---
title: "An electron of mass \\(m\\) and charge \\(-e\\) in a hydrogen atom moves in a circular Bohr orbit of radius \\(r_1\\) around a fixed nucleus of charge \\(+e\\). The electron transitions to a lower circular orbit with radius \\(r_2 = \\dfrac{r_1}{4}\\), emitting a single photon of energy \\(E_{\\text{photon}}\\). How does the change in the electron’s kinetic energy, \\(\\Delta K = K_2 – K_1\\), compare to the energy of the emitted photon?"
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url: "https://nerd-notes.com/ubq/116584/"
date_modified: "2026-08-04T05:02:48+00:00"
---

# An electron of mass \(m\) and charge \(-e\) in a hydrogen atom moves in a circular Bohr orbit of radius \(r_1\) around a fixed nucleus of charge \(+e\). The electron transitions to a lower circular orbit with radius \(r_2 = \dfrac{r_1}{4}\), emitting a single photon of energy \(E_{\text{photon}}\). How does the change in the electron’s kinetic energy, \(\Delta K = K_2 – K_1\), compare to the energy of the emitted photon?

An electron of mass \(m\) and charge \(-e\) in a hydrogen atom moves in a circular Bohr orbit of radius \(r_1\) around a fixed nucleus of charge \(+e\). The electron transitions to a lower circular orbit with radius \(r_2 = \dfrac{r_1}{4}\), emitting a single photon of energy \(E_{\text{photon}}\). How does the change in the electron's kinetic energy, \(\Delta K = K_2 - K_1\), compare to the energy of the emitted photon?

![A schematic diagram showing two concentric circular Bohr orbits around a central positive nucleus labeled +e. The outer orbit has radius r_1 and contains an electron labeled e-. An arrow points radially inward from the outer orbit to an inner orbit of radius r_2 = r_1/4. A wavy arrow representing an emitted photon points outward away from the atom, labeled E_photon. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785819768-CfXTgm.jpg)

- **A.** \(\Delta K = -E_{\text{photon}}\)
- **B.** \(\Delta K = +E_{\text{photon}}\)
- **C.** \(\Delta K = +2E_{\text{photon}}\)
- **D.** \(\Delta K = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116584/*