A given orbital is labelled by the magnetic quantum number, m = -1. This can not be

Options

A. s- orbital
B. p-orbital
C. d-orbital
D. f-orbital

Answer

To solve the question, we need to analyze the magnetic quantum number (m) and its relationship with the angular momentum quantum number (l).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The quantum numbers that describe an electron in an atom include the principal quantum number (n), angular momentum quantum number (l), and magnetic quantum number (m).
- The magnetic quantum number (m) can take values from -l to +l, including zero.

2. **Identifying the Relationship**:
- The value of m is dependent on the value of l. Specifically, for any given l, m can take values in the range of -l to +l.
- This means that for each value of l, there are (2l + 1) possible values for m.

3. **Determining Possible l Values**:
- For different types of orbitals, the values of l are as follows:
- s orbital: l = 0
- p orbital: l = 1
- d orbital: l = 2
- f orbital: l = 3

4. **Evaluating m = -1**:
- If m = -1, we need to find which l values allow for this value of m.
- For l = 0 (s orbital), m can only be 0.
- For l = 1 (p orbital), m can be -1, 0, or +1.
- For l = 2 (d orbital), m can be -2, -1, 0, +1, or +2.
- For l = 3 (f orbital), m can be -3, -2, -1, 0, +1, +2, or +3.

5. **Conclusion**:
- Since m = -1 is not a valid value for the s orbital (where l = 0), the statement that "a given orbital is labelled by the magnetic quantum number, m = -1" cannot be true for the s orbital.
- Therefore, the correct answer is that this cannot be an s orbital.

### Final Answer:
The given orbital labelled by the magnetic quantum number, m = -1 cannot be an **s orbital**.

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