Question

One of the radiographic devices used in a dentist's office emits an X-ray of wavelength 2.181 ✕ 10−11 m. What is the energy, in joules, and frequency, in hertz, of this X-ray?

Answer 1

The energy of the X-ray photon with a wavelength of 2.181 × 10−11 m is 9.111 × 10−16 joules and the frequency is 1.375 × 10−19 hertz, calculated using the Planck-Einstein relation.

Step-by-step explanation:

To calculate the energy and frequency of an X-ray with a given wavelength, we will use the formulas for energy (E) and frequency (f) derived from the Planck-Einstein relation. The energy of a photon is given by E = hv (where h is Planck's constant and v is the frequency), and frequency is given by f = c/λ (where c is the speed of light and λ is the wavelength).

First, we calculate the frequency:

• f = c/λ
• f = (3.00 × 108 m/s) / (2.181 × 10−11 m)
• f = 1.375 × 1019 Hz

Now, we calculate the energy:

• E = hv
• E = (6.626 × 10−34 J·s) × (1.375 × 1019 Hz)
• E = 9.111 × 10−16 J

Thus, the energy of the X-ray photon is 9.111 × 10−16 joules and the frequency is 1.375 × 1019 hertz.