Question

A photon has energy of 20 keV. What are its frequency and wavelength?

A) Frequency: 4.84×10¹⁸ Hz, Wavelength: 1.24×10−¹⁰ m
B) Frequency: 3.81×10¹⁷ Hz, Wavelength: 8.21×10−¹⁰ m
C) Frequency: 1.21×10¹⁹ Hz, Wavelength: 1.65×10−¹⁰ m
D) Frequency:2.42×10¹⁸ Hz, Wavelength: 5.15×10−¹¹ m

Answer 1

The frequency and wavelength of a photon with energy of 20 keV, use the equation E = hf. Rearrange the equation to find f and substitute the values to calculate the frequency. Then, use the equation c = fλ and rearrange it to find λ and substitute the values to calculate the wavelength.

Step-by-step explanation:

To find the frequency and wavelength of a photon with energy of 20 keV, we can use the equation E = hf, where E is the energy, h is Planck's constant (6.626 x 10^-34 J s), and f is the frequency.

First, convert 20 keV to joules by multiplying it by 1.602 x 10^-16 J/keV. This gives us 3.204 x 10^-15 J.

Now, rearrange the equation to solve for f: f = E / h. Substitute the values: f = (3.204 x 10^-15) / (6.626 x 10^-34). The frequency is approximately 4.84 x 10^18 Hz.

To find the wavelength, use the equation c = fλ, where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength.

Rearrange the equation to solve for λ: λ = c / f. Substitute the values: λ = (3 x 10^8) / (4.84 x 10^18). The wavelength is approximately 1.24 x 10^-10 m.