Hydrogen atom, energy level diagram

At this point we might recast the hydrogen atom energy level diagram to express what we know... 

Long after this energy level diagram for the hydrogen atom had been established, scientists still pondered its significance. Finally, in the late 1920 s, a mathematical scheme was developed that explained the facts. The mathematical scheme is called quantum mechanics. 

The energy level diagrams resemble the hydrogen atom level diagram except that the ri levels with the same value of n no longer all have the same energy. 

C07-0126. The series of emission lines that results from excited hydrogen atoms undergoing transitions to the n — 3 level Is called the Paschen series. Calculate the energies of the first five lines In this series of transitions, and draw an energy level diagram that shows them to scale. 

FIGURE 1.8 An energy level diagram for the hydrogen atom. 

Figure 3.4 shows a more correctly scaled energy level diagram that results for the hydrogen molecule. Note that the energy for the Is atomic orbital of a hydrogen atom is at — 1312 kJ moT1 because the... 

Figure 9.1. Energy level diagram for hydrogen molecule, H2, and separated atoms H R = 00) and He R = 0). R = the Rydberg constant = 13.6057 eV = 0.5 a.u. (atomic unit of energy). Value from ionization potential of He (Is 2p P). Value from ionization potential of H2. The experimental ionization potentials are quite precise but for systems containing more than one electron their interpretation in terms of orbital energies is an approximation.

Figure 3. Energy level diagram indicating modification of energy levels of titanium and hydrogen upon formation of titanium dihydride. The diagonally shaded line indicates the potential between the atoms.

Note that all the superscripts for an atom must add up to the total number of electrons in the atom—1 for hydrogen, 3 for lithium, 11 for sodium, and so forth. Also note that the orbitals are not always listed in order of principal quantum number. The 4s orbital, for example, is lower in energy than the 3 dorbitals, as is indicated on the energy-level diagram of Figure 5-22. The 4s orbital, therefore, appears before the 3dorbitaI. 

Figure 1.5 The energy-level diagram for the interaction of

There are a number of differences between the energy level diagram in Fig. 5.1 and that for hydrogen. They are highly significant in the understanding of many-electron atoms, and are discussed in more detail in later sections. 

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