The ratio of the energies of the hydrogen atom in the first and the second excited states is
Correct answer: D. 9/4
- A. 1/4:
- B. 4/9
- C. 4
- D. 9/4
Explanation
D is the right option Here's why:Following the formula E = -R_H / n², we calculated the energy levels (E_2 and E_3) for the two states and divided them:E_2 (first excited state): -R_H / 4 (negative sign indicates bound state)E_3 (second excited state): -R_H / 9Ratio = E_2 / E_3 = (-R_H / 4) / (-R_H / 9) = 9/4Since R_H is a constant, it cancels out, leaving us with the correct ratio of 9/4. The first excited state has a higher absolute value of energy (less negative) compared to the second excited state.
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