Which of the following best describes Louis de Broglie's central idea about the nature of electrons in atoms?

• A. Electrons are only particles and do not display wave behavior.
• B. Electrons travel in fixed circular orbits around the nucleus.
• C. Electrons exhibit both wave-like and particle-like properties.
• D. Electrons lose energy continuously as they orbit the nucleus.

Answer: (C)

Verified step by step guidance

1. Understand that Louis de Broglie's central idea relates to the dual nature of electrons, combining concepts from both classical and quantum physics.
2. Recall that before de Broglie, electrons were primarily considered as particles moving in defined orbits, but this view could not explain certain atomic behaviors.
3. De Broglie proposed that electrons have wave-like properties, meaning they can exhibit behaviors such as interference and diffraction, which are characteristic of waves.
4. This idea is summarized by the de Broglie wavelength formula: \(\lambda = \frac{h}{mv}\), where \(\lambda\) is the wavelength, \(h\) is Planck's constant, \(m\) is the mass of the electron, and \(v\) is its velocity.
5. Therefore, the best description of de Broglie's idea is that electrons exhibit both wave-like and particle-like properties, which was a foundational concept leading to quantum mechanics.