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Suppose potential energy between particle A and B at separation r is given by U = k ln r, where k is constant. For such hypothetical system, find the ratio of energy difference between energy
levels (n = 1 and n = 2) and (n = 2 and n = 4) (The energy of a particle in nth level is –13.6/n2)
Correct answer is '1'. Can you explain this answer?
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Suppose potential energy between particle A and B at separation r is g...
Energy Levels and Energy Difference Calculation
- Given potential energy: U = k ln r
- Energy of a particle in nth level: En = 13.6/n^2

Energy Difference between n=1 and n=2
- Energy at n=1: E1 = 13.6/1^2 = 13.6
- Energy at n=2: E2 = 13.6/2^2 = 3.4
- Energy difference: ΔE(1-2) = E2 - E1 = 3.4 - 13.6 = -10.2

Energy Difference between n=2 and n=4
- Energy at n=2: E2 = 13.6/2^2 = 3.4
- Energy at n=4: E4 = 13.6/4^2 = 0.85
- Energy difference: ΔE(2-4) = E4 - E2 = 0.85 - 3.4 = -2.55

Ratio of Energy Differences
- Ratio = ΔE(1-2) / ΔE(2-4)
- Ratio = (-10.2) / (-2.55) = 4
Therefore, the ratio of energy difference between energy levels (n=1 and n=2) and (n=2 and n=4) is 4.
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Suppose potential energy between particle A and B at separation r is given by U = k ln r, where k is constant. For such hypothetical system, find the ratio of energy difference between energylevels (n = 1 and n = 2) and (n = 2 and n = 4) (The energy of a particle in nth level is 13.6/n2)Correct answer is '1'. Can you explain this answer?
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