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6.4: The Compton Effect - Physics LibreTexts

Nov 5, 2020 ... The Compton effect is the term used for an unusual result observed when ... Describe how experiments with X-rays confirm the particle nature of radiation ... Here the photon's energy Ef is the same as that of a light quantum of ... The wave relation that connects frequency f with wavelength λ and speed c ...

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Wavelength of monochromatic light \lambda = 632.8nm = 632.8 * 10^{-9} m

Power emitted P = 9.42 mW = 9.42 * 10^{-3} W

a) Find the energy and momentum of each photon in the light beam.

      Energy of proton E=h\upsilon\ =\ \frac{hc}{\lambda}

            Where, h - Planck's constant (6.626*10^{-34}), speed of light c = 3*10^{8} m/s   and \upsilon - frequency

                         E = \frac{6.626 *10^{-34} * 3*10^8}{632.8 * 10^{-9}}

                         E = 3.14*10^{-19} J

          Momentum of each photon p = \frac{h}{\lambda}           

                         p = \frac{6.626 *10^{-34}}{632.8 * 10^{-9}}

                          p = 1.047*10^{-27} kg m/s

(b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area).

          Relation between power and energy of photon

                     P = nE

                     n = \frac{P}{E}   

                     n = \frac{9.42 * 10^{-3}}{3.14*10^{-19}}

                     n = 3.42 * 10^{16} potons/sec

c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

                  Momentum  p = 1.047*10^{-27} kg m/s

                  Mass of hydrogen atom m = 1.66 * 10^{-27}

                  Momentum formula p = mv

                                                   v = \frac{p}{m}

                                    Velocity   v = \frac{1.047*10^{-27}}{1.66 * 10^{-27}}

                                                   v = 0.621 m/s

                    Hence, Speed of hydrogen atom v = 0.621 m/s