Question

Show the steps to calculate the Compton wavelength of the electron (i.e. 2.4*10^-12) from equation 1.9 in the text.

The Compton Eedl One of the characteristics of particles is that they can scatter off of each other, conserving both energy and momentum in the scattering process. If light truly does behave like a particle, it should be possible to observe such sc and to predict the change in the energy and momentum of the light when it scatters One such process that is observed to occur is Compton scattering, which refers to the scattering of X-rays or gamma rays off of the electrons in a metal (Figure 1.7). Experimentally, it is observed that the wavelength of the scattered radiation λ/1s larger than that of the incident radiation , and the change in wavelength is well fit by the relation attering processes where c, called the Compton wavelength of the electron, is a constant with units of length c = 2.4 x 10-12 m and θ is the scattering angle shown in Figure 1.7. Note from Equation (1.9) that the change in wavelength is actually independent of the initial wavelength λ, it depends only on the scattering angle θ.

Use this equation if necessary:

Answer 1

According to Quantum machines E = nhv layer scattering linear momentum of the system Vertical-bar p Vertical-bar = h/lambda taking linear momentum conservation. Vertical-bar p Vertical-bar _before = Vertical-bar p Vertical-bar _after h/lambda = h/lambda' cos theta + Vertical-bar p'_e Vertical-bar cos phi horizontally 0 = h/lambda' sin theta - Vertical-bar p'_e Vertical-bar sin phi p = p' + p'_e total energy conservation hv + m_0 c^2 = hv' + squareroot c^2 p'^2_e + m^2_0 c^4 ----(1) K. E conservation hv + 0 = hv' + K. E hv = hv' + squareroot c^4 p'^2_e + (m_0 c^2)^2 - m_0 c^2 --(2) p = p' + p'_e Rightarrow p'_e = p - p' p'^2_e = (p - p') (p - p') p'^2_e = (h/lambda)^2 +(h/ lambda)^2 - 2 p middot p' c^2 p'^2_e = (hc/ lambda)^2 + (hc/ lambda)^2 - 2 h/ lambda h/ lambda' c^2 cos theta Now putting in equation (1) and taking sequence of each side (hc/ lambda - hc/ lambda' + m_0 c^2)^2 = c^2 p'^2_e + m^2_0 c^4