Question

It is presented without derivation in Equntion 3.3 (3.3) ( )--(2. 178 x10-i, J)를 where n identifies the orbit whose energy is belng caleulated; 2 is the atonie number of the atom or on eketron ion: m, is the mi of the electron; ro is the vacuum permittivity: e is the charge on the electron; and h is Planck's constant. The negative sign in Equation 3.3 ensures that all orbits have negative energe and is a result of taking the zero-point as the electron removed from the nucleus. The atomic ber(2) is retained so that the one electron ions of atoms other than hydrogen can be considered. The energy of Equation 3.1 is the eergy of the photon which is emitted when an electron drops fron a higher to a lower energy level. Combining with equation 3.3 gives 3.4) where the absolute value of the energy difference was used to ensure that calculations give a positive value for λ. Evaluation this equation in SI units, gives wavelengths in meters. Other common units for λ include angstrotns (A) and nanometers (nm). Hydrogen and one-electron ions are well described by Bohr's model. As soon as even one more electron is added, the model breaks down and quantum mechanics is required. The breakdown is due, in part, to the fact that electrons are not confined to specific orbits in multielectron systems. As a result, electrons can shield' each other from the full charge of the nucleus. Another important difference is that the quantum mechanical treatment of multielectron atoms and ions split the Bohr-like energy levels into sublevels. Procedure: The tasks are presented in outline form: 1. Use Equation 3.3 and calculate the five (5) lowest energy levels for the hydrogen atom. 2. Use the energies you caleulated in Step I to ealculate the energy and wavelength of the photon emitted as electrons in excited hydrogen atoms fall back to lower levels. There are a total of ten (10) possible transitions. 3. Label each of the transitions in the previous Step. For example, the wavelength for the transition from from nAigher-5 to niower 2 can be given the label As-2- 4. Assign the transitions for the following observed λ for the hydrogen atom: in nm Probable Transitionin mProbable Transition 97 102.6 121.6 433.4 486.1 1281.8 1875.1 4050.0 5. Repeat Steps1 through 3 for the Het ion. 6. Assign the transitions for the following observed λ for the He+ ion: in n Probable Transition 25.6 30.4

- Explain the trends in the magnitude of your errors for (a) the H atom and (b) the He^+ ion.

Answer 1