The energy of a photon is inversely proportional to its wavelength, which means that the shorter the wavelength, the higher the energy. This relationship is described by the equation:
E = hc / λ
Where:
- E = energy of the photon
- h = Planck’s constant (approximately 6.626 x 10-34 Js)
- c = speed of light in a vacuum (approximately 3.00 x 108 m/s)
- λ = wavelength of the photon in meters
For a 400 nm photon, the calculation is as follows:
1. Convert 400 nm to meters: 400 nm = 400 x 10-9 m
2. Calculate the energy:
E400 = (6.626 x 10-34 Js)(3.00 x 108 m/s) / (400 x 10-9 m) = 4.97 x 10-19 Joules
For a 700 nm photon, the calculation is similar:
1. Convert 700 nm to meters: 700 nm = 700 x 10-9 m
2. Calculate the energy:
E700 = (6.626 x 10-34 Js)(3.00 x 108 m/s) / (700 x 10-9 m) = 2.84 x 10-19 Joules
To find the factor difference in energy between the two photons, divide the energy of the 400 nm photon by the energy of the 700 nm photon:
Factor = E400 / E700 = (4.97 x 10-19 J) / (2.84 x 10-19 J) ≈ 1.75
This means that a 400 nm photon has approximately 1.75 times more energy than a 700 nm photon. The difference in energy between photons of different wavelengths is an important concept in physics and helps explain phenomena such as the color of light and its interaction with matter.