The energy of a photon can be related to its frequency and wavelength using the equation:
E = hf,
where E is the energy of the photon, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), and f is the frequency of the photon.
To find the frequency, we can rearrange the equation as:
f = E / h.
Given that the energy of the photon is 1 MeV (1 million electron volts), we need to convert it to joules since Planck's constant is expressed in joule-seconds. 1 electron volt (eV) is equal to 1.602 x 10^-19 joules.
Converting 1 MeV to joules:
1 MeV = 1 million electron volts = 1 million x 1.602 x 10^-19 joules = 1.602 x 10^-13 joules.
Now, we can calculate the frequency:
f = (1.602 x 10^-13 joules) / (6.626 x 10^-34 joule-seconds) ≈ 2.42 x 10^20 Hz.
To find the wavelength, we can use the equation:
c = λf,
where c is the speed of light (approximately 3 x 10^8 meters per second), λ (lambda) is the wavelength, and f is the frequency.
Rearranging the equation to solve for the wavelength:
λ = c / f.
Substituting the values:
λ = (3 x 10^8 meters per second) / (2.42 x 10^20 Hz) ≈ 1.24 x 10^-12 meters.
Therefore, the wavelength of a 1 MeV photon is approximately 1.24 x 10^-12 meters, and its frequency is approximately 2.42 x 10^20 Hz.