Understanding the Relationship

* Energy and Wavelength are inversely proportional: This means that as the energy of a photon increases, its wavelength decreases, and vice versa. This relationship is described by the following equation:

E = hc/λ

Where:

* E = energy of the photon

* h = Planck's constant (6.63 x 10^-34 J·s)

* c = the speed of light (3 x 10^8 m/s)

* λ = wavelength of the photon

Calculations

1. Find the initial energy: We need to first calculate the energy of the photon with a 779 nm wavelength.

* Convert the wavelength to meters: 779 nm = 779 x 10^-9 m

* Plug the values into the equation:

E = (6.63 x 10^-34 J·s) * (3 x 10^8 m/s) / (779 x 10^-9 m)

E ≈ 2.56 x 10^-19 J

2. Calculate the energy of the new photon:

* The new photon has three times the energy: 3 * (2.56 x 10^-19 J) ≈ 7.68 x 10^-19 J

3. Find the new wavelength:

* Use the energy-wavelength equation to solve for λ:

λ = hc/E

λ = (6.63 x 10^-34 J·s) * (3 x 10^8 m/s) / (7.68 x 10^-19 J)

λ ≈ 2.59 x 10^-7 m

4. Convert the wavelength to nanometers:

* 2.59 x 10^-7 m = 259 nm

Answer: The wavelength of the photon with three times the energy of the 779 nm photon is approximately 259 nm.