Gamma rays (γ-rays) are high-energy photons. In a certain nuclear reaction, a γ-ray of energy 0.306 MeV (million electronvolts) is produced. Compute the frequency of such a photon.
To compute the frequency of a gamma-ray photon with an energy of 0.306 MeV, we can use the equation relating energy, frequency, and Planck's constant (h):
E = h * f
Where:
E = Energy of the photon
h = Planck's constant (h = 4.1357 × 10^(-15) eV·s)
f = Frequency of the photon
First, we need to convert the energy from million electronvolts (MeV) to electronvolts (eV). Since 1 MeV = 1 million eV, we can multiply the energy by 1 million to convert it to eV:
0.306 MeV * 1,000,000 eV/1 MeV = 306,000 eV
Now, we can rearrange the equation to solve for frequency (f):
f = E / h
f = 306,000 eV / 4.1357 × 10^(-15) eV·s
Calculating this division, we get:
f ≈ 7.394 × 10^19 Hz
Therefore, the frequency of the gamma-ray photon with an energy of 0.306 MeV is approximately 7.394 × 10^19 Hz.