1. Calculate the energy of the 580 nm photon:
* Use the equation: E = hc/λ
* E = energy of the photon
* h = Planck's constant (6.626 x 10^-34 Js)
* c = speed of light (3 x 10^8 m/s)
* λ = wavelength (convert 580 nm to meters: 580 x 10^-9 m)
* Substitute the values: E = (6.626 x 10^-34 Js)(3 x 10^8 m/s) / (580 x 10^-9 m)
* Calculate: E ≈ 3.43 x 10^-19 J
2. Double the energy:
* E' = 2 * E = 2 * (3.43 x 10^-19 J) = 6.86 x 10^-19 J
3. Calculate the wavelength of the photon with double the energy:
* Rearrange the equation from step 1 to solve for λ: λ = hc/E'
* Substitute the values: λ = (6.626 x 10^-34 Js)(3 x 10^8 m/s) / (6.86 x 10^-19 J)
* Calculate: λ ≈ 2.90 x 10^-7 m
4. Convert the wavelength to nanometers:
* λ ≈ 2.90 x 10^-7 m * (10^9 nm/m) = 290 nm
Therefore, the wavelength of a photon with twice the energy of a 580 nm photon is approximately 290 nm.
