Understanding Electron Shells and Capacity

Atoms have electrons orbiting the nucleus in specific energy levels or shells. These shells are often designated by letters, starting with K closest to the nucleus, followed by L, M, N, and so on. They can also be represented by a principal quantum number, 'n', where n=1 for the K shell, n=2 for the L shell, n=3 for the M shell, n=4 for the N shell, and so on.

Each electron shell has a maximum capacity for holding electrons. This maximum number of electrons in a shell with principal quantum number 'n' is determined by a simple formula:

\[ \text{Maximum number of electrons} = 2n^2 \]

Calculating Maximum Electrons in the N Shell

The question asks for the maximum number of electrons in the N shell. To find this, we first need to identify the principal quantum number 'n' corresponding to the N shell.

• K shell corresponds to n = 1
• L shell corresponds to n = 2
• M shell corresponds to n = 3
• N shell corresponds to n = 4

Now we can use the formula \(2n^2\) with n = 4 to calculate the maximum capacity of the N shell.

\[ \text{Maximum electrons in N shell} = 2 \times (4)^2 \]

First, calculate \(4^2\):

\[ (4)^2 = 4 \times 4 = 16 \]

Then, multiply the result by 2:

\[ 2 \times 16 = 32 \]

Therefore, the maximum number of electrons that the N shell can hold is 32.

Comparing Shell Capacities

Let's quickly look at the maximum capacity of the first few electron shells using the same formula \(2n^2\):

As shown in the table and calculated, the maximum number of electrons in the N shell is 32.

Revision Table: Electron Shells and Capacity

Additional Information: Subshells and Orbitals

While the formula \(2n^2\) gives the total maximum capacity of a shell, each shell is further divided into subshells (s, p, d, f). Each subshell contains one or more orbitals, and each orbital can hold a maximum of two electrons.

• n=1 (K shell): Has 1 subshell (1s), capacity \(2 \times 1^2 = 2\) electrons. The 1s subshell has 1 orbital (\(1s^2\)).
• n=2 (L shell): Has 2 subshells (2s, 2p), capacity \(2 \times 2^2 = 8\) electrons. 2s has 1 orbital (\(2s^2\)), 2p has 3 orbitals (\(2p^6\)). Total \(2+6=8\).
• n=3 (M shell): Has 3 subshells (3s, 3p, 3d), capacity \(2 \times 3^2 = 18\) electrons. 3s (\(3s^2\)), 3p (\(3p^6\)), 3d has 5 orbitals (\(3d^{10}\)). Total \(2+6+10=18\).
• n=4 (N shell): Has 4 subshells (4s, 4p, 4d, 4f), capacity \(2 \times 4^2 = 32\) electrons. 4s (\(4s^2\)), 4p (\(4p^6\)), 4d (\(4d^{10}\)), 4f has 7 orbitals (\(4f^{14}\)). Total \(2+6+10+14=32\).

The number of subshells within a shell 'n' is equal to 'n'. The types of subshells present in shell 'n' are s, p, d, ..., up to a subshell type corresponding to the azimuthal quantum number l = n-1.

This subshell structure explains how the total capacity \(2n^2\) is achieved by adding up the capacities of the individual subshells within that main shell.