---
title: "A sample of atomic hydrogen gas is excited such that electrons populate the \\(n = 4\\) energy level. Photons emitted when these electrons transition directly from the \\(n = 4\\) level to the \\(n = 1\\) ground state are directed onto the cathode of a photoelectric apparatus, where the cathode material has a work function of \\(4.75 \\text{ eV}\\). The energy levels of the hydrogen atom are \\(E_1 = -13.60 \\text{ eV}\\), \\(E_2 = -3.40 \\text{ eV}\\), \\(E_3 = -1.51 \\text{ eV}\\), and \\(E_4 = -0.85 \\text{ eV}\\). What is the stopping potential required to prevent the ejected photoelectrons from reaching the anode?"
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url: "https://nerd-notes.com/ubq/123523/"
date_modified: "2026-09-28T12:00:01+00:00"
---

# A sample of atomic hydrogen gas is excited such that electrons populate the \(n = 4\) energy level. Photons emitted when these electrons transition directly from the \(n = 4\) level to the \(n = 1\) ground state are directed onto the cathode of a photoelectric apparatus, where the cathode material has a work function of \(4.75 \text{ eV}\). The energy levels of the hydrogen atom are \(E_1 = -13.60 \text{ eV}\), \(E_2 = -3.40 \text{ eV}\), \(E_3 = -1.51 \text{ eV}\), and \(E_4 = -0.85 \text{ eV}\). What is the stopping potential required to prevent the ejected photoelectrons from reaching the anode?

A sample of atomic hydrogen gas is excited such that electrons populate the \(n = 4\) energy level. Photons emitted when these electrons transition directly from the \(n = 4\) level to the \(n = 1\) ground state are directed onto the cathode of a photoelectric apparatus, where the cathode material has a work function of \(4.75 \text{ eV}\). The energy levels of the hydrogen atom are \(E_1 = -13.60 \text{ eV}\), \(E_2 = -3.40 \text{ eV}\), \(E_3 = -1.51 \text{ eV}\), and \(E_4 = -0.85 \text{ eV}\). What is the stopping potential required to prevent the ejected photoelectrons from reaching the anode?

![A vertical energy axis on the left has an upward arrow labeled E\text{ (eV)}. Four horizontal solid line segments are drawn at different vertical heights across the plot area. The lowest line segment is labeled n = 1 on its left and -13.60\text{ eV} on its right. The second line segment from the bottom is labeled n = 2 on its left and -3.40\text{ eV} on its right. The third line segment is labeled n = 3 on its left and -1.51\text{ eV} on its right. The top line segment is labeled n = 4 on its left and -0.85\text{ eV} on its right. The vertical spacing between successive horizontal lines decreases noticeably from bottom to top. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596801-vLChVg.jpg)

- **A.** \(8.00 \text{ V}\)
- **B.** \(8.85 \text{ V}\)
- **C.** \(12.75 \text{ V}\)
- **D.** \(17.50 \text{ V}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123523/*