead me on to wonder what can happen when an electron collides with an atom in general. If the energy of the incident electron is such that is slightly more than what is required to excite an electron to the next energy level , will the collision result in no energy being transferred to the atom? Or wil the energy transfer be such that an electron gets excited and the difference result in a phonon?


In my notes regarding the line spectrum (characteristic spectrum) of atoms in an Xray tube it says "The line spectrum is the result of electron transitions within the atoms of the target material. The electrons which bombard the target are very energetic and are capable of knocking electrons out of deep-lying energy levels of the target atoms."

So similarly does this suggest that if the incident high energy electron has more energy than what is required to eject a deep lying electron, the difference in energy could manufest as heat?

 

[Jame]

I'm taking Quantum Physics right now and therefore I'm also new to this, but why not give it a try!

You're right about the minimal PD required for the tube to operate. The transition from n = 3 to n = 1, showing as a so called $$K_{\beta}$$ in the line spectrum requires an energy different from the ionization energy. You're not interested in removing the electron from the atom completely.

Regarding your second question I understand that only electrons of an energy corresponding to an allowed transition are involved in producing characteristic xrays, and those able to knock out a highly bound electron are natuarally the ones giving rise to the hard xrays, ie. most energetic. The electrons another energy, ie. a forbidden one for making a transition, are just deccelerated when they approach the positive nucleus, giving rise to the continuous part of the spectrum. This is classically explained as an effect of an accelerated charge radiating EM waves, I think it's called something like "brahmstruhling".

 

[mentaaal]

Ah yes i see what you mean Jame thanks for the response.

Two more questions similar to the first:

If, as you say, the kinetic energy of the electron doesn't match the required transition energy it merely gets decelated and contributed to the continuous spectrum, how does it decelerate? Electrons are attracted to the nucleus..

1: I feel like i should know this one and I am pretty sure that it came up in class once but i have since fogotten ;-)

2: A question in my notes says "Explain briefly why a modern X-ray tuve can be operated directly from the output of a step-up transformer."

I always presumed this was allowed as electrons only get emitted from the filament by means of thermionic emission and not the other way around and left it at that without thinking about it anymore but HOWCOME electrons can't travel back in the opposite direction thermionically as well when the AC waveform is in the opposite polarity? Could it be because the Target, say tungsten for the sake of argument doesn't thermionically emit as much electrons? Surely thermionic emission could still occur in the target as it gets quite hot.

 

[Jame]

Ah sorry, I don't know what the decelerate stuff was about, I meant accelerate. I guess it just gets scattered by the atom, even if the atom is in total neutral. As an effect of the electron getting so close that the distribution of the charges matters, then you'll have both repelling and attracting forces in the works, accelerating the electron in one way or another. Giving rise to radiation in any case. Not too sure about this so don't take my words for true without checking!

 

[mentaaal]

Makes sense, I guess, something confusing though is the the minimum wavelength in the continuous spectrum equates to all of the energy of the incident electron, implying that it gets completely decelerated and not scattered at all as that would require a fraction of the kinetic energy being retained...

 

[HungryChemist]

If, as you say, the kinetic energy of the electron doesn't match the required transition energy it merely gets decelated and contributed to the continuous spectrum, how does it decelerate? Electrons are attracted to the nucleus..

You're thinking head on collision of electron to nucleus of an atom. But many more electrons will simply fly above the nucleus, and while it does that, due to attractive force, it will deflect and under go circular motion. This type of change in acceleration of an electron creates continuous energy spectrum of emitted photon since the distance electrons approach the nucleus vary continually for different electrons.

 

[mentaaal]

You're thinking head on collision of electron to nucleus of an atom. But many more electrons will simply fly above the nucleus, and while it does that, due to attractive force, it will deflect and under go circular motion. This type of change in acceleration of an electron creates continuous energy spectrum of emitted photon since the distance electrons approach the nucleus vary continually for different electrons.

Yes i quite agree, the confusion stems from the minimum wavelength, at which ALL of the kinetic energy gets transferred into a photon... that surely suggests that no more kinetic energy remains. How does this happen?

 

[HungryChemist]

Yes i quite agree, the confusion stems from the minimum wavelength, at which ALL of the kinetic energy gets transferred into a photon... that surely suggests that no more kinetic energy remains. How does this happen?

I'm sorry but I can not understand the question very well. Can you elaborate?

for example, what minimum wavelength are you talking about?

 

[mentaaal]

Sorry, in the Xray emission spectrum, in the continuous spectrum, the minimum wavelength of the emitted Xrays has energy equal to that of all the incident electron's kinetic energy. So, if the incident electron's kinetic energy is all transferred, then the electron has been completely stopped. I am just wondering how this happens

 

[sirchasm]

Electrons don't "completely stop" they reach a ground state in an atom, as a stable orbital or energy level, a bit like a ledge on the side of a slope, say.

They always have a certain energy, or intrinsic momentum, as well as kinetic energy.