The fundamental equation is derived from Mr. Planck: E=h \nu, where h is Planck’s constant and ν is the frequency. This relationship describes the energy per photon at a specific frequency. Although a wavelength is provided, it can easily be converted to frequency using the equation: c= lambda / nu, where c denotes the speed of light; λ (lambda) is the wavelength; and ν is the frequency. Once the energy of a photon with a wavelength of 550nm is determined, it will show how many photons are needed to gather 10^-18J. Remember to pay attention to the units.
The result is: 3 photons. To explain: The energy of a photon (E) can be formulated using: E = h*c/λ. Here, h represents Planck's constant (6.63x10⁻³⁴ J.s), λ signifies the wavelength (550 nm = 5.50x10⁻⁷m), and c stands for the speed of light (3.00x10⁸ m/s). Thus, E= (6.63x10⁻³⁴ * 3.00x10⁸)/(5.50x10⁻⁷) results in E = 3.62x10⁻¹⁹ J, which is the energy for one photon. Since the human eye can respond to 10⁻¹⁸ J, it follows that: 1 photon corresponds to 3.62x10⁻¹⁹ J, leading to a simple calculation resulting in approximately 2.76, which rounds to 3 photons.
