A photon whose wavelength is = 5.0 × 10−¹¹ m is scattered straight backward. What is the wavelength of the scattered wave? A) 5.0 × 10−¹¹ m B) 4.5 × 10−¹¹ m C) 5.5 × 10−¹¹ m D) 6.0 × 10−¹¹ m E) 6.5 × 10−¹¹ m

Question

Quizplus · Accepted Answer

When a photon is scattered straight backward, its wavelength increases due to the Compton effect. The change in wavelength ($\Delta \lambda$) is given by $\Delta \lambda = \frac{h}{m_e c} (1 - \cos \theta)$, where $h$ is Planck's constant, $m_e$ is the electron mass, $c$ is the speed of light, and $\theta$ is the scattering angle. For backward scattering ($\theta = 180^\circ$), $\Delta \lambda$ is maximized and equals $2 \frac{h}{m_e c}$, which is approximately $4.9 \times 10^{-7}$ meters or $0.49 \times 10^{-6}$ meters. Adding this change to the original wavelength (5.0 × 10−7 m), the new wavelength is approximately $5.5 \times 10^{-7}$ m.

A Photon Whose Wavelength Is = 5