Question

In a diagnostic x-ray procedure, 5.25*10^10 photons are absorbed by tissue with a mass of 0.590kg . The x-ray wavelength is 2.00*10^-2nm . What is the total energy absorbed by the tissue? What is the equivalent dose in rem?

Answer 1

Number of protons are n =5.25*10^10

Wavelength of the each proton is ?=2*10^-2nm=2*10^-11 m

Absorbed mass of the protons by tissue is m =0.590 kg

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Energy absorbed by tissue with one proton is E =hC/?

here C is speed of light is =3*10^8 m/s

and 'h' is Plank's constant =6.625*10^-34 J.s

therefore

Energy absorbed by tissue with one proton is E =hC/?

                                                                                 =(6.625*10^-34)*(3*10^8)/(2*10^-11 )

                                                                                 =9.9375*10^-15 J

total energy absorbed by the tissue with the number of protons n =5.25*10^10 is

E_total =nE

         =5.25*10^10*9.9375*10^-15 J

         =52.1719*10^-5 J

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Equivalent dose D =energy absorbed/mass

                                =53.1719*10^-5 J/0.590kg

                                =88.4269*10^-5 J/kg

                                =88.4269*10^-5/0.01 rem

                                =8842.69*10^-5 rem

                                                               since 1 rem =0.01 J/kg