Electrons will first enter into which set of quantum numbers-n = 5, l = 0 or n = 3, l = 2

Options

A. n = 5, l = 0
B. both possible
C. n = 3, l = 2
D. data insufficient

Explanation

To determine which set of quantum numbers electrons will first enter, we need to apply the principles of quantum mechanics, specifically the Aufbau principle and the n + l rule.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The quantum numbers describe the properties of electrons in an atom. The principal quantum number (n) indicates the energy level, while the azimuthal quantum number (l) indicates the shape of the orbital.

2. **Identify the Given Quantum Numbers**:
- We have two sets of quantum numbers:
- Set 1: n = 5, l = 0 (This corresponds to a 5s orbital)
- Set 2: n = 3, l = 2 (This corresponds to a 3d orbital)

3. **Apply the n + l Rule**:
- According to the n + l rule, we calculate the sum of n and l for both sets:
- For Set 1: n + l = 5 + 0 = 5
- For Set 2: n + l = 3 + 2 = 5

4. **Compare the Values**:
- Both sets yield the same value of n + l = 5. When two orbitals have the same n + l value, we look at the principal quantum number (n) to determine which orbital is filled first.
- The orbital with the lower principal quantum number (n) is filled first.

5. **Conclusion**:
- Since n = 3 (for Set 2) is less than n = 5 (for Set 1), electrons will first enter the set of quantum numbers n = 3, l = 2.

### Final Answer:
Electrons will first enter the set of quantum numbers n = 3, l = 2.

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