Understanding the Relationship
The energy of a photon (E) is directly proportional to its frequency (ν) and inversely proportional to its wavelength (λ). This relationship is described by the following equation:
* E = hν = hc/λ
Where:
* E is the energy of the photon (in Joules)
* h is Planck's constant (6.626 x 10^-34 J·s)
* ν is the frequency of the photon (in Hertz)
* c is the speed of light (3 x 10^8 m/s)
* λ is the wavelength of the photon (in meters)
Solving for Wavelength
1. Rearrange the equation to solve for λ:
λ = hc / E
2. Plug in the values:
λ = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (3.38 x 10^-19 J)
3. Calculate the wavelength:
λ ≈ 5.87 x 10^-7 m
Converting to Nanometers:
Since wavelengths are often expressed in nanometers (nm), let's convert the answer:
* 1 meter = 1 x 10^9 nanometers
* λ ≈ 5.87 x 10^-7 m * (1 x 10^9 nm / 1 m)
* λ ≈ 587 nm
Therefore, the wavelength of a photon with an energy of 3.38 x 10^-19 J is approximately 587 nanometers.
