---
title: "Monochromatic light of frequency \\(f\\) is directed onto a metal target of work function \\(\\Phi\\), where \\(hf > \\Phi\\). The emitted electrons, each having mass \\(m\\) and charge magnitude \\(e\\), immediately enter a region of uniform magnetic field of magnitude \\(B\\) directed perpendicular to their velocity. Which of the following correctly gives the maximum orbital radius \\(R_{\\max}\\) of the electrons in the magnetic field, and describes how \\(R_{\\max}\\) changes if the intensity of the incident light is doubled at constant frequency \\(f\\)?"
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url: "https://nerd-notes.com/ubq/123558/"
date_modified: "2026-09-28T12:00:10+00:00"
---

# Monochromatic light of frequency \(f\) is directed onto a metal target of work function \(\Phi\), where \(hf > \Phi\). The emitted electrons, each having mass \(m\) and charge magnitude \(e\), immediately enter a region of uniform magnetic field of magnitude \(B\) directed perpendicular to their velocity. Which of the following correctly gives the maximum orbital radius \(R_{\max}\) of the electrons in the magnetic field, and describes how \(R_{\max}\) changes if the intensity of the incident light is doubled at constant frequency \(f\)?

Monochromatic light of frequency \(f\) is directed onto a metal target of work function \(\Phi\), where \(hf > \Phi\). The emitted electrons, each having mass \(m\) and charge magnitude \(e\), immediately enter a region of uniform magnetic field of magnitude \(B\) directed perpendicular to their velocity. Which of the following correctly gives the maximum orbital radius \(R_{\max}\) of the electrons in the magnetic field, and describes how \(R_{\max}\) changes if the intensity of the incident light is doubled at constant frequency \(f\)?

![A schematic diagram showing an evacuated chamber. On the left, a vertical rectangle represents a metal plate labeled Target. Exactly three parallel wavy arrows, labeled Light, point downward and to the right toward the target plate. To the right of the plate is a region containing an array of twelve x symbols arranged in three horizontal rows of four, labeled with a symbol \vec{B} pointing into the page. A curved dashed arc with an arrowhead emerges horizontally from the target plate and curves upward into a semicircle of radius labeled R_{\max}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596809-WgeGtj.jpg)

- **A.** \(R_{\max} = \dfrac{\sqrt{2m(hf - \Phi)}}{eB}\), and \(R_{\max}\) remains unchanged because doubling the light intensity increases the rate of emitted electrons but does not change the maximum kinetic energy of any individual electron.
- **B.** \(R_{\max} = \dfrac{\sqrt{2m(hf - \Phi)}}{eB}\), and \(R_{\max}\) increases by a factor of \(\sqrt{2}\) because doubling the light intensity doubles the energy absorbed by each emitted electron.
- **C.** \(R_{\max} = \dfrac{\sqrt{2m(hf + \Phi)}}{eB}\), and \(R_{\max}\) remains unchanged because the energy of each individual photon depends only on the frequency of the light.
- **D.** \(R_{\max} = \dfrac{\sqrt{m(hf - \Phi)}}{eB}\), and \(R_{\max}\) increases by a factor of \(2\) because doubling the light intensity doubles the force exerted on each electron by the radiation.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123558/*