654 BELL SYSTEM TECHNICAL JOURNAL 



principle, only one electron can occupy a particular quantum state. 

 When the atom is in the arrangement of lowest energy, we can say 

 that each electron has a definite energy corresponding to whichever 

 quantum state it occupies. This energy is most conveniently de- 

 fined in terms of the amount of work required to take an electron 

 from its state in the atom and put it in a standard state defined 

 as zero energy. An electron in the zero energy state is to be thought 

 of as at rest and so far removed from the atom that there is no energy 

 of interaction between them. In this way we can define the energy 

 of every occupied quantum state in the atom. Each of these ener- 

 gies must be taken as negative — since potential energy is yielded up 

 when the electron returns to the atom — and by definition represents 

 how tightly the electron is bound to the atom. One of the electrons 

 will be the most loosely bound (it may be that there are several with 

 the same energy) and the energy required to remove it is called the 

 "ionization energy." From our definition this is obviously the mini- 

 mum energy required to convert the atom to a positive ion. The 

 definition of the energy of a quantum state given above can be used 

 only when an electron is in the quantum state; we can, however, 

 define the energy of an unoccupied state conveniently in terms of the 

 energy the atom would have if the state were occupied by "exciting" 

 one of the electrons to this state by giving it the proper amount of 

 energy.^* 



The Quantum States of the Atom 



Using this definition of the energy of a quantum state, we find that 

 for all atoms the arrangement of quantum states in energy is as shown 

 in Fig. 2, where the ordinates represent energies and states of equal 

 energy appear as divisions of the horizontal lines. Figure 2 does not 

 indicate which states are normally occupied, nor could it unless we 

 knew how many electrons there were in the atom. The general scheme 

 of Fig. 2 is applicable, with certain changes discussed below in the 

 energy scales, to any neutral atom in its normal state, and the energy 



'* This definition is subject to restrictions because the energy of an electron in 

 the state in question depends upon the arrangement of the other electrons in the 

 atom and this arrangement depends in turn upon which electron was excited to the 

 initially unoccupied state. In constructing the figures we have supposed that the 

 electron (or one of the electrons in case there are several) that is most easily removed 

 from the atom is caused to shift from its normal state to the unoccupied state in 

 question; this shift will change the state of the atom and since the atom was initially 

 supposed to be in the state of lowest energy, the change in energy cannot be negative 

 and will in general be positive but may in certain special cases be zero. The energy 

 of the unoccupied state is defined as the energy of the occupied state from which 

 the electron is taken plus the change of energy caused by shifting the electron. _ This 

 is equivalent to saying that the energy of the unoccupied state is the ionization 

 potential of the atom after an electron has been shifted from the highest state nor- 

 mally occupied to the normally unoccupied state in question. 



