Question

In a diagnostic x-ray procedure, 5.15×10¹⁰ photons are absorbed by tissue with a mass of 0.625 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

Given,

Number of protons are n =5.15*10^10

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

Absorbed mass of the protons by tissue is m = 0.625 kg

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 =5.15*10^10 is

Etotal = nE =5.15*10^10*9.9375*10^-15 J

= 51.178*10^-5 J

Equivalent dose D = energy absorbed/mass

= 51.178*10^-5 J/0.625 kg

= 8.19*10^-4 J/kg

= 8.19*10^-4/0.01 rem

= 0.0819 rem (since 1 rem =0.01 J/kg)