Question

X rays of wavelength 0.0100 nm are directed in the positive direction of an x axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of 180°, what are (a) the Compton shift, (b) the corresponding change in photon energy, (c) the kinetic energy of the recoiling electron, and (d) the angle between the positive direction of the x axis and the electron’s direction of motion?

Answer 1

Answer:

a)  $=4.84*10^{-12}$

b)$= -2.76*10^{-14} J$

c)$i.e -2.76*10^{-14} J$

d)= 0 and the direction of motion is equal to zero

Explanation:

a) compton shift

$\Delta\lambda = \frac{h}{mc} (1-cos\theta)$

$\Delta\lambda = \frac{6.626*10^{-34}}{9.11*10^{-11}3*10^8} (1-cos180)$

                        $=4.84*10^{-12}$

b) the new wavelength

$\lambda' = 10.0*10^{-12} +4.84^10^{-12}$

               $=14.84*10^{-12} m$

$\Delta E = E' - E$

              $=hc[\frac{1}{\lambda'}-\frac{1}{\lambda}]$

$\Delta E = 6.626*10^{-34}*(3*10^8)[\frac{1}{14.84*10^{-12}}-\frac{1}{4.8*10^{-12}}]$

$= -2.76*10^{-14} J$

C)By conservation of energy, the kinetic energy of recoiling electron is equal to the magnitude of energy between the photon energy

$i.e -2.76*10^{-14} J$

d) the angle between the positive direction of motion

$sin\phy = \frac{\lambda_t sin\theta}{\lambda'}$

            $=\frac{2.43*10^{-12}sin180}{14.84*10^{-12}}$  

             = 0

the direction of motion is equal to zero.