Understanding the Relationship
The energy of a photon is directly proportional to its frequency, and inversely proportional to its wavelength. This relationship is described by the following equation:
* E = h * c / λ
Where:
* E is the energy of the photon (in Joules)
* h is Planck's constant (approximately 6.63 x 10^-34 J*s)
* c is the speed of light (approximately 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 wavelength (λ), we need to rearrange the equation:
λ = h * c / E
2. Plug in the values:
λ = (6.63 x 10^-34 J*s) * (3 x 10^8 m/s) / (3.38 x 10^-19 J)
3. Calculate:
λ ≈ 5.88 x 10^-7 meters
Converting to Nanometers
It's often more convenient to express wavelengths in nanometers (nm). Since 1 meter equals 1 billion nanometers (10^9 nm), we can convert:
λ ≈ 5.88 x 10^-7 meters * (10^9 nm / 1 meter) ≈ 588 nm
Answer:
The wavelength of a photon with an energy of 3.38 x 10^-19 J is approximately 588 nanometers. This wavelength falls within the visible light spectrum, appearing as yellow-green light.
