---
title: "An alpha particle (charge \\(+2e\\), mass \\(4u\\)) and a proton (charge \\(+e\\), mass \\(1u\\)) are each fired horizontally with the same initial kinetic energy \\(K_0\\) into a uniform transverse electric field of magnitude \\(E\\) produced between two parallel plates of length \\(L\\). Gravitational effects are negligible. What is the ratio \\(y_\\alpha / y_p\\) of the vertical deflection of the alpha particle to the vertical deflection of the proton as they exit the electric field region?"
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/117942/"
date_modified: "2026-08-04T08:02:38+00:00"
---

# An alpha particle (charge \(+2e\), mass \(4u\)) and a proton (charge \(+e\), mass \(1u\)) are each fired horizontally with the same initial kinetic energy \(K_0\) into a uniform transverse electric field of magnitude \(E\) produced between two parallel plates of length \(L\). Gravitational effects are negligible. What is the ratio \(y_\alpha / y_p\) of the vertical deflection of the alpha particle to the vertical deflection of the proton as they exit the electric field region?

An alpha particle (charge \(+2e\), mass \(4u\)) and a proton (charge \(+e\), mass \(1u\)) are each fired horizontally with the same initial kinetic energy \(K_0\) into a uniform transverse electric field of magnitude \(E\) produced between two parallel plates of length \(L\). Gravitational effects are negligible. What is the ratio \(y_\alpha / y_p\) of the vertical deflection of the alpha particle to the vertical deflection of the proton as they exit the electric field region?

![Two horizontal parallel plates of length L are aligned vertically. The top plate is labeled with a positive sign, and the bottom plate is labeled with a negative sign. Between the plates, exactly three vertical arrows point downward from the top plate to the bottom plate, labeled with the variable \vec{E}. From the left edge midway between the plates, a horizontal axis line extends to the right. Two dashed curved trajectories begin at the left edge and bend upward toward the top plate. The lower curved path represents a particle labeled p, and the upper curved path represents a particle labeled \alpha. At the right edge of the plates, two vertical dimension lines indicate the deflections from the central horizontal axis, labeled y_p for the lower path and y_\alpha for the upper path. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830558-Qin7UE.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117942/*