A dental X-ray typically affects 194 g of tissue and delivers about 3.6 μJ of energy using X-rays that have wavelengths of 0.033 nm. What is

Question

A dental X-ray typically affects 194 g of tissue and delivers about 3.6 μJ of energy using X-rays that have wavelengths of 0.033 nm. What is the energy E photon , in electron volts, of X-ray photons? E photon = eV How many photons are absorbed during the dental X-ray? Assume the body absorbs all of the incident X-rays. number of photons absorbed: photons/s

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Thiên Hương 1 month 2021-08-03T11:23:09+00:00 1 Answers 2 views 0

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    2021-08-03T11:25:08+00:00

    Answer:

    The energy of a single photon is x= 37670.46eV

    The number of photon absorbed is z = 5.98*10^{8} \ photons

    Explanation:

    From the question we are told that

           The mass of  tissue affected is  m = 194g = \frac{194}{1000} = 0.194kg

            The energy realesed is E = 3.6 \mu J = 3.6 *10^{-6} J

           The wavelength is \lambda  = 0.033nm = 0.033 *10^{-9}m

    Generally the energy of a sigle photon is mathematically rpresented as

                       E = \frac{hc}{\lambda }

      Where h is the Planck constant with a value of   h =6.63*10^{-34} J \cdot s

                Substituting values

                         E = \frac{6.63*10^{-34}(3*10^8)}{0.033*10^{-9}}

                            = 6.0272 *10^{-15}J

      Now  

                1 eV  -------> 1.60*10^{-19}J

         

                xeV ---------> 6.02*10^{-15}J

    Making x the subject of the  formula

              x = \frac{6.02 *10^{-15}}{1.6 *10^{-19}}

                  x= 37670.46eV

    The the number of photon absorbed  is

         z = \frac{The \ energy \ deliverd \  by \  to \ tissue }{The \  energy \ of \  a \ single \ photon}

             = \frac{3.6 *10^{-6}}{6.02*10^{-15}}

       z = 5.98*10^{8} \ photons

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