Electronic Structure: Shells and Quantum Numbers

Electronic Structure: Shells

Potential Energy and Electron Shells

Electrons in atoms are arranged in shells, which are groups of electrons surrounding the nucleus. The energy of these shells is related to their potential energy—electrons farther from the nucleus have higher potential energy.

• Shell (n): The principal quantum number (n) describes the shell. As n increases, both the size and energy level of the shell increase.

• Energy Levels: The value of n can be determined from the period (row) of the Periodic Table for main group elements.

• Limitation: n must be a positive integer (1, 2, 3, ...).

Visualizing Shells and the Periodic Table

The periodic table is organized such that each row corresponds to a principal quantum number (n), indicating the shell being filled with electrons.

• For example, elements in the second row (period 2) have electrons filling the n = 2 shell.

Example Problem

Question: Which of the following is a possible value for the shell of an atom?

• a) n = 1

• b) n = 0

• c) n = -2

• d) n = 5

Answer: a) n = 1 and d) n = 5 are possible, since n must be a positive integer.

Practice Problems

• Identify the shell number (n) for a highlighted element on the periodic table (typically, the period number).

• Determine which electron possesses the lowest possible energy (the one closest to the nucleus, n = 1).

Key Terms and Concepts

• Principal Quantum Number (n): Specifies the shell and energy level of an electron in an atom.

• Potential Energy: Energy due to position; electrons farther from the nucleus have higher potential energy.

• Period: A horizontal row in the periodic table; indicates the value of n for main group elements.

Equations

• Allowed values for the principal quantum number: $n = 1, 2, 3, \ldots$

Summary Table: Principal Quantum Number and Periodic Table

Period (Row)	Principal Quantum Number (n)	Shell Name
1	1	K
2	2	L
3	3	M
4	4	N
...	...	...

Additional info: The shell names (K, L, M, N, ...) are traditional labels for the first four shells.