Question

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals that preceded Thomson's work, that the cathode rays are a wave phenomenon?

Short answer

Rutherford's experiments on the scattering of α particles by a gold foil demonstrated that atoms have a small, positively charged nucleus containing most of the mass, with electrons orbiting in mostly empty space. This paved the way for Bohr's theory, which proposed quantized energy levels for electrons in hydrogen atoms and explained their discrete emission spectra. De Broglie's hypothesis, which suggests wave-particle duality for all particles, is consistent with J.J. Thomson's conclusion that electrons have mass and the earlier proposals that cathode rays are a wave phenomenon, as it unifies their wave-like and particle-like properties.

Step-by-step solution

Rutherford's Experiments

Rutherford's experiments involved the bombardment of a thin gold foil with α particles (helium nuclei). He observed that most of the α particles went straight through the foil with little or no deflection, but a small fraction of the particles were deflected at large angles. This observation led him to propose a new model where the positive charge and most of the mass of the atom is concentrated in a very small nucleus, and the electrons move around the nucleus in an otherwise mostly empty space.

Bohr's Theory of the Hydrogen Atom

Rutherford's nuclear model of the atom paved the way for Bohr's theory, which was focused on explaining the behavior of electrons in hydrogen atoms. Bohr proposed that the electrons in an atom can only exist in well-defined energy levels, and when an electron transitions between these levels, it absorbs or emits a specific amount of energy in the form of light. The quantized energy levels explained the observed discrete emission spectra of the hydrogen atom, which could not be accounted for by classical electromagnetic theory.

De Broglie's Hypothesis

De Broglie's hypothesis proposed the wave-particle duality of matter, stating that all particles, including electrons, have both particle-like and wave-like properties. This idea was based on the observation that the behavior of electrons seemed to exhibit characteristics of both particles and waves.

Consistency with J.J. Thomson's Conclusion

De Broglie's hypothesis is consistent with J.J. Thomson's conclusion that the electron has mass because it does not deny the particle-like properties of the electron. Instead, it suggests that the electron has both particle-like and wave-like properties, allowing it to have mass as well as other properties associated with waves, such as interference and diffraction.

Consistency with Wave Phenomenon Proposals

De Broglie's hypothesis is also consistent with proposals preceding Thomson's work that cathode rays are a wave phenomenon because it unifies the wave-like and particle-like properties of the electron, suggesting that its behavior as a cathode ray can be adequately explained by considering both aspects of its nature.