---
title: "A beam of singly ionized atoms with charge \\(+e\\) enters a velocity selector consisting of a uniform downward electric field of magnitude \\(E\\) and a uniform magnetic field of magnitude \\(B_1\\) directed into the page. Ions that travel undeflected emerge through a narrow aperture into a separation chamber containing a uniform magnetic field of magnitude \\(B_2\\) directed into the page. Inside the separation chamber, the ions follow semicircular paths of radius \\(R\\) before colliding with a detector. In terms of the given quantities, what is the mass \\(m\\) of the detected ions?"
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url: "https://nerd-notes.com/ubq/121209/"
date_modified: "2026-08-23T04:58:51+00:00"
---

# A beam of singly ionized atoms with charge \(+e\) enters a velocity selector consisting of a uniform downward electric field of magnitude \(E\) and a uniform magnetic field of magnitude \(B_1\) directed into the page. Ions that travel undeflected emerge through a narrow aperture into a separation chamber containing a uniform magnetic field of magnitude \(B_2\) directed into the page. Inside the separation chamber, the ions follow semicircular paths of radius \(R\) before colliding with a detector. In terms of the given quantities, what is the mass \(m\) of the detected ions?

A beam of singly ionized atoms with charge \(+e\) enters a velocity selector consisting of a uniform downward electric field of magnitude \(E\) and a uniform magnetic field of magnitude \(B_1\) directed into the page. Ions that travel undeflected emerge through a narrow aperture into a separation chamber containing a uniform magnetic field of magnitude \(B_2\) directed into the page. Inside the separation chamber, the ions follow semicircular paths of radius \(R\) before colliding with a detector. In terms of the given quantities, what is the mass \(m\) of the detected ions?

![A schematic of a mass spectrometer oriented horizontally. On the left, two horizontal parallel plates define a velocity selector region: the top plate is labeled with a plus sign and the bottom plate with a minus sign. Between the plates, three downward vertical arrows represent a uniform electric field labeled \(E\), and four evenly spaced cross symbols represent a magnetic field into the page labeled \(B_1\). A horizontal dashed line with a rightward arrow indicates the path of an ion entering from the left and exiting through a narrow opening in a vertical barrier. To the right of the barrier, four cross symbols represent a uniform magnetic field into the page labeled \(B_2\). A semicircular counterclockwise dashed arc of radius labeled \(R\) curves upward from the slit and terminates at a rectangular detector strip on the vertical barrier. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461131-LRYJhL.jpg)

- **A.** \(m = \dfrac{e E R}{B_1 B_2}\)
- **B.** \(m = \dfrac{e B_1 B_2 R}{E}\)
- **C.** \(m = \dfrac{e B_1 R}{E B_2}\)
- **D.** \(m = \dfrac{2 e B_1 B_2 R}{E}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121209/*