Which one of the following sets of quantum numbers represents the hieghest energy level in atom?

Options

A. n=4, l=0, m=0,s=+1/2
B. n=3, l=01, m=1,s=+1/2
C. n=3, l=2, m=2,s=+1/2
D. n=3, l=0, m=0,s=+1/2

Answer

To determine which set of quantum numbers represents the highest energy level in an atom, we can use the n + l rule. This rule states that the energy of an electron in an atom is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The higher the value of n + l, the higher the energy level.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
We need to examine the given sets of quantum numbers. Each set will have values for n (principal quantum number) and l (azimuthal quantum number).

2. **Calculate n + l for Each Set**:
For each set of quantum numbers, calculate the sum of n and l.
- For example, if a set has n = 4 and l = 0, then n + l = 4 + 0 = 4.
- If another set has n = 3 and l = 1, then n + l = 3 + 1 = 4.

3. **Compare the n + l Values**:
After calculating n + l for all sets, compare the values. The set with the highest n + l value corresponds to the highest energy level.

4. **Identify the Highest Energy Level**:
The set with the highest n + l value indicates the highest energy level in the atom.

5. **Select the Correct Option**:
Based on the calculations, select the option that has the highest n + l value.

### Example Calculation:
Let's say we have the following sets of quantum numbers:
- Set 1: n = 4, l = 0 → n + l = 4 + 0 = 4
- Set 2: n = 3, l = 1 → n + l = 3 + 1 = 4
- Set 3: n = 3, l = 2 → n + l = 3 + 2 = 5
- Set 4: n = 2, l = 0 → n + l = 2 + 0 = 2

From the above calculations, Set 3 has the highest n + l value of 5, indicating it represents the highest energy level in the atom.

### Conclusion:
The correct answer is the set of quantum numbers from Set 3, which has the highest n + l value of 5.