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This peculiar code originated in the empirical classification of spectra into series called

sharp, principal, diffuse, and fundamental which occurred before the theory of the

atom was developed. Thus an sstate is one with no angular momentum, apstate has

the angular moment  2 , and so forth.

The combination of the total quantum number with the letter that represents orbital

angular momentum provides a convenient and widely used notation for atomic elec-

tron states. In this notation a state in which n2, l0 is a 2sstate, for example,

and one in which n4, l2 is a 4dstate. Table 6.2 gives the designations of electron

states in an atom through n6, l5.

6.6 MAGNETIC QUANTUM NUMBER

Quantization of angular-momentum direction

The orbital quantum number ldetermines the magnitude Lof the electron’s angular

momentum L. However, angular momentum, like linear momentum, is a vector quan-

tity, and to describe it completely means that its directionbe specified as well as its

magnitude. (The vector L, we recall, is perpendicular to the plane in which the rota-

tional motion takes place, and its sense is given by the right-hand rule: When the

fingers of the right hand point in the direction of the motion, the thumb is in the

direction of L. This rule is illustrated in Fig. 6.3.)

What possible significance can a direction in space have for a hydrogen atom? The

answer becomes clear when we reflect that an electron revolving about a nucleus is a

minute current loop and has a magnetic field like that of a magnetic dipole. Hence an

atomic electron that possesses angular momentum interacts with an external magnetic

field B. The magnetic quantum number mlspecifies the direction of Lby determining

the component of Lin the field direction. This phenomenon is often referred to as

space quantization.

If we let the magnetic-field direction be parallel to the zaxis, the component of L

in this direction is

Space quantization Lzml ml0, 1, 2,... , l (6.22)

The possible values of mlfor a given value of lrange fromlthrough 0 to l, so

that the number of possible orientations of the angular-momentum vector Lin a

magnetic field is 2l1. When l0, Lzcan have only the single value of 0; when

l1, Lzmay be , 0, or ; when l2, Lzmay be 2, , 0, , or  2 ; and

so on.

210 Chapter Six

Fingers of right hand in

direction of rotational motion

Thumb in

direction

of angular-

momentum

vector

L

Figure 6.3The right-hand rule

for angular momentum.

Table 6.2 Atomic Electron States

l 0 l 1 l 2 l 3 l 4 l 5

n 11 s

n 22 s 2 p

n 33 s 3 p 3 d

n 44 s 4 p 4 d 4 f

n 55 s 5 p 5 d 5 f 5 g

n 66 s 6 p 6 d 6 f 6 g 6 h

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