Question Video: Identifying the Effect on a Coolidge Tube of Beam Current Variation | Nagwa Question Video: Identifying the Effect on a Coolidge Tube of Beam Current Variation | Nagwa

Question Video: Identifying the Effect on a Coolidge Tube of Beam Current Variation Physics • Third Year of Secondary School

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Which of the following must change if the beam current in the electron beam of a Coolidge tube is changed? [A] The maximum energy of the X-ray photons that are produced [B] The average energy of the X-ray photons that are produced [C] The speed of the X-ray photons that are produced [D] The presence of characteristic lines in the X-ray spectrum produced [E] The rate at which X-ray photons are produced

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Video Transcript

Which of the following must change if the beam current in the electron beam of a Coolidge tube is changed? (A) The maximum energy of the X-ray photons that are produced. (B) The average energy of the X-ray photons that are produced. (C) The speed of the X-ray photons that are produced. (D) The presence of characteristic lines in the X-ray spectrum produced. Or (E) the rate at which X-ray photons are produced.

Let’s recall the structure of a typical Coolidge tube and how it produces an electron beam. A negatively charged cathode coil and positively charged anode target are both inside a mostly airless tube. A potential difference, called the acceleration potential difference, is what causes the cathode coil and anode target to be negatively charged and positively charged, respectively. The potential difference across the cathode coil and anode target causes electrons to be accelerated from the coil to the anode target, with the kinetic energy, or KE, of these electrons being proportional to the acceleration potential difference of the Coolidge tube. But the acceleration potential difference is not proportional to the beam current in the electron beam.

To change the beam current, we must change a different potential difference over here, the potential difference that is responsible for heating up the cathode coil, causing electrons to escape from it in a process called thermionic emission. Because of the name of this process, this potential difference here is called the thermionic potential difference. The thermionic potential difference allows the electron beam to form. If we were to increase the thermionic potential difference, the temperature of the cathode coil would also increase, allowing it to release more electrons and thus increasing the electron beam current. Therefore, the thermionic potential difference is proportional to the beam current.

So, in summary, the acceleration potential difference is responsible for the kinetic energy of the electrons in the beam, which is related to the square of their speed. And the thermionic potential difference is responsible for the beam current or the number of electrons in the electron beam. With these proportions in mind, let’s start looking at the answers which all deal with X-ray photons. To help us, we have here a typical X-ray spectrum, which shows X-ray photon energy and X-ray intensity.

Now, if the beam current in the electron beam changes, answer (A) says that the maximum energy of the X-ray photons that are produced will also change. In a Coolidge tube, the maximum energy of the X-ray photons that can be produced is equal to the maximum kinetic energy of the electrons in the beam, or the product of 𝑞, the charge of an electron, and 𝑉 t, the potential difference across the Coolidge tube, which in this case would be the acceleration potential difference. So, we can see that the maximum energy of the X-ray photons that can be produced is proportional to the acceleration potential difference, not the thermionic potential difference, which is the one that is related to beam current. So, changing the beam current will in no way change the energy of the X-ray photons that can be produced within this tube. Thus, answer (A) cannot be it.

Similarly, answer (B) looks at the average energy of the X-ray photons that are produced. And we’ve already seen that the energy of these X-ray photons is not proportional to the beam current. So, (B) is not the correct answer either. Answer (C) looks at the speed of the X-ray photons that are produced. It is true that the speed, and thus the kinetic energy of the electrons in the beam, is proportional to the acceleration potential difference, which means it is related to the energy. However, we are looking at the speed of the X-ray photons, not the electrons. And photons only have one speed, light speed, which does not depend on the beam current or the kinetic energy of the electrons. (C) is not it.

Answer (D) has us looking at the presence of characteristic lines or these peaks in the X-ray spectrum produced. Whether or not these peaks appear in an X-ray spectrum depends on the maximum energy of the X-ray spectrum. If the maximum X-ray photon energy is below the point where the peaks would normally occur, then the peaks won’t show up at all. Only the smooth bremsstrahlung curve would be present. And so, because the presence of the characteristic lines in an X-ray spectrum depend on the maximum X-ray photon energy, the characteristic lines are not related to the beam current, since it is not related to the energy.

This leaves us with the last answer (E). The rate at which X-ray photons are produced must be dependent on the beam current. To see why this is, let’s recall the structure of the Coolidge tube and how a greater thermionic potential difference increases the beam current or number of electrons that are produced. When there are more electrons present in the electron beam, more electrons will strike the anode target, meaning a greater number of X-ray photons are produced, which creates a higher X-ray intensity across the entire spectrum even though the maximum energy is still the same. Note that this does not change the average energy of the X-ray photons that are being produced, like we saw in answer (B), because we are not looking at the average X-ray photon intensity. We are looking at the average X-ray energy, which stays the same.

So, if the beam current in the electron beam of a Coolidge tube is changed, the rate at which X-ray photons are produced also changes. The correct answer is (E).

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