---
title: "Two stationary radioactive parent nuclei, Nucleus 1 with mass number \\(A_1 = 204\\) and Nucleus 2 with mass number \\(A_2 = 104\\), each undergo alpha decay by emitting an alpha particle (\\(^4_2\\text{He}\\)). Let \\(R_1 = \\dfrac{K_{\\alpha,1}}{K_{D,1}}\\) represent the ratio of the kinetic energy of the emitted alpha particle to that of the recoiling daughter nucleus for Nucleus 1, and let \\(R_2 = \\dfrac{K_{\\alpha,2}}{K_{D,2}}\\) represent the corresponding ratio for Nucleus 2. Assuming the mass of each nucleus is directly proportional to its mass number, what is the value of the ratio \\(\\dfrac{R_1}{R_2}\\)?"
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/123512/"
date_modified: "2026-09-28T11:59:59+00:00"
---

# Two stationary radioactive parent nuclei, Nucleus 1 with mass number \(A_1 = 204\) and Nucleus 2 with mass number \(A_2 = 104\), each undergo alpha decay by emitting an alpha particle (\(^4_2\text{He}\)). Let \(R_1 = \dfrac{K_{\alpha,1}}{K_{D,1}}\) represent the ratio of the kinetic energy of the emitted alpha particle to that of the recoiling daughter nucleus for Nucleus 1, and let \(R_2 = \dfrac{K_{\alpha,2}}{K_{D,2}}\) represent the corresponding ratio for Nucleus 2. Assuming the mass of each nucleus is directly proportional to its mass number, what is the value of the ratio \(\dfrac{R_1}{R_2}\)?

Two stationary radioactive parent nuclei, Nucleus 1 with mass number \(A_1 = 204\) and Nucleus 2 with mass number \(A_2 = 104\), each undergo alpha decay by emitting an alpha particle (\(^4_2\text{He}\)). Let \(R_1 = \dfrac{K_{\alpha,1}}{K_{D,1}}\) represent the ratio of the kinetic energy of the emitted alpha particle to that of the recoiling daughter nucleus for Nucleus 1, and let \(R_2 = \dfrac{K_{\alpha,2}}{K_{D,2}}\) represent the corresponding ratio for Nucleus 2. Assuming the mass of each nucleus is directly proportional to its mass number, what is the value of the ratio \(\dfrac{R_1}{R_2}\)?

- **A.** \(2\)
- **B.** \(4\)
- **C.** \(25\)
- **D.** \(50\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123512/*