CT-scans: Medical X-rays used for CT (computed tomography) scans have a frequenc
ID: 1465377 • Letter: C
Question
CT-scans: Medical X-rays used for CT (computed tomography) scans have a frequency of 5*10^18 Hz. Calculate the following properties of these X-rays:
a) The wavelength in vacuum, and in the patient’s body (assume that the human body has an average refractive index the same as glycerin).
b) The period and angular frequency of these X-rays.
c) If the average power delivered by such an X-ray beam on a surface of 5 mm^2 is 500 W, calculate the intensity of this X-ray beam.
d)Would be these rays harmful for the living cells? Why or why not? Support your answer with relevant numbers. You should do some internet research for finding out what is “a radiation harmful for living cells”.
Explanation / Answer
we know, refractive index of glycerin, n = 1.4746
a) In vacuum
lamda_o = C/f
= 3*10^8/(5*10^18)
= 6*10^-11 m
in patient's body, lamda = lamda_o/n
= 6*10^-11/1.4746
= 4.07*10^-11 m
b)
time periode, T = 1/f
= 1/(5*10^18)
= 2*10^-19 s
angular frequency, w = 2*Pi/T
= 2*pi/(2*10^-19)
= 3.14*10^19 hz
c) Intensity = power/Area
= 500*10^-6/(5*10^-6)
= 100 W/m^2
d) No