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Jose Antonio Moreno/age fotostock Spain, S.L./Alamy
C05_026A
n
=
4 (4 sublevels)
n
=
3 (3 sublevels)
n
=
2 (2 sublevels)
n
=
1 (1 sublevel)
Figure 16
Energy levels can be thought of as rows of seats in a theater. The rows that are higher up and
farther from the stage contain more seats. Similarly, energy levels related to orbitals farther from the nucleus
contain more sublevels.
Hydrogen’s Atomic Orbitals
Because the boundary of an atomic orbital is fuzzy, the orbital does not have an exact
defined size. To overcome the inherent uncertainty about the electron’s location,
chemists arbitrarily draw an orbital’s surface to contain 90% of the electron’s total
probability distribution. This means that the probability of finding the electron within
the boundary is 0.9 and the probability of finding it outside the boundary is 0.1. In
other words, it is more likely to find the electron close to the nucleus and within the
volume defined by the boundary, than to find it outside the volume. The circle shown in
Figure 15b
encloses 90% of the lowest-energy orbital of hydrogen.
Principal quantum number
Recall that the Bohr atomic model assigns quantum numbers to electron orbits.
Similarly, the quantum mechanical model assigns four quantum numbers to atomic
orbitals. The first one is the
principal quantum number
(
n
) and indicates the relative
size and energy of atomic orbitals. As
n
increases, the orbital becomes larger, the
electron spends more time farther from the nucleus, and the atom’s energy increases.
Therefore,
n
specifies the atom’s major energy levels. Each major energy level is called a
principal energy level.
An atom’s lowest principal energy level is assigned a principal
quantum number of 1. When the hydrogen atom’s single electron occupies an orbital
with
n
=
1, the atom is in its ground state. Up to 7 energy levels have been detected for
the hydrogen atom, giving
n
values ranging from 1 to 7.
Energy sublevels
Principal energy levels contain
energy sublevels.
Principal energy level 1 consists of a
single sublevel, principal energy level 2 consists of two sublevels, principal energy
level 3 consists of three sublevels, and so on. To better understand the relationship
between the atom’s energy levels and sublevels, picture the seats in a wedge-shaped
section of a theater, as shown in
Figure 16
. As you move away from the stage, the rows
become higher and contain more seats. Similarly, the number of energy sublevels in a
principal energy level increases as
n
increases.
Get It?
Explain
the relationship between energy levels and sublevels.
Lesson 2 • Quantum Theory and the Atom
123