How does the energy gap between successive energy levels in an atom vary from low to high n values?

Options

A. All energy gaps are the same
B. The energy gap decreases as n increases
C. The energ gap increases as n increases
D. the energy gap changes unpredictable as n increases

Explanation

To understand how the energy gap between successive energy levels in an atom varies from low to high n values, we can break down the explanation into several steps:

### Step-by-Step Solution

1. **Understanding Energy Levels**:
- Atoms have distinct energy levels, denoted by the principal quantum number \( n \). Each energy level corresponds to a shell around the nucleus where electrons can reside.

2. **Energy Gap Definition**:
- The energy gap refers to the difference in energy between two successive energy levels (for example, between \( n=1 \) and \( n=2 \), or \( n=2 \) and \( n=3 \)).

3. **Behavior of Energy Gaps with Increasing n**:
- As \( n \) increases (moving to higher energy levels), the energy gap between successive levels decreases. This means that the difference in energy between, say, the second and third energy levels is greater than the difference between the third and fourth energy levels.

4. **Reason for Decreasing Energy Gaps**:
- The decrease in energy gaps as \( n \) increases can be attributed to the effective nuclear charge (\( Z_{eff} \)). As we move to higher energy levels, the electrons are further away from the nucleus, and the shielding effect from inner electrons becomes more significant.
- This results in a higher effective nuclear charge felt by the outer electrons, which causes them to be more attracted to the nucleus, thereby reducing the energy difference between the levels.

5. **Conclusion**:
- Therefore, the correct statement is that the energy gap between successive energy levels decreases as \( n \) increases.

### Final Answer:
The energy gap between successive energy levels in an atom decreases as the principal quantum number \( n \) increases.

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