An electron is in one of the 3d orbitals. Give the possible values of n, l and m for this electron.

Explanation

To determine the possible values of the quantum numbers \( n \), \( l \), and \( m \) for an electron in one of the 3d orbitals, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (\( n \))
The principal quantum number (\( n \)) indicates the energy level of the electron. For a 3d orbital, the principal quantum number is:
\[ n = 3 \]

### Step 2: Determine the Azimuthal Quantum Number (\( l \))
The azimuthal quantum number (\( l \)) is associated with the shape of the orbital. For d orbitals, the value of \( l \) is:
\[ l = 2 \]
This is because the d orbitals correspond to \( l = 2 \).

### Step 3: Calculate the Magnetic Quantum Number (\( m \))
The magnetic quantum number (\( m \)) can take on integer values ranging from \( -l \) to \( +l \). Therefore, for \( l = 2 \), the possible values of \( m \) are:
\[ m = -2, -1, 0, +1, +2 \]

### Summary of Values
Thus, the possible values for the quantum numbers of the electron in the 3d orbital are:
- \( n = 3 \)
- \( l = 2 \)
- \( m = -2, -1, 0, +1, +2 \)

### Final Answer
- \( n = 3 \)
- \( l = 2 \)
- \( m = -2, -1, 0, +1, +2 \)

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