Question

In a diagnostic x-ray procedure, 4.85×10¹⁰ photons are absorbed by tissue with a mass of 0.575 kg . The x-ray wavelength is 2.00×10⁻² nm .

A) What is the total energy absorbed by the tissue?

B) What is the equivalent dose in rem?

Answer 1

Number of protons are n =4.85*10^10

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

Absorbed mass of the protons by tissue is m =0.575 kg

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

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/λ

=(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 =4.85 *10^10 is

E_total =nE

         =4.85*10^10*9.9375*10^-15 J

         =48.1968*10^-5 J

Equivalent dose D =energy absorbed/mass

                                =48.1968*10^-5 J/0.575 kg

                                =83.820*10^-5 J/kg

                                =83.820*10^-5/0.01 rem

                                =8382.05*10^-5 rem

                                                               since 1 rem =0.01 J/kg

I hope help you !!