---
title: "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\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/116556/"
date_modified: "2026-08-04T05:02:32+00:00"
---

# 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 \(n\)?

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 \(n\)?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785819752-q2GgL7.jpg)

- **A.** \(\lambda = \dfrac{n r}{2\pi}\)
- **B.** \(\lambda = \dfrac{\pi r}{n}\)
- **C.** \(\lambda = \dfrac{2\pi r}{n^2}\)
- **D.** \(\lambda = \dfrac{2\pi r}{n}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116556/*