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4 In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two "-rays of equal energy. What is the wavelength associated with each "-ray? ( 1 BeV = 10^{9} eV)
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Anonym0us
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Pravalika
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Given that

      Total energy of two rays 2E = 10.2 BeV

                                               2E = 10.2 * 10^9 eV

                                               2E = 10.2 * 10^9 * 1.6*10^{-10} J

    

        Energy of ray E = \frac{10.2 * 10^9 * 1.6*10^{-10}}{2} J

                               E = 8.16 *10^{-10} J  

          

Step 1: Finding the wavelength of y-rays  

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

                   Where, h - Planck's constant( 6.63*10^{-34} Js}), speed of light c = 3*10^{8} m/s   and \upsilon - frequency.

                               \lambda = \frac{h c}{ E }       

                               \lambda = \frac{(6.63*10^{-34})*(3* 10^{8})}{8.16 *10^{-10}}

                               \lambda = 2.436 * 10^{-16} m

  

                   Therefore, wavelength of y-rays \lambda = 2.436 * 10^{-16} m