Understanding X-ray Emission: Unraveling the Confusion

[Pavoo]

Homework Statement

Although not a computational problem, I still have difficulties understanding emission of characteristic X-rays.

Can someone please clear up my confusions about the topic? Here's where I'm stuck, with two texts as an example:

X-ray production typically involves bombarding a metal target in an x-ray tube with high speed electrons which have been accelerated by tens to hundreds of kilovolts of potential. The bombarding electrons can eject electrons from the inner shells of the atoms of the metal target. Those vacancies will be quickly filled by electrons dropping down from higher levels, emitting x-rays with sharply defined frequencies associated with the difference between the atomic energy levels of the target atoms.

Source for the above: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html

Following this explanation, let's say we shoot out an electron from the K-shell, and an electron from the L-shell fills its place. The X-ray that will then be emitted will be of equivalent energy size as the difference between binding energies of the K-shell and L-shell of the atom.

However, look at the following text:

1. When electrons are knocked out of their orbit, they leave behind vacancies, making the atom unstable. The atom must immediately correct the instability by filling the vacancies that the displaced electrons left behind. Those vacancies can be filled from higher orbits that move down to a lower orbit where a vacancy exits. For example, if an electron is displaced from the innermost shell of the atom (the one closest to the nucleus), an electron from the next shell up can move down to fill the vacancy. This is fluorescence.
2. Electrons have higher binding energies the further they are from the nucleus of the atom. Therefore, an electron loses some energy when it drops from a higher electron shell to an electron shell closer to the nucleus. The amount of energy lost is equivalent to the difference in energy between the two electron shells, which is determined by the distance between them. The distance between the two orbital shells is unique to each element, as mentioned above.

Source: https://www.bruker.com/products/x-r...ntal-analysis/handheld-xrf/how-xrf-works.html

Here confusion begins. How can an electron have a higher binding energy if it is further away from the nucleus? Looking at this table, I can't understand how an electron further away from the nucleus can have higher binding energy: http://xdb.lbl.gov/Section1/Table_1-1a.htm

My question is this: what type of difference of energy is an x-ray made of? The difference between the shells or the difference in the energy state of an electron?

Hope my confusion made sense.

P.S. Not used the template for posting assignment, since this is not a computational problem.

 

[DrClaude]

The second text is in error: it should be higher potential energy, not binding energy.

 

[Jonathan Scott]

The amount of energy that has to be supplied to remove the electron is greater when it is closer to the nucleus, so the binding energy has the opposite sign to the potential energy of the electron. I think it should refer to higher potential energy, not binding energy.

 

[ZapperZ]

There might be a confusion due to the SIGN.

A binding energy is often quoted with the knowledge that it is negative. For example, the ground state of H atom is E_b = -13.6 eV. While the magnitude of the binding energy is large, it is considered to be "lower" than, say, the vacuum level which, by definition, has 0 eV. So mathematically, the vacuum level has a "higher binding energy" than the ground state.

Zz.

 

[Pavoo]

DrClaude and Jonathan Scott

That certainly clears up my confusion! Thanks for pointing that out!