What is the ratio of the total energy of the second excited state to that of the third excited state in a hydrogen atom?
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A.
9/16
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B.
9/4
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C.
16/9
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D.
4/9
Correct Answer:
C. 16/9
Explanation:
The energy of an electron in a hydrogen atom is determined by the formula E = -13.6/n^2 eV, where n represents the principal quantum number. In this scale, the ground state is n = 1. The first excited state is n = 2, the second excited state is n = 3, and the third excited state is n = 4.
To find the ratio of the total energy of the second excited state (E3) to the third excited state (E4): - The energy of the second excited state (n = 3) is proportional to 1/3^2, which is 1/9.
- The energy of the third excited state (n = 4) is proportional to 1/4^2, which is 1/16.The ratio E3 / E4 is calculated as (1/9) / (1/16), which simplifies to 16/9. Therefore, the correct option is C.
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