1. Single dental x-rays: [tex]5.0\cdot 10^{-11}m[/tex]
The energy of the photon is
[tex]E=25 keV = 25,000 eV[/tex]
Using the conversion factor
[tex]1 eV=1.6\cdot 10^{-19} J[/tex]
we can convert it into Joules:
[tex]E=(25,000 eV)(1.6\cdot 10^{-19}J/eV)=4\cdot 10^{-15} J[/tex]
The relationship between photon energy and wavelength is
[tex]\lambda=\frac{hc}{E}[/tex]
where
[tex]h=6.63\cdot 10^{-34} Js[/tex] is the Planck constant
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light
E is the energy
Substituting into the formula, we find
[tex]\lambda=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{4\cdot 10^{-15} J}=5.0\cdot 10^{-11}m[/tex]
2. Microtomography: [tex]2.0\cdot 10^{-11} m[/tex]
The energy of these photons is 2.5 times greater, so
[tex]E=(2.5)(4\cdot 10^{-15} J)=1\cdot 10^{-14} J[/tex]
And by applying the same formula used at point 1, we find the corresponding wavelength:
[tex]\lambda=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{1\cdot 10^{-14} J}=2.0\cdot 10^{-11}m[/tex]
