Medical X-rays used for CT (computed tomography) scans have a freqency of F Hz.

Question

Medical X-rays used for CT (computed tomography) scans have a freqency of F 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 refrative indexthe 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 A mm2 is P, calculate the intensity fo this X-ray beam.

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

x-ray frequency is F Hz

wave length, lambda=C/F

here, C is speed of the light

a)

wave length of x-ray in vaccum, lambda=C/F=(3*10^8)/F

refractive index of glycerin n=1.473

wave length of x-ray in human body is,

lambda'=lambda/n

lambda'=(3*10^8/F)/(1.473)

lambda'=(2.037*10^8)/F

b)

perod T=1/F

c)

power is P

area=A mm^2

area =A*10^-6 m^2

Intensirt I=P/A

I=(P/A*10^-6)

I=(P*10^6)/A

d)

x-rays are harmful for the living cells,

they kills the living cells and it damage the living cells

genrally frequency range of x-ray is F=3*10^16 to 3*10^19 Hz

lambda'=(2.037*10^8)/(3*10^19)

lambda'=6.79*10^-12m to 6.79*10^-9 m

which give the energy of X-ray nearly 100 kev

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