Final answer:
The energy of a photon can be calculated using the equation E = hf. To find the wavelength, use the equation c = λf. Rearrange the equation to solve for λ, and substitute the given values to find the frequency and wavelength.
Step-by-step explanation:
The energy of a photon can be calculated using the equation E = hf, where E is the energy in joules, h is Planck's constant (6.626 × 10-34 J·s), and f is the frequency of the radiation. To find the wavelength, we can use the equation c = λf, where c is the speed of light (3.00 × 108 m/s), λ is the wavelength, and f is the frequency. Rearranging this equation, we get λ = c/f.
In this case, the given energy of the photons is 6.36 × 10-19 J. Let's assume the wavelength is λ. Using the equation E = hf, we can substitute the given values to find the frequency f. Then using λ = c/f, we can solve for λ.
To calculate the frequency of the radiation, we rearrange the equation E = hf to solve for f: f = E/h = 6.36 × 10-19 J / (6.626 × 10-34 J·s) = 9.61 × 1014 Hz. Now, using the equation λ = c/f, we can substitute the known values to find the wavelength: λ = (3.00 × 108 m/s) / (9.61 × 1014 Hz) = 3.12 × 10-7 m, or 312 nm.