Which of the following statements is true? The existence of the de Broglie wavelength \(\lambda_{d B}\) implies (A) that matter particles should undergo interference. (B) that matter waves travel at the speed of light. (C) that the frequency of matter waves is \(c / \lambda_{d B}\), where \(c\) is the speed of the particle. (D) that matter waves are given off by accelerating charges. (E) that matter waves are polarized.

The de Broglie wavelength is a concept in quantum mechanics that defines the wave-like behavior of matter particles. It is expressed as \[\lambda_{dB} = \frac{h}{p}\] where \(h\) is Planck's constant and \(p\) is the momentum of the particle. It is important to note that the wave-like behavior of matter particles, as described by the de Broglie wavelength, is connected to the wave-particle duality concept.

We will now go through each statement and determine its truthfulness. (A) that matter particles should undergo interference. This statement is true. The existence of the de Broglie wavelength implies wave-like behavior for matter particles, and one of the key features of wave behavior is interference. (B) that matter waves travel at the speed of light. This statement is false. Matter waves do not travel at the speed of light. Only electromagnetic waves, like light, always travel at the speed of light. (C) that the frequency of matter waves is \(c / \lambda_{d B}\), where \(c\) is the speed of the particle. This statement is false. The expression \(c / \lambda_{d B}\) defines the frequency of electromagnetic waves like light, but not matter waves. (D) that matter waves are given off by accelerating charges. This statement is false. This description applies to electromagnetic waves, such as radio waves, microwaves, and light, which are emitted by accelerating charges. Matter waves don't have the same origin. (E) that matter waves are polarized. This statement is false. Polarization is a property of transverse waves, especially electromagnetic waves. Matter waves, on the other hand, do not exhibit polarization.

Based on our examination of each statement, we can conclude that statement (A) is the only true statement: The existence of the de Broglie wavelength implies that matter particles should undergo interference.