---
title: "An X-ray photon with initial wavelength \\(\\lambda_0\\) moves along the positive \\(x\\)-axis and collides with an electron initially at rest. The photon scatters at an angle of \\(90^\\circ\\) relative to its initial direction of motion, as illustrated in the vector momentum diagram. In terms of Planck’s constant \\(h\\), electron mass \\(m_e\\), speed of light \\(c\\), and initial wavelength \\(\\lambda_0\\), which of the following expressions represents the magnitude of the momentum transferred to the electron?"
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url: "https://nerd-notes.com/ubq/117471/"
date_modified: "2026-08-04T06:52:16+00:00"
---

# An X-ray photon with initial wavelength \(\lambda_0\) moves along the positive \(x\)-axis and collides with an electron initially at rest. The photon scatters at an angle of \(90^\circ\) relative to its initial direction of motion, as illustrated in the vector momentum diagram. In terms of Planck’s constant \(h\), electron mass \(m_e\), speed of light \(c\), and initial wavelength \(\lambda_0\), which of the following expressions represents the magnitude of the momentum transferred to the electron?

An X-ray photon with initial wavelength \(\lambda_0\) moves along the positive \(x\)-axis and collides with an electron initially at rest. The photon scatters at an angle of \(90^\circ\) relative to its initial direction of motion, as illustrated in the vector momentum diagram. In terms of Planck's constant \(h\), electron mass \(m_e\), speed of light \(c\), and initial wavelength \(\lambda_0\), which of the following expressions represents the magnitude of the momentum transferred to the electron?

![A 2D Cartesian momentum vector diagram on a plain white background. Horizontal dashed line represents the positive x-axis, and vertical dashed line represents the positive y-axis, intersecting at the origin. An arrow labeled \vec{p}_0 points horizontally to the right along the positive x-axis toward the origin. An arrow labeled \vec{p}' points vertically upward along the positive y-axis from the origin, forming a 90-degree angle relative to \vec{p}_0 marked with a right-angle symbol \theta = 90^\circ. A third arrow labeled \vec{p}_e originates from the origin and extends down and to the right into the fourth quadrant, representing the recoil electron momentum. A small circle labeled e^- sits at the origin. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826335-kjb8WV.jpg)

- **A.** \( h \left( \dfrac{1}{\lambda_0} - \dfrac{1}{\lambda_0 + \dfrac{h}{m_e c}} \right) \)
- **B.** \( h \left( \dfrac{1}{\lambda_0} + \dfrac{1}{\lambda_0 + \dfrac{h}{m_e c}} \right) \)
- **C.** \( h \sqrt{\dfrac{1}{\lambda_0^2} + \dfrac{1}{\left(\lambda_0 - \dfrac{h}{m_e c}\right)^2}} \)
- **D.** \( h \sqrt{\dfrac{1}{\lambda_0^2} + \dfrac{1}{\left(\lambda_0 + \dfrac{h}{m_e c}\right)^2}} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117471/*