91影视

$\mathit{位}\mathbf{\text{'}}\mathbf{-}\mathit{位}\mathbf{=}\frac{\mathbf{h}}{\mathbf{m}\mathbf{c}}\left(1-cos胃\right)$

Where $\mathit{位}\mathbf{\text{'}}$is the wavelength of the scattered photon, $\mathit{位}$ is the wavelength of the incident photon, and 胃 is angle with which the photon scatters with its incident direction.

From the Compton scattering equation,

$位\text{'}=位+\frac{h}{mc}\left(1-\cos 胃\right)$

Substituting 位 = 0.071 nm, mass of carbon= 12 amu = 1.99脳10^-26kg.

Hence,

$\begin{array}{rcl}位\text{'}& =& \left(0.071脳{10}^{-9}m\right)+\left(\frac{6.625脳{10}^{-34}J路s}{\left(1.99脳{10}^{-26}kg\right)脳\left(3脳{10}^{8}m/s\right)}\right)\left(1-\cos 胃\right)\\ & =& 7.1脳{10}^{-11}m+1.11脳{10}^{-16}\left(1-\cos 胃\right)\\ & =& 7.1脳{10}^{-11}m\end{array}$

We can see from the above equation that 1.11脳10^-16 is much smaller compared to 7.1脳10^-11. Hence for all values of 胃, the cos胃 value does not change much.

Therefore the wavelength of the scattered photon does not change much compared to the incident X-ray wavelength if the mass of an electron is replaced by the mass of carbon.