THE QUANTUM PHYSICS OF SOLIDS 



657 



Variation of the Energy Levels with Atomic Number 

 All atoms have the same general scheme of quantum states indicated 

 in Fig. 2. Quantitatively the energy scale varies from atom to atom. 

 Thus the Is state lies at — 13.5 ev for hydrogen and at — 24 ev for 

 helium. This decrease (i.e., becoming more negative or moving lower 

 down on Fig. 2) is due to the increase in nuclear charge, Z = 1 for 

 hydrogen and 2 for helium, which results in greater attraction and 

 tighter binding for electrons in helium. This steady downward motion 

 of the levels continues as one goes from element to element in the 

 periodic table. However, the ionization potential, the energy required 

 to remove the most easily removed electron, does not steadily increase. 

 In Fig. 3 we show the ionization potentials of the first twenty elements. 



ATOMIC NUMBER 

 Fig. 3 — Ionization potential versus atomic number. 



Since we are interested in the energies of electrons rather than in 

 ionization per se, the ionization potentials have been plotted as nega- 

 tive giving in this way the energies of the states in the atom. The 

 main features of this figure can be explained by using Fig. 2 and the 

 Pauli principle. 



The Pauli principle, also known as the exclusion principle, permits 

 only one electron to occupy each of the states of Fig. 2. The electrons 

 in a many-electron atom will tend to go to the states of lowest energy. 



