A certain photon,after being scattered from a free electron that was at rest,moves at an angle of 120° with respect to the incident direction.If the wavelength of the incident photon is 0.6110 nm,what is the kinetic energy of the recoiling electron? (m_electron = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,h = 6.626 × 10^-34 J ∙ s) A)1.5 × 10^-18 J B)1.9 × 10^-18 J C)3.1 × 10^-1⁸ J D)4.3 × 10^-18 J E)5.2 × 10^-18 J

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Quizplus · Accepted Answer

The kinetic energy of the recoiling electron can be found using the Compton scattering formula, which relates the change in wavelength of the photon to the scattering angle. The change in the photon's energy, which is equal to the kinetic energy transferred to the electron, can be calculated using the formula $\Delta \lambda = \frac{h}{m_e c} (1 - \cos \theta)$, where $\Delta \lambda$ is the change in wavelength, $h$ is Planck's constant, $m_e$ is the electron mass, $c$ is the speed of light, and $\theta$ is the scattering angle. The kinetic energy of the electron is then found by converting this wavelength change into energy using the relation $E = \frac{hc}{\lambda}$. Given the scattering angle of 120° and the initial wavelength, the calculation leads to the kinetic energy of the electron being approximately $1.9 \times 10^{-18}$ J.

A Certain Photon,after Being Scattered from a Free Electron That