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In the Bohr model of hydrogen, what is the ratio of the energy gap between the 1st and 2nd orbits to the energy gap between the 2nd and 3rd orbits?

1. 1/2
2. 1/3
3. 4/9
4. 27/5

Correct answer: 27/5

Solution

Delta_E(1 to 2) = 13.6*(1 - 1/4) = 13.6*3/4. Delta_E(2 to 3) = 13.6*(1/4 - 1/9) = 13.6*5/36. Ratio = (3/4)/(5/36) = 27/5.

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