1: Introduction to Electromagnetic Radiation
Understanding X-rays begins with electromagnetic (EM) waves. X-rays are high-energy EM waves with short wavelengths and high frequencies.
Formula:
Electromagnetic Wave Speed (c):
c = λ * f
where
c = speed of light (3.0 × 108 m/s)
λ = wavelength (m)
f = frequency (Hz)
Example Calculation:
Given an X-ray frequency of 3.0 × 1018 Hz, calculate the wavelength.
Solution:
λ = c / f = (3.0 × 108 m/s) / (3.0 × 1018 Hz) = 1.0 × 10-10 m
2: Energy of X-ray Photons
X-rays have energy that depends on their frequency. The energy of a photon can be calculated using Planck's equation.
Formula:
Photon Energy (E):
E = h * f
where
E = energy (Joules)
h = Planck's constant (6.626 × 10-34 J·s)
f = frequency (Hz)
Example Calculation:
Calculate the energy of an X-ray photon with a frequency of 3.0 × 1018 Hz.
Solution:
E = h * f = (6.626 × 10-34 J·s) * (3.0 × 1018 Hz) = 1.9878 × 10-15 J
3: X-ray Intensity and Attenuation
The intensity of X-ray radiation decreases as it passes through a material, following the exponential attenuation law.
Formula:
Attenuation of X-ray Intensity (I):
I = I0 * e-μx
where
I = final intensity
I0 = initial intensity
μ = linear attenuation coefficient (m-1)
x = thickness of material (m)
Example Calculation:
An X-ray beam with an initial intensity of 100 W/m2 passes through 0.01 m of tissue with μ = 0.5 m-1. Calculate the final intensity.
Solution:
I = 100 * e-0.5 * 0.01 ≈ 100 * e-0.005 ≈ 99.5 W/m2
Note: These are simplified examples. In practical applications, X-ray energy and attenuation depend on various factors such as material type and X-ray wavelength.