Final answer:
The energy needed for a high energy EMR transition in the hydrogen atom with a given wavelength of 91 nm is calculated using the equation E= hc / λ, resulting in approximately 13.63 eV. The closest option is D, which is 13.6 eV.
Step-by-step explanation:
The student has asked about the energy required for a high energy electromagnetic radiation (EMR) transition in the hydrogen atom, with a wavelength of 91 nm. To find this energy, we use the relationship between the energy (E) of a photon, its wavelength (λ), and the Planck constant (h), given by the equation E = hc / λ. Here, h is the Planck constant and c is the speed of light in a vacuum. The product of these constants, hc, can be expressed as 1240 eV·nm. Using this conversion factor and the wavelength provided (91 nm), the calculation for the photon's energy is as follows:
E = (1240 eV·nm) / (91 nm) ≈ 13.63 eV
This calculated energy aligns best with the option stating 13.6 eV, which makes it the value needed for the transition within the hydrogen atom at the given wavelength. Hence, the correct answer from the provided choices is:
Option D: 13.6 eV