What did de Broglie propose to account for the fixed energy levels in Bohr's model of the atom?

• A. Electrons exhibit wave-like properties and their allowed orbits correspond to standing waves with integer multiples of wavelengths fitting around the nucleus.
• B. Electrons move in elliptical orbits determined by their angular momentum.
• C. Electrons are stationary particles located at fixed points around the nucleus.
• D. Electrons emit photons continuously as they orbit the nucleus.

Answer: (A)

Verified step by step guidance

1. Understand that Bohr's model explained fixed energy levels by quantizing angular momentum but did not explain why only certain orbits are allowed.
2. Recognize that de Broglie proposed that electrons have wave-like properties, meaning they can be described as waves rather than just particles.
3. Apply the idea that for an electron wave to be stable around the nucleus, the circumference of its orbit must fit an integer number of wavelengths, forming a standing wave.
4. Express this condition mathematically as \(n \lambda = 2 \pi r\), where \(n\) is an integer (the quantum number), \(\lambda\) is the wavelength of the electron, and \(r\) is the radius of the orbit.
5. This standing wave condition explains why only certain discrete orbits (and thus energy levels) are allowed, corresponding to the fixed energy levels observed in Bohr's model.