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Learning objectives

By the end of this section, you will be able to:

  • Define x-ray tube and its spectrum.
  • Show the x-ray characteristic energy.
  • Specify the use of x rays in medical observations.
  • Explain the use of x rays in CT scanners in diagnostics.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 5.B.8.1 The student is able to describe emission or absorption spectra associated with electronic or nuclear transitions as transitions between allowed energy states of the atom in terms of the principle of energy conservation, including characterization of the frequency of radiation emitted or absorbed. (S.P. 1.2, 7.2)

Each type of atom (or element) has its own characteristic electromagnetic spectrum. X rays lie at the high-frequency end of an atom’s spectrum and are characteristic of the atom as well. In this section, we explore characteristic x rays and some of their important applications.

We have previously discussed x rays as a part of the electromagnetic spectrum in Photon Energies and the Electromagnetic Spectrum . That module illustrated how an x-ray tube (a specialized CRT) produces x rays. Electrons emitted from a hot filament are accelerated with a high voltage, gaining significant kinetic energy and striking the anode.

There are two processes by which x rays are produced in the anode of an x-ray tube. In one process, the deceleration of electrons produces x rays, and these x rays are called bremsstrahlung , or braking radiation. The second process is atomic in nature and produces characteristic x rays , so called because they are characteristic of the anode material. The x-ray spectrum in [link] is typical of what is produced by an x-ray tube, showing a broad curve of bremsstrahlung radiation with characteristic x-ray peaks on it.

A graph of X-ray intensity versus frequency is shown. The curve starts from a point near the origin in the first quadrant and increases. Before the frequency attains its maximum value, two sharp peaks are formed, after which the X-ray intensity decreases sharply to zero at f max. Below the graph appears the equation q V equals h f max.
X-ray spectrum obtained when energetic electrons strike a material, such as in the anode of a CRT. The smooth part of the spectrum is bremsstrahlung radiation, while the peaks are characteristic of the anode material. A different anode material would have characteristic x-ray peaks at different frequencies.

The spectrum in [link] is collected over a period of time in which many electrons strike the anode, with a variety of possible outcomes for each hit. The broad range of x-ray energies in the bremsstrahlung radiation indicates that an incident electron’s energy is not usually converted entirely into photon energy. The highest-energy x ray produced is one for which all of the electron’s energy was converted to photon energy. Thus the accelerating voltage and the maximum x-ray energy are related by conservation of energy. Electric potential energy is converted to kinetic energy and then to photon energy, so that E max = hf max = q e V . size 12{E rSub { size 8{"max"} } = ital "hf" rSub { size 8{"max"} } =q rSub { size 8{e} } V "." } {} Units of electron volts are convenient. For example, a 100-kV accelerating voltage produces x-ray photons with a maximum energy of 100 keV.

Some electrons excite atoms in the anode. Part of the energy that they deposit by collision with an atom results in one or more of the atom’s inner electrons being knocked into a higher orbit or the atom being ionized. When the anode’s atoms de-excite, they emit characteristic electromagnetic radiation. The most energetic of these are produced when an inner-shell vacancy is filled—that is, when an n = 1 size 12{n=1} {} or n = 2 size 12{n=2} {} shell electron has been excited to a higher level, and another electron falls into the vacant spot. A characteristic x ray (see Photon Energies and the Electromagnetic Spectrum ) is electromagnetic (EM) radiation emitted by an atom when an inner-shell vacancy is filled. [link] shows a representative energy-level diagram that illustrates the labeling of characteristic x rays. X rays created when an electron falls into an n = 1 size 12{n=1} {} shell vacancy are called K α when they come from the next higher level; that is, an n = 2 to n = 1 size 12{n=1} {} transition. The labels K, L, M,... size 12{K, L, M, "." "." "." } {} come from the older alphabetical labeling of shells starting with K size 12{K} {} rather than using the principal quantum numbers 1, 2, 3, …. A more energetic K β size 12{K rSub { size 8{β} } } {} x ray is produced when an electron falls into an n = 1 size 12{n=1} {} shell vacancy from the n = 3 shell; that is, an n = 3 size 12{n=3} {} to n = 1 size 12{n=1} {} transition. Similarly, when an electron falls into the n = 2 size 12{n=2} {} shell from the n = 3 size 12{n=3} {} shell, an L α size 12{L rSub { size 8{α} } } {} x ray is created. The energies of these x rays depend on the energies of electron states in the particular atom and, thus, are characteristic of that element: every element has it own set of x-ray energies. This property can be used to identify elements, for example, to find trace (small) amounts of an element in an environmental or biological sample.

Questions & Answers

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Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in [link] . (b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.
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Practice Key Terms 2

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