Question

the wavelength of x-rays used in dental imaging is 1.054 x 10-10 m. a typical x-ray source used in a dentist office produces x-rays with a power of 25 kj/s. what is the energy (in units of kilo-eletronvolts, kev) of a single, dental x-ray photon ?

Answer 1

The energy of a single dental X-ray photon with a wavelength of 1.054 x 10^-10 m is approximately 11.782 keV.

Step-by-step explanation:

To determine the energy of a single dental X-ray photon, given its wavelength, we can use the Planck-Einstein relation which relates the photon's energy (E) in joules to its frequency (f), with Planck's constant (h): E = h x f. Since we have the wavelength (λ), we need to first find the frequency using the speed of light (c): f = c / λ. Then we can convert the energy from joules to electronvolts (eV) and finally to kilo-electronvolts (keV).

Using the given wavelength of 1.054 x 10-10 m, the speed of light being 3.0 x 108 m/s, and Planck's constant as 6.626 x 10-34 J·s:

f = c / λ = (3.0 x 108 m/s) / (1.054 x 10-10 m) = 2.847 x 1018 Hz

E = h x f = (6.626 x 10-34 J·s) x (2.847 x 1018 Hz) = 1.887 x 10-15 J

To convert joules to electronvolts, we use the conversion 1 eV = 1.602 x 10-19 J:

E = (1.887 x 10-15 J) / (1.602 x 10-19 J/eV) = 11782 eV

Finally, to convert to keV, we divide by 1000:

E = 11782 eV / 1000 = 11.782 keV

The energy of a single dental X-ray photon is approximately 11.782 keV.