Bohr's Model
An electron in a hydrogen atom transitions from the third energy level to the first energy level. What is the wavelength of the photon emitted during this transition? (Given: R_H = 1.097 × 10^7 m^-1)
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About This Question
- Subject
- chemistry
- Chapter
- atomic structure
- Topic
- bohr's model
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
102.6 nm
Bohr's model defines the energy of each orbit in hydrogen as E_n = -13.6/n^2 eV, and the Rydberg formula 1/λ = R_H(1/n1^2 - 1/n2^2) relates wavelength to the transition. For the transition from n=3 to n=1 (Lyman series), we substitute n1=1 and n2=3: 1/λ = 1.097 × 10^7 × (1/1 - 1/9) = 1.097 × 10^7 × (8/9) = 9.751 × 10^6 m^-1. Therefore λ = 1/(9.751 × 10^6) = 1.026 × 10^-7 m = 102.6 nm. Option 121.5 nm is incorrect because it corresponds to the n=2 to n=1 transition, not n=3 to n=1. Option 656.3 nm is the Balmer series line for n=3 to n=2, which lies in the visible region. Option 97.2 nm corresponds to n=4 to n=1 in the Lyman series. This question tests the Rydberg formula, a core JEE topic under Bohr's atomic model and spectral line series. Plausibility check: all Lyman transitions produce UV photons below 122 nm, and 102.6 nm falls correctly in the UV range, confirming the answer.
This medium difficulty chemistry question is from the chapter atomic structure, covering the topic of bohr's model. It appeared in the 2025 exam.
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