---
title: "A stationary parent nucleus with atomic mass number \\(A\\) undergoes alpha decay, emitting an alpha particle of mass number \\(4\\) and leaving behind a recoiling daughter nucleus. Assuming the speeds of the decay products are non-relativistic and the mass of each nucleus is directly proportional to its mass number, which of the following expressions represents the ratio \\(\\dfrac{K_\\alpha}{K_D}\\) of the kinetic energy of the alpha particle to the kinetic energy of the recoiling daughter nucleus?"
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url: "https://nerd-notes.com/ubq/117227/"
date_modified: "2026-08-04T06:45:02+00:00"
---

# A stationary parent nucleus with atomic mass number \(A\) undergoes alpha decay, emitting an alpha particle of mass number \(4\) and leaving behind a recoiling daughter nucleus. Assuming the speeds of the decay products are non-relativistic and the mass of each nucleus is directly proportional to its mass number, which of the following expressions represents the ratio \(\dfrac{K_\alpha}{K_D}\) of the kinetic energy of the alpha particle to the kinetic energy of the recoiling daughter nucleus?

A stationary parent nucleus with atomic mass number \(A\) undergoes alpha decay, emitting an alpha particle of mass number \(4\) and leaving behind a recoiling daughter nucleus. Assuming the speeds of the decay products are non-relativistic and the mass of each nucleus is directly proportional to its mass number, which of the following expressions represents the ratio \(\dfrac{K_\alpha}{K_D}\) of the kinetic energy of the alpha particle to the kinetic energy of the recoiling daughter nucleus?

![A two-panel schematic showing the alpha decay process. The left panel labeled Before shows a single stationary circular parent nucleus labeled with mass number A. The right panel labeled After shows two particles moving in opposite horizontal directions: a smaller circle on the right labeled alpha particle with mass 4 and a velocity arrow pointing to the right labeled v_alpha, and a larger circle on the left labeled daughter nucleus with mass A minus 4 and a velocity arrow pointing to the left labeled v_D. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/fig-alpha-decay-1785825902-J3WhdF.jpg)

- **A.** \(\dfrac{A-4}{4}\)
- **B.** \(\dfrac{4}{A-4}\)
- **C.** \(\dfrac{A}{4}\)
- **D.** \(\dfrac{(A-4)^2}{16}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117227/*