The following quantum numbers are possible for how many orbitals `(s) n = 3, l = 2, m = + 2` ?

Options

A. 1
B. 3
C. 2
D. 4

Explanation

To determine how many orbitals correspond to the given quantum numbers \( n = 3 \), \( l = 2 \), and \( m = +2 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 3 \) means we are in the third energy level.
- The azimuthal quantum number \( l \) indicates the shape of the orbital. For \( l = 2 \), this corresponds to the d orbitals.
- The magnetic quantum number \( m \) indicates the orientation of the orbital in space. The possible values of \( m \) range from \( -l \) to \( +l \).

### Step 2: Determine the Possible Values of \( m \)
- For \( l = 2 \), the possible values of \( m \) are:
\[ m = -2, -1, 0, +1, +2 \]
- This gives us a total of 5 possible orientations for the d orbitals.

### Step 3: Identify the Validity of the Given \( m \)
- The question specifies \( m = +2 \). This is one of the valid values of \( m \) for \( l = 2 \).
- Since \( m = +2 \) corresponds to one specific orientation of the d orbital, it indicates that there is only one orbital that can have this orientation.

### Conclusion
- Therefore, the number of orbitals corresponding to the quantum numbers \( n = 3 \), \( l = 2 \), and \( m = +2 \) is **1**.

### Final Answer
The answer is **1 orbital**.

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