Physics · University
Infinite-well energy ratio
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
Method and conditions
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
En ∝ n²/L²
Worked examples
For the same particle in ideal infinite wells, compare state n=8 at width 3L with state n=9 at width L. Find E(8,3L)/E(9,L). Round the final result to 4 decimal places if needed.
The mass and constants cancel. The ratio is (8²/3²)/9².
0.0878
For the same particle in ideal infinite wells, compare state n=1 at width 7L with state n=5 at width L. Find E(1,7L)/E(5,L). Round the final result to 4 decimal places if needed.
The mass and constants cancel. The ratio is (1²/7²)/5².
0.0008
Try it
For the same particle in ideal infinite wells, compare state n=1 at width 4L with state n=12 at width L. Find E(1,4L)/E(12,L). Round the final result to 4 decimal places if needed.
For the same particle in ideal infinite wells, compare state n=1 at width 3L with state n=12 at width L. Find E(1,3L)/E(12,L). Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0.0004
The mass and constants cancel. The ratio is (1²/4²)/12².
- 0.0008
The mass and constants cancel. The ratio is (1²/3²)/12².
Further reading and review references
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