1. Understand the Relationship
The energy (E) of a photon is related to its wavelength (λ) by the following equation:
E = hc/λ
Where:
* E = energy (in Joules)
* h = Planck's constant (6.626 x 10^-34 J⋅s)
* c = the speed of light (3.00 x 10^8 m/s)
* λ = wavelength (in meters)
2. Rearrange the Equation
To solve for wavelength (λ), we need to rearrange the equation:
λ = hc/E
3. Plug in the Values
* E = 3.38 x 10^-19 J
* h = 6.626 x 10^-34 J⋅s
* c = 3.00 x 10^8 m/s
λ = (6.626 x 10^-34 J⋅s * 3.00 x 10^8 m/s) / (3.38 x 10^-19 J)
4. Calculate the Wavelength
λ ≈ 5.88 x 10^-7 meters
5. Convert to Nanometers (nm)
Since wavelengths are often expressed in nanometers, convert the answer:
λ ≈ 588 nm
Therefore, the wavelength of a photon with an energy of 3.38 x 10^-19 J is approximately 588 nm.
