The energy of a photon can be related to its frequency and wavelength through the following equations:
- Energy of a photon (E) = Planck's constant (h) × Frequency (ν)
- Speed of light (c) = Frequency (ν) × Wavelength (λ)
Given that the energy of the photon is 30 pJ (picojoules), we can convert it to joules by multiplying by 10^(-12):
E = 30 × 10^(-12) J
Now we can use Equation 1 to find the frequency (ν). Rearranging the equation, we have:
ν = E / h
where Planck's constant (h) is approximately 6.626 × 10^(-34) J·s. Substituting the values, we get:
ν = (30 × 10^(-12) J) / (6.626 × 10^(-34) J·s)
Calculating the result:
ν ≈ 4.529 × 10^21 Hz
To find the wavelength (λ), we can use Equation 2. Rearranging the equation, we have:
λ = c / ν
where the speed of light (c) is approximately 3.0 × 10^8 m/s. Substituting the values, we get:
λ = (3.0 × 10^8 m/s) / (4.529 × 10^21 Hz)
Calculating the result:
λ ≈ 6.62 × 10^(-14) meters or 66.2 femtometers (fm)
Therefore, the frequency of the photon is approximately 4.529 × 10^21 Hz, and the wavelength is approximately 6.62 × 10^(-14) meters (66.2 femtometers).