Incident X-rays in a Compton scattering experiment have a wavelength of 0.400 nm.Determine the wavelength of the scattered X-rays that are detected at an angle of 80.0°.The Compton wavelength of the electron is 2.43 × 10^-¹² m. A)0.041 nm B)0.398 nm C)0.399 nm D)0.402 nm E)0.403 nm

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Quizplus · Accepted Answer

The wavelength of the scattered X-rays can be calculated using the Compton scattering formula: $\lambda' = \lambda + h/m_ec \cdot (1 - \cos \theta)$, where $\lambda'$ is the wavelength of the scattered X-rays, $\lambda$ is the initial wavelength (0.400 nm), $h/m_ec$ is the Compton wavelength of the electron (2.43 × 10^-12 m), and $\theta$ is the scattering angle (80.0°). Converting $\lambda$ to meters (0.400 nm = 4.00 × 10^-10 m) and using $\cos(80.0°)$, the calculation yields a new wavelength $\lambda'$ slightly larger than the initial wavelength, which corresponds to option D, 0.402 nm.

Incident X-Rays in a Compton Scattering Experiment Have a Wavelength