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Question Video: Determining the Greatest X-Ray Energy Emitted From an Atom Physics

The diagram shows an atom in the target material used in a Coolidge tube that generates X-rays. An electron in the electron beam used in the tube could eject either an electron in the K-shell or an electron in the L-shell of the atom. Which of the following would result in the greatest energy X-ray photon being emitted from the atom? [A] An electron in the L-shell of the atom is ejected. [B] An electron in the K-shell of the atom is ejected. [C] The energy of the X-ray photon emitted from the atom will be the same whichever electron is ejected. [D] The energy of the X-ray photon emitted from the atom will depend on the initial energy of the electron in the beam as well as which electron in the atom is ejected.

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Video Transcript

The diagram shows an atom in the target material used in a Coolidge tube that generates X-rays. An electron in the electron beam used in the tube could eject either an electron in the K-shell or an electron in the L-shell of the atom. Which of the following would result in the greatest energy X-ray photon being emitted from the atom? (A) An electron in the L-shell of the atom is ejected. (B) An electron in the K-shell of the atom is ejected. (C) The energy of the X-ray photon emitted from the atom will be the same whichever electron is ejected. (D) The energy of the X-ray photon emitted from the atom will depend on the initial energy of the electron in the beam as well as which electron in the atom is ejected.

We’ve compressed these answers to give us some space. And we’re now going to do the same thing to the original question text.

Now, in order for an X-ray photon to be emitted from this atom, a process called an energy level transition must occur. An energy level transition occurs when an electron in a high energy level moves down or transitions down to a lower energy level. When this happens, the difference in energy between the energy levels is released as an X-ray photon. The energy of this X-ray photon is equal to the difference in energy between the electron energy levels the electron transitioned from and to.

This means that a large difference in electron energy levels will produce a high energy photon, whereas a smaller difference will produce a smaller energy photon. This means that a high energy level electron that transitions down to some intermediate energy level will produce a photon that has a smaller energy than if it transitioned down to, say, the L-shell due to the difference in the electron energy levels.

But in order for an energy level transition to occur at all, the high energy level electron must have a spot to move down to. There has to be a vacancy in a lower electron energy level, a vacancy that can be caused by the electron in the electron beam ejecting either the electron in the K-shell or the L-shell. Now, because we’re looking for the greatest energy X-ray photon being emitted from the atom, the initial energy of the electron in the beam doesn’t matter and neither does the energy of the electron that is so ejected from the atom either. These energies only matter for Bremsstrahlung, or breaking radiation, which occurs outside of atoms.

Only energy level transitions will produce X-ray photons from within the atoms, which is what we’re looking for. Because of this, answer (D) cannot be correct since it talks about depending on the initial electron beam energy and energy of the ejected electron, which only matters for Bremsstrahlung. Our answer has to involve an energy level transition. And because of this, we know that (C) cannot be correct because the energy of the X-ray photon depends on the difference in electron energy levels the electron is transitioning through.

If the electron in the electron beam knocked out the electron in the K-shell, then the difference in energy level between the high energy level electron and the K-shell would be greater than if the high energy level electron went down to the L-shell due to the electron beam knocking out that electron instead. The difference in energy level of the X-ray photons produced is not the same. So (C) is certainly not it.

If we’re looking for the greatest energy X-ray photon, then it has to be the one that causes the electron and the high energy level to transition between the most energy levels and thus the greatest total energy. This occurs when the high energy level electron transitions down to the K-shell. Therefore, the event that would result in the greatest energy X-ray photon being emitted from the atom is when an electron in the K-shell of the atom is ejected by the electron in the beam. The correct answer is (B).

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