What is the maximum number of electrons that the third orbit or M-shell can have?
Understanding Electron Shells and Capacity
Atoms have a central nucleus containing protons and neutrons, and electrons orbit the nucleus in specific energy levels or shells. These shells are also referred to as orbits. Each shell can hold a maximum number of electrons. The shells are numbered starting from the shell closest to the nucleus.
- The first shell is \(n=1\), also known as the K-shell.
- The second shell is \(n=2\), also known as the L-shell.
- The third shell is \(n=3\), also known as the M-shell.
- The fourth shell is \(n=4\), also known as the N-shell, and so on.
Calculating Maximum Electrons per Shell
The maximum number of electrons that can occupy a specific shell can be calculated using a simple formula based on the shell number. The formula is:
Maximum electrons in a shell \( = 2n^2 \)
where \(n\) is the principal quantum number, which represents the shell number.
Maximum Electrons in the Third Orbit (M-Shell)
The question asks for the maximum number of electrons in the third orbit, which is the M-shell. For the third orbit or M-shell, the principal quantum number \(n\) is 3.
Using the formula \(2n^2\), we can calculate the maximum capacity of the third orbit:
Maximum electrons in the 3rd shell \( = 2 \times (3)^2 \)
Maximum electrons in the 3rd shell \( = 2 \times 9 \)
Maximum electrons in the 3rd shell \( = 18 \)
Therefore, the maximum number of electrons that the third orbit or M-shell can hold is 18.
Analysis of Options
Let's look at the given options and compare them with our calculated result:
- Option 1: 32. This is the maximum capacity for the fourth shell (N-shell), where \(n=4\), so \(2 \times 4^2 = 2 \times 16 = 32\).
- Option 2: 8. This is the maximum capacity for the second shell (L-shell), where \(n=2\), so \(2 \times 2^2 = 2 \times 4 = 8\).
- Option 3: 18. This matches our calculation for the third shell (M-shell), where \(n=3\), so \(2 \times 3^2 = 2 \times 9 = 18\).
- Option 4: 2. This is the maximum capacity for the first shell (K-shell), where \(n=1\), so \(2 \times 1^2 = 2 \times 1 = 2\).
Based on the calculation using the \(2n^2\) rule, the maximum number of electrons in the third orbit (M-shell) is 18.
| Shell Number (\(n\)) | Shell Name | Maximum Electrons (\(2n^2\)) |
|---|---|---|
| 1 | K | \(2 \times 1^2 = 2\) |
| 2 | L | \(2 \times 2^2 = 8\) |
| 3 | M | \(2 \times 3^2 = 18\) |
| 4 | N | \(2 \times 4^2 = 32\) |
This table summarizes the maximum electron capacity for the first four shells.
Revision Table: Electron Shells
| Concept | Description | Key Formula/Rule |
|---|---|---|
| Electron Shells | Energy levels around the nucleus where electrons are found. Numbered \(n=1, 2, 3, ...\) or named K, L, M, ... | Shell number \(n\) corresponds to shell name K, L, M, etc. (1st, 2nd, 3rd, etc.) |
| Maximum Electron Capacity | The highest number of electrons a specific shell can hold. | \(2n^2\) |
| Third Orbit / M-Shell | The shell with principal quantum number \(n=3\). | Maximum electrons = \(2 \times 3^2 = 18\) |
Additional Information: Electron Configuration and Subshells
While the \(2n^2\) rule gives the maximum capacity of a main shell, it's important to know that shells are further divided into subshells: s, p, d, and f. These subshells have their own maximum electron capacities:
- s subshell: maximum 2 electrons
- p subshell: maximum 6 electrons
- d subshell: maximum 10 electrons
- f subshell: maximum 14 electrons
The third shell (\(n=3\) or M-shell) contains the s, p, and d subshells:
- 3s (capacity 2 electrons)
- 3p (capacity 6 electrons)
- 3d (capacity 10 electrons)
Adding the capacities of the subshells in the third shell gives the total maximum capacity:
Total capacity of M-shell \( = \) capacity of 3s + capacity of 3p + capacity of 3d
Total capacity of M-shell \( = 2 + 6 + 10 = 18 \) electrons.
This subshell structure explains why the total maximum capacity of the third shell is 18, as calculated by the \(2n^2\) rule. Electrons fill these shells and subshells according to rules like the Aufbau principle, Hund's rule, and the Pauli exclusion principle, but the \(2n^2\) rule gives the overall maximum number of electrons a shell can theoretically hold.
Important Questions from Nucleus
- The binding energy B of a nucleus is approximated by the formula B = a 1 A − a 2 A 2/3 − a 3 Z 2 A −1/3 − a 4 (A − 2Z) 2 A −1 where Z is the atomic number and A is the mass number of the nucleus. If \(\rm\frac{a_4}{a_3}\) ≃ 30, the atomic number Z for naturally stable isobars (constant value of A) is
What are the main constituents of biogas?
The energy equivalent of mass associated with the rest mass of an electron, is nearly:
- Considering that the radius of an atomic nucleus, $R$, can be approximated by the formula $R = R_0 A^{1/3}$, where $R_0 \approx 1.2 \times 10^{-15}$ m is the Fermi radius constant and $A$ is the mass number, and the average mass of a single nucleon is approximately $1.67 \times 10^{-27}$ kg. Calculate the approximate order of magnitude of nuclear matter density in $\text{kg/m}^3$.
- The mass number of argon is 40. Which one of the following statements is correct?
