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AP Physics 2
15.2 The Bohr Model of Atomic Structure
15.1 Quantum Theory and Wave-Particle Duality
IntermediateMCQMathematicalConceptual21.9k
A central solid dot labeled +e represents an atomic nucleus in a two-dimensional view. A thin dashed black circle centered on the nucleus represents the classical electron orbit of radius r. A straight line segment with a single arrowhead labeled r extends from the central dot to the dashed line. A smooth, continuous sinusoidal wave line oscillates symmetrically inside and outside along the perimeter of the dashed circle, forming a closed standing wave pattern around the center. The wave pattern completes a whole number of wavelengths along the circular loop. No other labels, lines, text, or axes appear.
Electron standing wave pattern along a circular orbit of radius \(r\).
An electron in a hydrogen atom moves in a circular orbit of radius \(r\) in a stationary state characterized by the principal quantum number \(n\). The electron's orbital angular momentum is quantized according to \(L = \dfrac{n h}{2\pi}\), where \(h\) is Planck's constant. Which of the following expressions correctly represents the electron's de Broglie wavelength \(\lambda\) in terms of \(r\) and \(n\)?

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