-
Chapter 4 “Directed Quanta of Scattered X-rays”
- University of Pittsburgh Press
- Chapter
- Additional Information
38 • In 1923 Arthur Compton (1923) calculated, using Einstein’s quantum (photon) theory of electromagnetic radiation (Energy = hυ, momentum = hυ/c, where h is Planck’s constant, υ is the frequency of the radiation, and c is the speed of light) and relativistic kinematics, that, in the scattering of electromagnetic radiation from electrons, “the energy in the scattered quantum is thus less than the energy in the primary quantum by the kinetic energy of recoil of the scattering electron. The corresponding increase in the wave-length of the scattered beam is λθ – λ0 = 2h/mc sin2 (θ/2) = 0.0484 sin2 (θ/2), where h is the Planck constant, m is the mass of the scattering electron, c is the velocity of light, and θ is the angle between the incident and scattered ray” (483). Compton tested this using the Kα X-rays from molybdenum scattered from graphite at 90º and found that λθ – λo (experimental) = 0.022 Angstroms, whereas theory predicted λθ – λ0 = 0.024 Angstroms, which he regarded as “very satisfactory agreement” (495). He concluded that “this remarkable agreement between our formulas and experiments can leave but little doubt that the scattering of X-rays is a quantum phenomenon” (501). In 1924 Compton presented additional scattering data and remarked that it required a “revolutionary change in our ideas regarding the process of scattering of electromagnetic waves” (Compton 1924, 57). He further noted that “we thought we could explain the scattering of X-rays on the assumption that radiation proceeds in spherical waves, spreading in all directions in space. We now find that to retain this assumption, if our recent results are correct,1 we must abandon both the principle of the conservation of momentum and the principle of the conservation of energy—a hard choice, indeed; but that our observations are explained simply if we are willing to imagine the rays as consisting of discrete quanta proceeding in definite directions” (57). CHAPTER 4 “Directed Quanta of Scattered X-rays” “Directed Quanta of Scattered X-rays” • 39 Compton, in collaboration with Alfred Simon, performed a more rigorous test of the quantum idea. They remarked that an increasingly large group of phenomena has recently been investigated which finds its simplest interpretation on the hypothesis of radiation quanta, proposed by Einstein to account for heat radiation and the photo-electric effect. It has not been possible, however, to show that any of these phenomena necessarily demand this hypothesis for its explanation. Thus, for example, the photo-electric effect is not inconsistent with the view that the light energy proceeds from its source in expanding waves, if we postulate the existence within atoms of a mechanism for storing energy until a quantum has been received. It is true that no such mechanism is known; but until our knowledge of atomic structure is increased it would be premature to assert that such a storing mechanism cannot exist. The change in wave-length of X-rays when scattered and the existence of recoil electrons associated with scattered X-rays, it is true, appear to be inconsistent with the assumption that X-rays proceed in spreading waves if we retain the principle of the conservation of momentum. Bohr, Kramers, and Slater (1924) have shown that both these phenomena and the photo-electric effect may be reconciled with the view that radiation proceeds in spherical waves if the conservation of energy and momentum are interpreted as statistical principles. (Compton and Simon 1925, 289–90; emphasis added) Using the concept of quanta of radiation, they calculated that in the scattering of X-rays from electrons each quantum is deflected through a definite angle φ from its incident direction and that the electron from which the quantum scatters recoils at an angle θ where tan (1/2φ) = −1/[(1 + α) tan θ] Eq. (1) where α = h/mcλ and h is Planck’s constant, m is the electron mass, c the speed of light, and λ the wavelength of the radiation. Compton and Simon proposed to clarify the situation using X-rays impinging on a cloud chamber (figure 4.1). They would observe both the recoil electron and the secondary electron track produced by the scattered X-ray and measure both the recoil angle of the electron and the angle to the start of the secondary track. They would then compute Δ, the difference between the measured and computed angle of the scattered X-ray using the photon nature of X-rays. If Δ was zero, this would confirm the quantum nature of electromagnetic radiation. The apparatus used was a “comparatively large” cloud...