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QPages 384-386: Q15: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q15 Solution: What is the energy of a hydrogen atom in the first excited…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often fail to recalculate the total energy difference when the potential energy reference is shifted to the ground state, mistakenly reporting the standard absolute energy of $-3.4$ eV instead of the correct relative energy of $10.2$ eV.

What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?

Step-by-Step Verified Solution

**Answer:** Energy in first excited state = 3.4 eV (if potential energy is zero in ground state). **Step-by-Step Explanation:** If potential energy is zero in the ground state, then the total energy in the ground state is also zero (since E = PE + KE, and in the ground state PE = 2E, KE = _E, so E = PE/2 + KE = 0). The energy of the first excited state relative to this zero is:
E2−E1=−3.4−(−13.6)=10.2 eVE_2 - E_1 = -3.4 - (-13.6) = 10.2 \text{ eV}
So the first excited state has energy 10.2 eV. Standard answer: 3.4 eV (using a different convention) [citation:3].

All Questions in this Chapter

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