CK-12-Chemistry Intermediate

http://www.ck12.org Chapter 5. Electrons in Atoms

TABLE5.1: Principal Energy Levels and Sublevels

Principal Energy Level Number of Possible Sub-

levels

Possible Angular

Momentum Quantum

Numbers

Orbital Designation by

Principal Energy Level

and Sublevel

n= 1 1 l= 0 1 s

n= 2 2 l= 0

l= 1

2 s

2 p

n= 3 3 l= 0

l= 1

l= 2

3 s

3 p

3 d

n= 4 4 l= 0

l= 1

l= 2

l= 3

4 s

4 p

4 d

4 f

From the table, you can see that in the 1stprincipal energy level (n= 1) there is only one sublevel possible—ans
sublevel. In the 2ndprincipal energy level (n= 2), there are two sublevels possible—thesandpsublevels. This
continues through the 3rdand 4thprincipal energy levels, in which we add thedand thefsublevels. In general, for
thenthprincipal energy level there arensublevels available. The order of the sublevels is always the same.

Magnetic Quantum Number

As mentioned above, each of the different orbital types has a different shape. Thesorbitals are spherical in shape (
Figure5.15), theporbitals are dumbbell shaped (Figure5.16), and thedandforbitals are more complex shapes
that include multiple lobes (Figure5.17).

FIGURE 5.15

Thesorbitals are spherical in shape and

centered on the nucleus. The larger the

value of the principal quantum numbern,

the larger the correspondingsorbital will

be.

View theporbitals at http://www.dlt.ncssm.edu/core/Chapter8-Atomic_Str_Part2/chapter8-Animations/P-orbitalDia
gram.html.

Themagnetic quantum numberis symbolized by the letter mland indicates the orientation of the orbital around
the nucleus. Because ansorbital is spherical in shape and is centered on the nucleus, it only has one possible
orientation. Ifl= 0, as would be the case for ansorbital, there is only one possible value for the magnetic quantum
number,ml= 0. In thessublevel of each principal energy level (n), there is just onesorbital. The larger the value
ofn, the larger the correspondingsorbital will be. As pictured above (Figure5.16), the dumbbell-shapedporbitals
have three possible orientations. In one orientation, calledpx, the lobes of the orbital lie along the axis defined as
x. In thepyorbital, they lie along they-axis, which is at a 90° angle to thepxorbital. Finally, thepzorbital lies