What is the wavelength and the frequency of a 50-MeV gamma ray photon.
To determine the wavelength and frequency of a gamma ray photon with an energy of 50 MeV, we can use the equation that relates energy, wavelength, and frequency for photons:
E = hf
Where:
E is the energy of the photon (in joules),
h is Planck's constant (approximately 6.626 x 10^-34 J·s), and
f is the frequency of the photon (in hertz).
First, we need to convert the energy from 50 MeV to joules. The conversion factor is 1 MeV = 1.602 x 10^-13 J. So, multiplying 50 MeV by this conversion factor gives us the energy in joules:
E = 50 MeV × (1.602 x 10^-13 J/1 MeV) = 8.01 x 10^-12 J
Now, we can rearrange the equation to solve for frequency (f):
f = E/h
Plugging in the values, we get:
f = (8.01 x 10^-12 J) / (6.626 x 10^-34 J·s) = 1.209 x 10^22 Hz
To find the wavelength (λ), we can use the speed of light equation:
c = λf
Where:
c is the speed of light (approximately 3 x 10^8 m/s),
λ is the wavelength of the photon (in meters), and
f is the frequency of the photon (in hertz).
Rearranging the equation to solve for wavelength (λ), we have:
λ = c/f
Plugging in the values, we get:
λ = (3 x 10^8 m/s) / (1.209 x 10^22 Hz) = 2.483 x 10^-14 meters
Therefore, the wavelength of a 50-MeV gamma ray photon is approximately 2.483 x 10^-14 meters, and the frequency is approximately 1.209 x 10^22 Hz.