A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.

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autosmut6p · Accepted Answer

For the photon:      E    1    =            h      c              λ      1          ⇒      λ    1    =            h      c              E      1      Substitute   100  ×      10    6     eV for       E    1    ,     3  ×      10    8     m/s for c, and   6.63  ×      10          −      34           J  ⋅  s for h      λ    1    =            (      6.63      ×              10                  −          34                           J      ⋅      s      )      (      3      ×              10        8             m/s      )              (      100      ×              10        6             eV      )          =            (      6.63      ×              10                  −          34                           J      ⋅      s      )      (      3      ×              10        8             m/s      )              (      100      ×              10        6             eV      )      ×      (                        1.6          ×                      10                          −              19                                           J                          1           eV                    )          =            (      6.63      ×              10                  −          34                           J      ⋅      s      )      (      3      ×              10        8             m/s      )              (      100      ×              10        6            ×      1.6      ×              10                  −          19                    )      J              λ    1    =  12.43125  ×      10          −      15           mBy using the Compton&#039;s effect:      λ    2    −      λ    1    =      h                  m        p            c        (  1  −  cos  ⁡  θ  )Here, the maximum possible change of energy takes place when the photon recoils in the opposite direction to that of the incident direction.When   cos  ⁡  θ  =  −  1 therefore,  θ  =      cos          −      1        ⁡  (  −  1  )    θ  =      180    ∘  Substitute   12.43125  ×      10          −      15           m for       λ    1    ,         180    ∘   for   θ  ,  1.6  ×      10          −      27           k  g for       m    p    ,  3  ×      10    8     m/s for  c, and   6.63  ×      10          −      34           J  ⋅  s for h into equation.      λ    2    −  12.4  ×      10          −      15           m  =            6.63      ×              10                  −          34                           J      ⋅      s              (      1.6      ×              10                  −          27                     kg      )      (      3      ×              10        8             m/s      )        (  1  −  cos  ⁡      180    ∘    )        λ    2    −  12.4  ×      10          −      15           m  =  2.76  ×      10          −      15              λ    2    =  15.16  ×      10          −      15           mThe lose of energy is,  △  E  =      E    2    −      E    1      =            h      c              λ      2        −            h      c              λ      1      So:  △  E  =            6.63      ×              10                  −          34                    J      ⋅      s      ×      3      ×              10        8             m/s              15.16      ×              10                  −          15                           m        −            6.63      ×              10                  −          34                    J      ⋅      s      ×      3      ×              10        8             m/s              12.4      ×              10                  −          15                           m          =  1.312  ×      10          −      11           J  −  1.604  ×      10          −      11           J    △  E  =  2.916  ×      10          −      11           JHence, the maximum energy loss that the photon can suffer is   2.916  ×      10          −      11           J

A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.

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