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title: "In the Bohr model of the hydrogen atom, an electron in an allowed circular orbit of radius \\(r\\) forms a standing de Broglie wave along its orbital circumference. The allowed orbital radii scale with the principal quantum number \\(n\\) according to \\(r_n = n^2 r_1\\), where \\(r_1\\) is the radius of the ground state. Which of the following best describes the shape of a graph of the electron’s de Broglie wavelength \\(\\lambda\\) as a function of orbital radius \\(r\\)?"
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url: "https://nerd-notes.com/ubq/123460/"
date_modified: "2026-09-28T11:59:49+00:00"
---

# In the Bohr model of the hydrogen atom, an electron in an allowed circular orbit of radius \(r\) forms a standing de Broglie wave along its orbital circumference. The allowed orbital radii scale with the principal quantum number \(n\) according to \(r_n = n^2 r_1\), where \(r_1\) is the radius of the ground state. Which of the following best describes the shape of a graph of the electron’s de Broglie wavelength \(\lambda\) as a function of orbital radius \(r\)?

In the Bohr model of the hydrogen atom, an electron in an allowed circular orbit of radius \(r\) forms a standing de Broglie wave along its orbital circumference. The allowed orbital radii scale with the principal quantum number \(n\) according to \(r_n = n^2 r_1\), where \(r_1\) is the radius of the ground state. Which of the following best describes the shape of a graph of the electron's de Broglie wavelength \(\lambda\) as a function of orbital radius \(r\)?

- **A.** A straight line passing through the origin with a constant positive slope
- **B.** A curve passing through the origin that is concave upward with an increasing positive slope
- **C.** A curve passing through the origin that is concave downward with a decreasing positive slope
- **D.** A curve that decreases asymptotically toward zero as radius increases

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123460/*