Rydberg example

[emmaferry2D]

Light with a wavelength of 102.557 nm excites a hydrogen atom gas sample. Is the change in energy of a hydrogen atom positive or negative when it absorbs a photon? What is the principal quantum level of the state that the electron was excited to?

could someone explain to me how to solve this question

[Lea Chamoun 2J]

To answer the first part of the question, the hydrogen is absorbing the photon, so that means that the change in energy is positive because the H atom has more energy than it did before it absorbed the photon. Since the wavelength of the photon is 102.557 nm, it is in the UV region of the EM spectrum. That means that, when the electron falls back down to the state it was excited from, the spectroscopic lines that the electron will emit will be in the Lyman series. This means that the electron started from the n=1 level. Since we now know the initial energy level of the electron, we can calculate the frequency of the wavelength it absorbes using v= c/λ. After you have calculated the frequency, you can solve for the n level that the electron was excited to from n=1 using: V= R[1/n^2 - 1/n^2].