3. It turns out that any one-electron atom, i.e., an atom with all of its electrons removed except one, behaves like hydrogen. Such a species is termed a hydrogenic atom . These species are actually ions , that is electrically charged species. For example, He (atomic # = Z = 2 in the periodic table), with 2 protons and 2 electrons, would be hydrogenic if one electron were removed. Thus, He + ion would be hydrogenic. Likewise, the Li +2 ion (atomic # = Z = 3) would also be hydrogenic. Read more about this in .pdf # 5 - Quantum Theory, Atoms, & the Periodic Table , in Course Documents, pages 4-6. Then, please complete the following. For this question, imagine the hydrogen-like atom (ion) that can be created from elemental beryllium (Be) for which Z = 4. [For this problem it may be useful for some of the questions below to construct an energy level diagram like we did in class to “follow the electron” as it “jumps” between energy levels. You do not have to submit the diagram - only the reasoning and calculations used to answer any related questions.]

(a) What must be the net charge (+1, +2, …) on the Be atom for it to become hydrogen-like? How do you know? If it can only have 1 electron for it to be Hydrogen like, A Be atom usually has 4 electrons, to be Hydrogen like it has to lose 3 of them. It would have 3 more protons than electrons, so it would be a +3.

(b) Determine the wavelength (in nm) and the frequency (in Hz) of the first spectral line in the Balmer emission series. [The first spectral line, is the one of longest possible wavelength (i.e., least photon energy). Recall, that all Balmer photon emissions involve the electron undergoing an energy level transition in which the final n = 2 and the initial energy level can be any n ≥ 3. ]

Z2 ⊗ R E = − y n2

− 1 1  E =−⊗(42 2.18 ⊗ 10 18 )  −  42 3 2  E=1.696 ⊗ 10 −18 J

λ = hc E − ⊗34J ⊗ ⊗ 8 m λ = 6.63 10s 3 10 s 1.696⊗ 10 −18 J λ =11.7 nm