Page 64 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 4] ELECTRONIC CONFIGURATION OF THE ATOM 53

used interchangeably. The shells are sometimes designated by capital letters, with K denoting the lowest energy
level, as follows:
Energy level 1 2 3 4 5 ...
Shell notation K L M N O ...

The electrons in atoms other than hydrogen also occupy various energy levels. With more than one electron
in each atom, the question of how many electrons can occupy a given level becomes important. The maximum
number of electrons that can occupy a given shell depends on the shell number. For example, in any atom, the
first shell can hold a maximum of only 2 electrons, the second shell can hold a maximum of 8 electrons, the third
shell can hold a maximum of 18 electrons, and so forth. The maximum number of electrons that can occupy any
2
particular shell is 2n , where n is the shell number.
EXAMPLE 4.1. What is the maximum number of electrons that can occupy the N shell?

Ans. The N shell in an atom corresponds to the fourth energy level (n = 4); hence the maximum number of electrons it
can hold is
2
2
2n = 2(4) = 2 × 16 = 32
4.3. QUANTUM NUMBERS
The modern theory of the electronic structure of the atom stems from a complex mathematical equation
(called the Schr¨odinger equation), which is beyond the mathematical requirements for the general chemistry
course. We therefore take the results of the solution of this equation as postulates. Solution of the equation
yields three quantum numbers, with a fourth and final quantum number obtained from experimental results. The
quantum numbers are named and have limitations as shown in Table 4-1. Each electron is specified in terms of
its four quantum numbers that govern its energy, its orientation in space, and its possible interactions with other
electrons. Thus, listing the values of the four quantum numbers describes the probable location of the electron,
somewhat analogously to listing the section, row, seat, and date on a ticket to a rock concert. To learn to express the
electronic structure of an atom, it is necessary to learn (1) the names, symbols, and permitted values of the quantum
numbers and (2) the order of increasing energy of electrons as a function of their sets of quantum numbers.

Table 4-1 Quantum Numbers
Name Symbol Limitations

Principal quantum number n Any positive integer
Angular momentum quantum number
or Azimuthal quantum number l 0,..., n − 1 in integer steps
Magnetic quantum number m l −l,..., 0,..., +l in integer steps
1
Spin quantum number m s − , + 1
2 2
The principal quantum number of an electron is denoted n. It is the most important quantum number in
determining the energy of the electron. In general, the higher the principal quantum number, the higher the energy
of the electron. Electrons with higher principal quantum numbers are also apt to be farther away from the nucleus
than electrons with lower principal quantum numbers. The values of n can be any positive integer: 1, 2, 3, 4, 5, 6,
7, ... . The first seven principal quantum numbers are the only ones used for electrons in ground states of atoms.
The angular momentum quantum number is denoted l. It also affects the energy of the electron, but in general
not as much as the principal quantum number does. In the absence of an electric or magnetic field around the
atom, only n and l have any effect on the energy of the electron. The value of l can be 0 or any positive integer
up to, but not including, the value of n for that electron.
The magnetic quantum number, denoted m l , determines the orientation in space of the electron, but does
not ordinarily affect the energy of the electron. Its values depend on the value of l for that electron, ranging