Question

A dental X‑ray typically affects 175 g of tissue and delivers about 4.05 μJ of energy using X‑rays that have wavelengths of 0.0235 nm. What is the energy in electron volts of a single photon of these X‑rays?

Answer 1

Answer:

The energy of a single photon of X‑rays is  $E_v = 52898.9 \ eV$

Explanation:

From the question we are told that

    The mass of the tissue is $m = 175 \ g = 0.175 \ kg$

    The amount of energy delivered is  $E_T = 4.05 \mu J = 4.05 *10^{-6} \ J$

    The wavelength is  $\lambda = 0.0235 \ nm = 0.0235 *10^{-9} \ m$

Generally the energy of a single photon is mathematically represented as

         $E = \frac{hc}{\lambda }$

Where h is the Planck's  constant with values $h = 6.63 *10^{-34}\ J\cdot s$

and c is the speed of light with values $c = 3.0 *10^{8} \ m/s$

      Substituting values

       $E = \frac{6.63 *10^{-34} * 3.0*10^{8}}{0.0235 *10^{-9} }$

      $E = 8.463 *10^{-15} \ J$

Converting this to electron  volt we have

       $E_v = 8.464 *10^{-15} * [\frac{1 }{1.6*10^{-19}} ]$

      $E_v = 52898.9 \ eV$