The maximum number of electrons in an atom with quantum number n=3, l=2 is

Options

A. 2
B. 6
C. 10
D. 30

Answer

To determine the maximum number of electrons in an atom with quantum numbers n=3 and l=2, we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number (n) indicates the energy level of an electron in an atom. Here, n=3 means we are looking at the third energy level.
- The azimuthal quantum number (l) defines the shape of the orbital. For l=2, this corresponds to the d orbitals.

### Step 2: Identify the Orbital Type
- Since l=2, we are dealing with d orbitals. The d subshell can hold a maximum of 10 electrons.

### Step 3: Calculate the Maximum Number of Electrons
- Each d orbital can hold a maximum of 2 electrons, and there are 5 d orbitals in total (dxy, dyz, dxz, dx2-y2, dz2).
- Therefore, the maximum number of electrons in the 3d subshell is calculated as follows:
\[ \text{Maximum electrons} = \text{Number of orbitals} \times \text{Electrons per orbital} = 5 \times 2 = 10 \]

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

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