The Power of Photons: Calculating Energy in Kilojoules

How can we calculate the energy of a mole of photons with a specific wavelength?

Consider a photon with a wavelength of 583 nm. What is the energy of a mole of photons of this wavelength (in kJ)?

Answer:

The energy of a mole of photons with a wavelength of 583 nm is approximately 120 kilojoules.

Photon energy is a fascinating concept that showcases the immense power of light particles. By understanding the relationship between wavelength and energy, we can unlock the secrets of photon energy calculations.

In this scenario, we are tasked with determining the energy of a mole of photons with a specific wavelength of 583 nm. To achieve this, we utilize the fundamental equation E = hc/λ, where E represents energy, h is the Planck constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters.

First, we convert the given wavelength of 583 nm to meters, resulting in 583 x 10^-9 meters. By applying the energy equation, we calculate the energy of a single photon with this wavelength. Once we have the energy of one photon, we multiply it by Avogadro's number (6.022 x 10^23) to determine the energy of a mole of photons.

The final result is approximately 120 kilojoules, showcasing the substantial energy contained within a mole of photons at the specified wavelength. This calculation highlights the profound impact of photons and their energy levels on various processes and phenomena.