Final answer:
The energy of a photon with a wavelength of 1550 nm is calculated using the formula E = \( \frac{hc}{\lambda} \), resulting in approximately 1.28×10⁻ joules.
Step-by-step explanation:
To calculate the photon energy for light with a free space wavelength of 1550 nm, we can use the formula E = \( \frac{hc}{\lambda} \) where E is the energy of the photon, h is Planck's constant, c is the speed of light, and \( \lambda \) is the wavelength of the light.
We are given that Planck's constant (h) is 6.626×10⁻³⁴ J·s and the wavelength (\( \lambda \)) is 1550 nm, which is 1550×10⁻⁹ m. The speed of light (c) is a constant at approximately 3.00×10⁻³ m/s.
Substitute these values into the equation to get the photon energy:
E = \( \frac{6.626×10⁻⁴ J·s × 3.00×10⁻³ m/s}{1550×10⁻⁹ m} \)
E = 1.28×10⁻ J (joules)
Thus, the energy of a photon with a wavelength of 1550 nm is approximately 1.28×10⁻ joules.