Question Video: Determining Which Mechanism Produces a Specific X-Ray Spectrum | Nagwa Question Video: Determining Which Mechanism Produces a Specific X-Ray Spectrum | Nagwa

# Question Video: Determining Which Mechanism Produces a Specific X-Ray Spectrum Physics • Third Year of Secondary School

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The graph shows the relative intensity of X-rays in an X-ray spectrum of different X-ray photon energies. Which of the following mechanisms could result in the production of an X-ray spectrum with this shape due to an electron beam striking a target? [A] Excitement of electrons in high-energy states in target atoms [B] Ejection of electrons in low-energy states in target atoms [C] Ejection of electrons in high-energy states in target atoms [D] Deceleration of free electrons [E] Acceleration of free electrons

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### Video Transcript

The graph shows the relative intensity of X-rays in an X-ray spectrum of different X-ray photon energies. Which of the following mechanisms could result in the production of an X-ray spectrum with this shape due to an electron beam striking a target? (A) Excitement of electrons in high-energy states in target atoms. (B) Ejection of electrons in low-energy states in target atoms. (C) Ejection of electrons in high-energy states in target atoms. (D) Deceleration of free electrons. (E) Acceleration of free electrons.

When an electron, represented by one of these blue dots here, strikes a target which is usually made of metal, it can produce X-rays of various energies. These energies depend on two things. The first is the initial energy of the electron beam, given by the equation 𝑞𝑉 t, where 𝑞 is the charge of an electron and 𝑉 t is the potential difference across the Coolidge tube that is producing the electron beam.

Okay, now before we look at the second thing that controls the X-ray photon energies, let’s clear some space. Okay, now, when an electron strikes a target, there are two different processes that could potentially occur that could produce X-rays. The first is when an electron slows down when it strikes the target, the energy the electron had outside of the target, which we’ll call 𝐸 one, is greater than the energy that it has after it slows down inside the target, which we’ll call 𝐸 two. The energy that the electron loses as it slows down is released as an X-ray or several X-rays depending on how many steps it took to slow down.

When produced this way, these X-ray photons are called bremsstrahlung or braking radiation. This is braking like the brakes on a car not breaking like smashing something with a hammer. And the reason this is called braking radiation is because it is produced when the electrons slow down or decelerate.

The opposite case, where an electron accelerates, does not produce any photons nor would it make sense for an electron to accelerate when it strikes a target. So answer (E) is not correct here.

But while an electron doesn’t accelerate inside of a target, it doesn’t always slow down either. As the electron speeds towards this target, there’s a chance that it directly strikes an already present electron in one of the target’s atoms, which causes this already present electron to be ejected from the atom entirely. This leaves behind an empty space in that electron shell that is easy to fill with another electron, which will happen if the atom happens to have an electron in a higher-energy shell.

The electron in the higher-energy shell will drop down to the empty space in the lower-energy shell, releasing an X-ray photon as it does so, the energy of which is equal to the difference in energy levels that the electron transitioned through. This whole process is called an energy level transition.

So then looking at our answers, with both processes of bremsstrahlung and energy level transition in our minds, we know that neither process involves the excitement of electrons in high-energy states, only the ejection in energy level transition, which means answer (A) is not correct.

And when we look at answer (C), the ejection of electrons in high-energy states in target atoms, if an electron in a high-energy state is ejected, leaving behind an empty space in this higher-energy level, then it’s possible that it might never get filled by an electron from within the atom since there may not be any yet higher-energy level electrons that could transition down. Nor can we say that a lower-energy level electron will transition up to fill this space since in order to do so, it must absorb energy. And this does not produce a photon. An X-ray photon is only produced when there is an ejection of an electron in a low-energy state, meaning answer (C) is not correct.

This leaves behind two possible answers. (B) The ejection of electrons in low-energy states in target atoms describes the process of an energy level transition, while (D) describes bremsstrahlung. Now let’s consider this graph which has been here the whole time and determine which of these processes will produce a curve of X-rays like this.

The X-ray photons produced by energy level transitions are of extremely specific energies since they’re always the difference in energy of the energy levels that the electron transitions through. On an X-ray spectrum of X-ray intensity versus X-ray photon energy, the photons produced by energy level transitions will appear as peaks of very specific energy with little anywhere else.

In contrast, bremsstrahlung is a braking or slowing down of an electron. And this slowing down can occur all in one big step or in several smaller steps, which means the photons produced will create a very wide X-ray spectrum with a smooth curve where the average energies are more likely to occur. Because the curve of this graph is smooth and we do not see the sharp peaks of the energy level transitions, it must be that this spectrum is caused by bremsstrahlung, which is the deceleration of free electrons.

So the correct answer to “Which mechanism produces this X-ray spectrum shape when an electron strikes a target?” is bremsstrahlung, which is answer (D) the deceleration of free electrons.

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