Which of the following set of quantum numbers is not possible ?

Options

A. `n=3, l = 0, m = 0`
B. `n = 3, l = 1, m = -1`
C. `n = 2, l = 0, m = -1`
D. `n = 2, l = 1, m = 0`

Explanation

To determine which set of quantum numbers is not possible, we need to analyze each option based on the rules governing quantum numbers. The quantum numbers are:

1. Principal quantum number (n): It can take positive integer values (1, 2, 3,...).
2. Azimuthal quantum number (l): It can take values from 0 to (n-1).
3. Magnetic quantum number (m): It can take values from -l to +l.

Let's evaluate the options step by step.

### Step 1: Analyze the first set of quantum numbers
- **Given:** n = 1, l = 0, m = 0
- **Analysis:**
- For n = 1, l can be 0 (0 to n-1).
- For l = 0, m can only be 0 (from -l to +l).
- **Conclusion:** This set is possible.

### Step 2: Analyze the second set of quantum numbers
- **Given:** n = 3, l = 1, m = -1
- **Analysis:**
- For n = 3, l can be 0, 1, or 2 (0 to n-1).
- For l = 1, m can be -1, 0, or +1 (from -l to +l).
- **Conclusion:** This set is possible.

### Step 3: Analyze the third set of quantum numbers
- **Given:** n = 2, l = 0, m = -1
- **Analysis:**
- For n = 2, l can be 0 or 1 (0 to n-1).
- For l = 0, m can only be 0 (from -l to +l).
- **Conclusion:** This set is **not possible** because m cannot be -1 when l = 0.

### Step 4: Analyze the fourth set of quantum numbers
- **Given:** n = 2, l = 1, m = 0
- **Analysis:**
- For n = 2, l can be 0 or 1 (0 to n-1).
- For l = 1, m can be -1, 0, or +1 (from -l to +l).
- **Conclusion:** This set is possible.

### Final Conclusion
The set of quantum numbers that is not possible is the third option: **n = 2, l = 0, m = -1**.

---