The correct wavelength is found by using the equation E = hc/λ and substituting the values for the constants and the energy given. After rearranging and solving for the wavelength, it is determined to be 204 nm.
The student is asking to find the wavelength of light if the energy of one photon is 9.75 x 10^-19 J. To find the wavelength, we use the equation E = hc/ λ, where E is the energy of the photon, h is Planck's 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. After rearranging the equation to solve for λ, it becomes λ = hc/E. Substituting the values in, we get λ = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) / (9.75 x 10^-19 J) which simplifies to λ = 2.04 x 10^-7 m or 204 nm when converted to nanometers. Therefore, the correct answer is A) 204 nm.