A certain photon, after being scattered from a free electron that was at rest, moves at an angle of $120 ^ { \circ }$ with respect to the incident direction. If the wavelength of the incident photon is $0.591 \mathrm {~nm}$, what is the wavelength of the scattered photon? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$, $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )
A) $0.380 \mathrm {~nm}$
B) $0.550 \mathrm {~nm}$
C) $0 \mathrm {~nm}$
D) $0.591 \mathrm {~nm}$
E) $0.595 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The wavelength change of the 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, $h$ is Planck's constant, $m_e$ is the mass of the electron, $c$ is the speed of light, and $\theta$ is the scattering angle. Substituting the given values and solving for $\lambda'$ gives a result close to $0.595 \, \mathrm{nm}$.

A Certain Photon, After Being Scattered from a Free Electron 120∘120 ^ { \circ }120∘

A Certain Photon, After Being Scattered from a Free Electron $120 ^ { \circ }$