Question

In a diagnostic x-ray procedure, 5.25×10¹⁰ photons are absorbed by tissue with a mass of 0.595 kg . The x-ray wavelength is 2.00×10^?2 nm .

What is the total energy absorbed by the tissue? The answer should be in mJ.

What is the equivalent dose in rem?

Answer 1

Number of protons are n = 5.25 x 10^10

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

Absorbed mass of the protons by tissue is m = 0.595 kg

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

C = 3 x 10^8 m/s

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

therefore

Energy absorbed by tissue with one proton,

E = hC/?

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

E = 9.9375 x 10^-15 J

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

E_total = nE

E_total = 5.25 x 10^10 x 9.9375 x 10^-15 J

E_total = 52.172 x 10^-5 J

E_total = 0.52172 mJ

Equivalent dose,

D = energy absorbed / mass

D = 52.172 x 10^-5 J / 0.595 kg

D = 87.68 x 10^-5 J/kg

D = 87.68 x 10^-5 / 0.01 rem

D = 0.08768 rem