An $x$-ray photon with wavelength $15.0 \mathrm{pm}$ is scattered at $84.0^{\circ}$ by an electron. What is the wavelength of the scattered photon?
A) $31.0 \mathrm{pm}$
B) $12.8 \mathrm{pm}$
C) $14.9 \mathrm{pm}$
D) $1.57 \mathrm{pm}$
E) $17.2 \mathrm{pm}$

Question

Quizplus · Accepted Answer

The wavelength of the scattered photon can be calculated using the Compton scattering formula: $\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos \theta)$, where $\lambda'$ is the wavelength of the scattered photon, $\lambda$ is the initial wavelength (15.0 pm), $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg} / \text{s}$), $m_e$ is the electron mass ($9.109 \times 10^{-31} \, \text{kg}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\theta$ is the scattering angle ($84.0^\circ$). Plugging in the values and solving for $\lambda'$ gives a result that matches the option indicating a wavelength of $17.2 \, \text{pm}$.

An xxx -Ray Photon with Wavelength 15.0pm15.0 \mathrm{pm}15.0pm Is Scattered At 84.0∘84.0^{\circ}84.0∘ By an Electron

An $x$ -Ray Photon with Wavelength $15.0 \mathrm{pm}$ Is Scattered At $84.0^{\circ}$ By an Electron