IB Physics 2015 Higher level Paper 2 Question 7

Question: Diffracted electrons through a thin layer of graphite are incident on a fluorescent layer. Students are expected to explain how an observable pattern demonstrates that electrons have wave properties.

Mark Scheme: 
(1) bright and dark rings / circles / circular fringes. 
(2) maximum and minimum / constructive and destructive. 
(3) mention of interference / mention of superposition. 
(4) link to interference being characteristic of waves.

Comments:

Based on the mark scheme, students are expected to state circular fringes (or similar descriptions) and link the observable pattern to a characteristic of waves. That is, they have to specify the observable pattern when electrons are incident on a fluorescent layer in the tube. As a suggestion, students could mention that “bright and dark rings or circular fringes could be observed at the end of the tube.” The bright rings (or circular fringes) are due to constructive interference, whereas dark rings are due to destructive interference. Importantly, the circular fringes can be linked to the wave-like properties of electrons instead of particle-like properties.

Furthermore, students could explain that “the circular fringes are a result of interference (or superposition) which is a wave-like property of electrons.” That is, the formation of fringes follows the principle of superposition because electrons behave like waves. However, interference is not the only characteristic of a wave. For example, Knight (2004) suggests that wave properties could be described as non-localized, continuous, and collective (Knight, 2004). On the other hand, in Hertz’s experiment, “[t]he waves were found to exhibit the properties of: 1. reflection; 2. refraction; 3. interference; 4. diffraction; 5. polarization; and 6. they travelled at c (the speed of light) (Warren, 2003, p. 108).”

However, in Physics for the IB diploma, it is stated that: “when an electron moves inside a crystal whose interatomic spacing has similar dimensions as the de Broglie wavelength will diffraction take place (Tsokos’s 2008, p. 395).” That is, wave-like properties of electrons may include “diffraction” and “de Broglie wavelength.” Thus, students could specify that “the de Broglie wavelength of the diffracted electrons is dependent on their speeds and it should have similar dimensions as the interatomic spacing.” It is worth mentioning that the circular fringes occur where the path difference of the electron waves from the sources is zero or they differ by an integral multiple of the de Broglie wavelength.

Feynman insights?:

Interestingly, Feynman mentions that “[i]f we take these neutrons and let them into a long block of graphite, the neutrons diffuse and work their way along. They diffuse because they are bounced by the atoms, but strictly, in the wave theory, they are bounced by the atoms because of diffraction from the crystal planes (Feynman et al., 1963, section 38–3 Crystal diffraction).” In essence, diffraction is an important wave property of neutrons when they move inside a block of graphite. However, it is the slowest neutrons that pass through the long block of graphite. These neutrons have longer wavelengths and behave more like waves.

Importantly, Feynman explains that “[n]o one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do, roughly speaking, is to say that when there are only a few sources, say two, interfering, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used. So, we shall not worry about whether it is interference or diffraction (Feynman et al., 1963, section 30–1 The resultant amplitude due to n equal oscillators).” In short, there is diffraction in the phenomenon “interference,” and there is interference in the phenomenon “diffraction.” In other words, interference involves diffraction or spreadings of waves, whereas diffraction involves interference or summings of waves.

In addition, Feynman clarifies that “[h]istorically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither (Feynman et al. 1963, section 37–1 Atomic mechanics).” Simply phrased, the electrons are neither particles nor waves. More importantly, Feynman elaborates that “[t]he electrons arrive in lumps, like particles, and the probability of arrival of these lumps is distributed like the distribution of intensity of a wave. It is in this sense that an electron behaves sometimes like a particle and sometimes like a wave (Feynman et al., 1963, section 37–5 The interference of electron waves).” In short, it is the distribution of electrons that is guided by a wave function or a probability wave. Moreover, electrons could be observed to have particle-like properties or wave-like properties depending on the experimental set-up.

Note:

In a sense, the phrase “wave properties” in the question should be changed to “wave-like properties.” For example, in Feynman’s own words, “the particle has wavelike properties (Feynman et al., 1966, section 3-1 The laws for combining amplitudes).”

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

2. Feynman, R. P., Leighton, R. B., & Sands, M. L. (1966). The Feynman Lectures on Physics, Vol III: Quantum mechanics. Reading, MA: Addison-Wesley.

3. Knight, R. D. (2004). Physics for Scientists and Engineers with Modern Physics. California: Addison-Wesley.

4. Tsokos, K. A. (2008). Physics for the IB diploma (5th ed.). Cambridge: Cambridge University Press.

5. Warren, N. (2003). Excel HSC Physics. Glebe, NSW: Pascal.