Production and use of X-rays
Seeing your bones
- An X-ray photo shows your bones in white against the dark soft tissue.
- X-rays are high-energy photons that pass through flesh but are stopped by bone.
- First we make them, then we use them to image.
Making X-rays
- A heated cathode emits electrons; a high voltage accelerates them onto a metal target.
- They slow sharply, giving out X-ray photons (Bremsstrahlung) plus sharp characteristic lines. Most energy becomes heat.
X-rays are produced when fast electrons:
The sudden deceleration on the target gives out X-ray photons (Bremsstrahlung).
Most of the electrons' kinetic energy in an X-ray tube becomes heat, not X-rays.
Only a small fraction becomes X-rays — which is why the target must be cooled.
Minimum wavelength
- The most energetic photon comes from one electron losing all its KE at once: $hf_{\max} = eV$.
- So there is a sharp cut-off: $\lambda_{\min} = \dfrac{hc}{eV}$ — a higher voltage gives a shorter $\lambda_{\min}$.
The minimum X-ray wavelength from a tube at accelerating voltage $V$ is:
From $hf_{\max} = eV$ and $c = f\lambda$: $\lambda_{\min} = \dfrac{hc}{eV}$.
A higher accelerating voltage gives a ____ minimum wavelength.
$\lambda_{\min} = \dfrac{hc}{eV}$, so a larger $V$ gives a smaller $\lambda_{\min}$ (more energetic X-rays).
Imaging and CT
- X-rays are absorbed more by dense tissue: $I = I_0 e^{-\mu x}$. Bone attenuates more, so it looks white.
- A CT scan rotates the tube and detectors, imaging a slice from many angles to build a 3-D picture.
Bone looks white on an X-ray image because it:
Dense, high-$Z$ bone absorbs more ($I = I_0 e^{-\mu x}$ with large $\mu$), casting a stronger shadow.
A CT scan takes X-ray images from many angles to build a 3-D image.
Rotating the tube and detectors and reconstructing the slices separates overlapping tissues into a 3-D picture.
You've got it
- X-rays form when fast electrons hit a target (Bremsstrahlung + characteristic); most energy → heat
- minimum wavelength $\lambda_{\min} = \dfrac{hc}{eV}$ (shorter at higher voltage)
- attenuation $I = I_0 e^{-\mu x}$; bone attenuates more (white); CT images from many angles