Question

What is the frequency and wavelength of light that has energy of $5.09 x 10^{-19}$

Answer 1

Let's first Find the frequency. Energy E and frequency ν are related by the Equation E = hν, where h is the constant of Planck h = 6.63 * 10^-34 J.s
By hypothesis, E = 5.09*10^19 J
E = hv so v = E/h = (5.09*10^-19) / (6.63 * 10^-34) ≈ 7.677 * 10^14 s.

Now Wavelength λ = celerity c / frequency ν, where c = 3 * 10^8 m/s
So λ = (3*10^8) / (7.677 * 10^14) ≈ 3.907 * 10^-7 m = 390.7 nm

Hope this Helps! :)