For which of the following set of quantum numbers, an electron will have the highest energy ?

Options

A. 3,2, +1, +1/2
B. 4, 2, -1, +1/2
C. 4, 1, 0, -1/2
D. 5, 0, 0, +1/2

Explanation

To determine which set of quantum numbers corresponds to an electron with the highest energy, we will follow these steps:

### Step 1: Identify the Quantum Numbers
We are given different sets of quantum numbers. Each set includes:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

### Step 2: Write Down the Quantum Numbers
Let's assume we have the following sets of quantum numbers:
1. Set A: n = 3, l = 2, m = +1, s = +1/2
2. Set B: n = 4, l = 2, m = -1, s = -1/2
3. Set C: n = 5, l = 0, m = 0, s = +1/2
4. Set D: n = 4, l = 1, m = 0, s = -1/2

### Step 3: Calculate N + L for Each Set
Using the N + L rule, we calculate the sum of n and l for each set:
- For Set A: N + L = 3 + 2 = 5
- For Set B: N + L = 4 + 2 = 6
- For Set C: N + L = 5 + 0 = 5
- For Set D: N + L = 4 + 1 = 5

### Step 4: Compare N + L Values
Now we compare the N + L values:
- Set A: 5
- Set B: 6
- Set C: 5
- Set D: 5

From this calculation, Set B has the highest N + L value of 6.

### Step 5: Determine the Highest Energy
According to the N + L rule, the higher the N + L value, the higher the energy of the electron. Therefore, Set B (n = 4, l = 2) corresponds to the electron with the highest energy.

### Conclusion
The set of quantum numbers that corresponds to the electron with the highest energy is **Set B** (n = 4, l = 2, m = -1, s = -1/2).

---