Question

One of the radiographic devices used in a dentist's office emits an X-ray of wavelength 2.090 × 10^(-11) m. What is the energy, in joules, and frequency of this X-ray?

a) Energy of the X-ray
b) Frequency of the X-ray
c) Wavelength of the X-ray
d) Type of radiographic device

Answer 1

The energy of an X-ray photon with a wavelength of 2.090 × 10^(-11) m is approximately 9.52 × 10^(-15) J.

Step-by-step explanation:

To calculate the energy of an X-ray photon, we can use the equation E = hf, where E is the energy, h is the Planck's constant (6.63 × 10-34 J·s), and f is the frequency. Given that the wavelength of the X-ray is 2.090 × 10-11 m, we can find the frequency using the equation f = c/λ, where c is the speed of light (3 × 108 m/s). Therefore, the frequency of the X-ray is f = 3 × 108 / (2.090 × 10-11) = 1.437 × 1019 Hz. Plugging this frequency into the energy equation, we get E = (6.63 × 10-34)(1.437 × 1019) ≈ 9.52 × 10-15 J. Therefore, the energy of the X-ray photon is approximately 9.52 × 10-15 J.