F Electron Binding Energies

Every elemental atom has electrons in orbitals whose energy provides a unique signature called characteristic energies that identify the element. The binding energy EB is the energy required to remove an electron from a specific orbital to a position at rest outside the atom. In Figure F.4 we show schematically the innermost orbitals (n = 1, 2, and 3) and the labels K, L, M used in x-ray notation to identify the specific orbitals. At the side we show the actual binding energies in kilo electron volts (keV) for two elements. The symbols at the side (1s, 2s, 2p, 3s ... ) are the electron notation. Table F.2 gives the x-ray notation.

The binding energy is the difference in the total energy between the initial and final states of the atom in which one electron has been removed. That is, it requires an input energy of one binding energy EB to remove an electron from a state characterized by EB. In Figure F.4 we use the x-ray symbols where the K-shell refers to n = 1, L shell to n = 2, and L1 refers to the 2s subshell.

Binding Energy Oxygen Electron
Fig. F.4. Schematic of the energy levels of an atom indicated by the x-ray symbol (K, Lj, L2, ... ) and the electron shell 1s, 2s, 2p, ... ). On the right side, the binding energies in kilo electron volts (keV) in the various shells of arsenic and cadmium are given.

TABLE F.2

Number of Electrons and X-Ray Symbols

Atomic levels

Electron

Number of

Singly Ionized Atom

n

l

Shell

Electrons

X-ray Symbol

1

0

1s

2

K

2

0

2s

2

Li

1

2p

6

L2

lb

3

0

3s

2

M1

1

3p

6

m2

m3

2

3d

10

m4

m5

4

0

4s

2

Ni

1

4p

6

N2

Nb

2

4d

10

N4

N5

3

4f

14

N6

N7

5

0

5s

2

Oi

Notation for atomic levels with principal (n) and azimuthal (l) quantum numbers, electron shell, number of electrons in the shell, and x-ray symbol for singly ionized atom with a vacancy in the shell.

Three aspects to note about binding energies EB:

(1) Eb increases approximately as Z2.

(2) EB (K-shell) is nearly a factor of ten greater than EB (L-shell), which in turn is nearly a factor of ten greater than the binding energies in the M shell.

(3) Each shell and subshell have a characteristic EB.

Tabulated values of the binding energy (Table F.3) also show these same trends. These values are important because an incident photon must have an energy E = hf greater than EB to eject an electron from the shell. For example, a 2.0 keV x-ray would have sufficient energy to eject a silicon (Si) K-shell electron (EB = 1.839 keV) but not enough for a phosphorous (P) K-shell electron (EB = 2.149 keV). The same considerations are true for L-shell electrons. A 2.0 keV x-ray would eject an arsenic (As) L-shell electron (EB = 1.4 keV) but not the L electrons of cadmium (Cd) (Eb = 3.5 keV).

Fig. F.5. Two energy levels separated by an energy AE. Radiation is absorbed in an electron transition from the low to the high energy state. Radiation is emitted in the transition from the high to the low energy state.
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