the number of electrons accommodated in an orbital with principal quantum number 3 is

Options

A. 2
B. 6
C. 8
D. 18

Answer

To determine the number of electrons accommodated in an orbital with a principal quantum number of 3, we can follow these steps:

### Step 1: Understand the Principal Quantum Number
The principal quantum number (n) indicates the shell or energy level of an electron in an atom. For n = 3, we are referring to the third shell, also known as the M-shell.

**Hint:** The principal quantum number (n) defines the energy level and size of the electron cloud.

### Step 2: Identify the Subshells in the Third Shell
The third shell (n = 3) contains the following subshells:
- 3s
- 3p
- 3d

**Hint:** Each shell has specific subshells that can hold electrons.

### Step 3: Determine the Number of Orbitals in Each Subshell
- The 3s subshell has 1 orbital.
- The 3p subshell has 3 orbitals.
- The 3d subshell has 5 orbitals.

**Hint:** Each type of subshell has a fixed number of orbitals: s has 1, p has 3, and d has 5.

### Step 4: Calculate the Total Number of Orbitals in the Third Shell
Total number of orbitals in the third shell:
- 1 (from 3s) + 3 (from 3p) + 5 (from 3d) = 9 orbitals.

**Hint:** Add the number of orbitals from each subshell to find the total.

### Step 5: Determine the Maximum Number of Electrons
Each orbital can hold a maximum of 2 electrons (one with clockwise spin and one with anticlockwise spin). Therefore, the total number of electrons that can be accommodated in the third shell is:
- Total electrons = Number of orbitals × 2 = 9 orbitals × 2 = 18 electrons.

**Hint:** Remember that each orbital can hold a maximum of 2 electrons.

### Final Answer
The number of electrons accommodated in an orbital with principal quantum number 3 is **18 electrons**.