The photon energies used in different types of medical x-ray imaging vary widely, depending upon the application. single dental x rays use photons with energies of about 25 {\rm kev}. the energies used for x-ray microtomography, a process that allows repeated imaging in single planes at varying depths within the sample, is 2.5 times greater.

what are the wavelengths of the x rays used for these two purposes? answer in m
\lambda_{\rm dental}
\lambda_{\rm microtomography}

A)

The energy of an x-ray photon used for single dental x-rays is

The energy of a photon is related to its wavelength by the equation

where

is the Planck constant

is the speed of light

is the wavelength

Re-arranging the equation for the wavelength, we find

B)

The energy of an x-ray photon used in microtomography is 2.5 times greater than the energy of the photon used in part A), so its energy is

And so, by using the same formula we used in part A), we can calculate the corresponding wavelength: