Question:
As the quantum number increases, the difference in energy between consecutive energy levels:
As the quantum number increases, the difference in energy between consecutive energy levels:
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Energy levels get closer as quantum number increases; higher levels are more densely spaced.
Updated On: Jul 18, 2026
- Remains the same
- Increases
- Decreases
- Sometimes increases and sometimes decreases
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The Correct Option is C
Solution and Explanation
Step 1: Recall energy levels in hydrogen-like atoms.
\[ E_n = - \frac{13.6 \, \text{eV}}{n^2} \]
Step 2: Find difference between consecutive levels.
\[ \Delta E = E_{n+1} - E_n = - \frac{13.6}{(n+1)^2} + \frac{13.6}{n^2} \]
Step 3: Simplify.
\[ \Delta E = 13.6 \left( \frac{1}{n^2} - \frac{1}{(n+1)^2} \right) \]
Step 4: Analyze behavior as \(n\) increases.
As \(n\) increases, \(\frac{1}{n^2} - \frac{1}{(n+1)^2}\) decreases.
Step 5: Conclusion.
Hence, the energy difference between consecutive levels decreases with increasing quantum number.
Step 6: Final answer.
\[ \boxed{\text{Decreases}} \]
\[ E_n = - \frac{13.6 \, \text{eV}}{n^2} \]
Step 2: Find difference between consecutive levels.
\[ \Delta E = E_{n+1} - E_n = - \frac{13.6}{(n+1)^2} + \frac{13.6}{n^2} \]
Step 3: Simplify.
\[ \Delta E = 13.6 \left( \frac{1}{n^2} - \frac{1}{(n+1)^2} \right) \]
Step 4: Analyze behavior as \(n\) increases.
As \(n\) increases, \(\frac{1}{n^2} - \frac{1}{(n+1)^2}\) decreases.
Step 5: Conclusion.
Hence, the energy difference between consecutive levels decreases with increasing quantum number.
Step 6: Final answer.
\[ \boxed{\text{Decreases}} \]
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