What is the maximum number of electrons in a subshell that can have the quantum numbers n = 3 and l = 2 ?

Options

A. 2
B. 5
C. 6
D. 10

Answer

To find the maximum number of electrons in a subshell with the quantum numbers n = 3 and l = 2, follow these steps:

### Step 1: Identify the Principal Quantum Number (n) and Azimuthal Quantum Number (l)
- The principal quantum number (n) is given as 3.
- The azimuthal quantum number (l) is given as 2.

### Step 2: Determine the Type of Subshell
- The value of l indicates the type of subshell:
- l = 0 corresponds to the s subshell
- l = 1 corresponds to the p subshell
- l = 2 corresponds to the d subshell
- l = 3 corresponds to the f subshell
- Since l = 2, we are dealing with a d subshell.

### Step 3: Calculate the Number of Orbitals in the Subshell
- The number of orbitals in a subshell can be calculated using the formula:
\[ \text{Number of orbitals} = 2l + 1 \]
- Substituting the value of l:
\[ \text{Number of orbitals} = 2(2) + 1 = 4 + 1 = 5 \]

### Step 4: Determine the Maximum Number of Electrons
- Each orbital can hold a maximum of 2 electrons.
- Therefore, the maximum number of electrons in the d subshell is calculated as:
\[ \text{Maximum number of electrons} = \text{Number of orbitals} \times 2 \]
- Substituting the number of orbitals:
\[ \text{Maximum number of electrons} = 5 \times 2 = 10 \]

### Conclusion
- The maximum number of electrons in the subshell with quantum numbers n = 3 and l = 2 is **10**.

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