Final answer:
The frequency of a 1.00-MeV γ-ray photon is calculated using the formula E = hf and converting the energy from MeV to joules before dividing by Planck's constant, resulting in a frequency of 2.42×1020 Hz.
Step-by-step explanation:
To calculate the frequency in hertz of a 1.00-MeV (mega-electronvolt) γ-ray photon, we can use the equation that relates energy (E) with frequency (f) and Planck's constant (h):
E = hf
First, we must convert the energy in MeV to joules (J), since Planck's constant is expressed in joule seconds (J·s).
1 MeV = 1.602×10−19 joules (since 1 eV = 1.602×10−19 J).
Therefore, 1.00 MeV = 1.00 × 1.602−19 J = 1.602×10−13 J.
Using Planck's constant h = 6.626×10−34 J·s:
f = E/h
f = 1.602×10−13 J / 6.626×10−34 J·s = 2.42×1020 Hz
The frequency of a 1.00-MeV γ-ray photon is 2.42×1020 Hz, which corresponds to option (a).