The total magnetic quantum numbers for d-orbitals is given by

Options

A. 2
B. `0,pm1, pm2`
C. 0,1,2
D. 5

Explanation

To find the total magnetic quantum numbers for d-orbitals, we can follow these steps:

### Step 1: Identify the Quantum Numbers
There are four quantum numbers that describe the state of an electron in an atom:
1. Principal quantum number (n)
2. Azimuthal (or angular momentum) quantum number (l)
3. Magnetic quantum number (m)
4. Spin quantum number (s)

### Step 2: Determine the Azimuthal Quantum Number for d-orbitals
For d-orbitals, the azimuthal quantum number \( l \) is equal to 2. This is because:
- \( l = 0 \) corresponds to s-orbitals
- \( l = 1 \) corresponds to p-orbitals
- \( l = 2 \) corresponds to d-orbitals
- \( l = 3 \) corresponds to f-orbitals

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

### Step 4: Count the Total Magnetic Quantum Numbers
The total number of distinct magnetic quantum numbers for d-orbitals is the count of the values obtained in Step 3:
- The values are: \( -2, -1, 0, +1, +2 \)
- This gives us a total of 5 magnetic quantum numbers.

### Conclusion
Thus, the total magnetic quantum numbers for d-orbitals is 5.

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