Question

In a diagnostic x-ray procedure, 4.75×1010 photons are absorbed by tissue with a mass of 0.585 kg . The x-ray wavelength is 2.00×10−2 nm .

Part A

What is the total energy absorbed by the tissue?

Part B

What is the equivalent dose in rem?

Answer 1

Part A The energy of one X-ray photon is given by, hc Here, h is the plank constant, c is the speed of light and 2 is the wavelength of X-ray. Substitute 6.626176x10-34 J·s for h, 3x109 m/s for c and 2x10-nm for î. (6.626176x10-34 J.s)(3x109 m/s) E, = 2x10-2 nm 19.87x10-26 J. m 2x10-2x10-ºm = 9.939x10-15J

Energy of N photons can be calculated as: E=NE, Substitute 4.75x100 for N and 9.939x10-1J for E, E = (4.75x1010)(9.939x10-15J) = 4.721x10 - J Therefore, the value of absorbed energy by tissue is 4.721x10*]. Part B Equivalent dose is the ratio of total absorbed energy by the and mass of the object, which is given by, E D = — m

Here, Dis equivalent dose, E is absorbed energy and mis mass of tissue. Substitute 4.721x10* J for E and 0.585 kg for m. D _ 4.721x10-4 J 0.585 kg =8.07x10* J/kg( o.dii/kg) rem = 8.07x10-2rem

Therefore, the equivalent dose is 8.07 x 10-2 rem