The maximum number of electrons that can be accommodated in M shell is:
18
Understanding Electron Shells and Maximum Capacity
In an atom, electrons occupy specific energy levels or shells around the nucleus. These shells are designated by letters starting from the one closest to the nucleus: K, L, M, N, and so on. Each shell corresponds to a principal quantum number, denoted by 'n'.
- K shell: n = 1
- L shell: n = 2
- M shell: n = 3
- N shell: n = 4
Calculating Maximum Electrons in a Shell
The maximum number of electrons that can be accommodated in a principal shell with quantum number 'n' is given by the formula:
\begin{equation*} \text{Maximum electrons} = 2n^2 \end{equation*}
Applying the Formula to the M Shell
The question asks for the maximum number of electrons in the M shell. As established, the M shell corresponds to the principal quantum number n = 3.
Using the formula, we substitute n = 3:
\begin{equation*} \text{Maximum electrons in M shell} = 2 \times (3)^2 \end{equation*}
\begin{equation*} = 2 \times 9 \end{equation*}
\begin{equation*} = 18 \end{equation*}
Therefore, the maximum number of electrons that can be accommodated in the M shell is 18.
Analyzing the Options
Let's look at the given options based on our calculation:
- 8: This is the maximum capacity of the L shell (n=2, $2 \times 2^2 = 8$).
- 2: This is the maximum capacity of the K shell (n=1, $2 \times 1^2 = 2$).
- 18: This matches our calculation for the M shell (n=3, $2 \times 3^2 = 18$).
- 32: This is the maximum capacity of the N shell (n=4, $2 \times 4^2 = 32$).
Based on the formula and calculation, the correct number for the M shell is 18.
| Shell | Principal Quantum Number (n) | Maximum Electrons ($2n^2$) |
|---|---|---|
| K | 1 | $2 \times 1^2 = 2$ |
| L | 2 | $2 \times 2^2 = 8$ |
| M | 3 | $2 \times 3^2 = 18$ |
| N | 4 | $2 \times 4^2 = 32$ |
Revision Table: Electron Shells and Capacity
| Shell Name | n Value | Maximum e- Capacity ($2n^2$) |
|---|---|---|
| K | 1 | 2 |
| L | 2 | 8 |
| M | 3 | 18 |
| N | 4 | 32 |
Additional Information: Subshells within the M Shell
While the maximum capacity of the M shell is 18 electrons, these electrons are distributed among subshells within the M shell. The M shell (n=3) contains three types of subshells:
- s subshell (l=0): Can hold a maximum of 2 electrons.
- p subshell (l=1): Can hold a maximum of 6 electrons.
- d subshell (l=2): Can hold a maximum of 10 electrons.
The total maximum capacity of the M shell is the sum of the capacities of its subshells: 2 (s) + 6 (p) + 10 (d) = 18 electrons. This distribution aligns with the $2n^2$ formula for the principal shell.
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