A detector absorbs 1.0 × 10⁹ photons of monochromatic light and their total energy is found to be 0.33 nJ.What is the wavelength associated with these photons? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s) A)600 nm B)540 nm C)400 nm D)500 nm

Question

Quizplus · Accepted Answer

The energy of a single photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The total energy of the photons is given, so first, we find the energy of a single photon by dividing the total energy by the number of photons. Then, we rearrange the formula to solve for λ.Total energy = 0.33 nJ = 0.33 × 10^-9 JNumber of photons = 1.0 × 10^19Energy per photon = (0.33 × 10^-9 J) / (1.0 × 10^19) = 3.3 × 10^-28 JUsing E = hc/λ, we solve for λ:λ = hc/E  = (6.63 × 10^-34 J⋅s)(3.00 × 10^8 m/s) / (3.3 × 10^-28 J)  = 6.03 × 10^-7 m  = 600 nm

A Detector Absorbs 1