Final answer:
The energy of a photon with a wavelength of 1094.9 nm is calculated using Planck's equation, converting the wavelength to meters, and then calculating the energy in joules and converting it to GeV to compare with the theoretical energy needed for unification of forces.
Step-by-step explanation:
The energy (E) of a photon is calculated using the equation E = hc/λ, where h is Planck's constant (6.626 × 10-34 J × s), c is the speed of light (3.00 × 108 m/s), and λ is the wavelength of the photon. First, convert the wavelength from nanometers to meters by dividing by 109. Then substitute h, c, and λ into the equation to calculate the photon's energy.
For a wavelength of 1094.9 nm, the energy calculation would be:
- Convert wavelength to meters: λ = 1094.9 nm × 10-9 nm/m.
- Substitute values into the equation: E = (6.626 × 10-34 J × s)(3.00 × 108 m/s) / λ.
- Perform the calculation to find E in joules.
- Convert the energy from joules to giga-electronvolts (GeV) by using the conversion factor: 1 GeV = 1.602 × 10-10 J.
The result can be compared to the average particle energy of 1019 GeV which is vastly higher than the energy of a single photon and represents the energy scales involved in unification theories.