bei48482_FM

Atomic Structure 133

n 2 rn n1, 2, 3,... (4.12)

where rndesignates the radius of the orbit that contain nwavelengths. The integer n

is called the quantum numberof the orbit. Substituting for , the electron wavelength

given by Eq. (4.11), yields

 ^2 rn

and so the possible electron orbits are those whose radii are given by

rn n1, 2, 3,... (4.13)

The radius of the innermost orbit is customarily called the Bohr radiusof the hydrogen

atom and is denoted by the symbol a 0 :

Bohr radius a 0 r 1 5.292 10 ^11 m

The other radii are given in terms of a 0 by the formula

rnn^2 a 0 (4.14)

4.5 ENERGY LEVELS AND SPECTRA

A photon is emitted when an electron jumps from one energy level to a

lower level

The various permitted orbits involve different electron energies. The electron energy

Enis given in terms of the orbit radius rnby Eq. (4.5) as

En

Substituting for rnfrom Eq (4.13), we see that

Energy levels En  n1, 2, 3, (4.15)

E 1 2.18 10 ^18 J13.6 eV

The energies specified by Eq. (4.15) are called the energy levelsof the hydrogen atom

and are plotted in Fig. 4.15. These levels are all negative, which signifies that the elec-

tron does not have enough energy to escape from the nucleus. An atomic electron can

have only these energies and no others. An analogy might be a person on a ladder,

who can stand only on its steps and not in between.

E 1



n^2

1



n^2

me^4



8 ^20 h^2

e^2



8  0 rn

n^2 h^2  0



me^2

Orbital radii in

Bohr atom

4  0 rn



m

nh



e

Condition for orbit

stability

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