What is the energy and wavelength of a photon with a frequency of 91.5 MHz?
To determine the energy and wavelength of a photon with a given frequency, you can use the formulas relating these quantities to each other:
1. Energy of a photon (E) = Planck's constant (h) × frequency (f),
where h = 6.62607015 × 10^(-34) J·s (Planck's constant)
2. Speed of light (c) = wavelength (λ) × frequency (f),
where c = 299,792,458 m/s (speed of light)
Let's calculate the energy first.
Given:
Frequency (f) = 91.5 MHz = 91.5 × 10^6 Hz,
Using formula 1:
E = h × f
Substituting the values:
E = 6.62607015 × 10^(-34) J·s × 91.5 × 10^6 Hz
Calculating the energy:
E = 6.06 × 10^(-26) J (Joules)
Now, let's calculate the wavelength.
Using formula 2:
c = λ × f
Since we want to find wavelength (λ), rearrange the formula as follows:
λ = c / f
Substituting the values:
λ = 299,792,458 m/s / 91.5 × 10^6 Hz
Calculating the wavelength:
λ ≈ 3.275 m (meters)
To summarize, the energy of a photon with a frequency of 91.5 MHz is approximately 6.06 × 10^(-26) Joules, and the wavelength is approximately 3.275 meters.