A hydrogen atom has its electron initially in the third Bohr orbit. The electron makes a direct transition to the second orbit and emits a single photon. If the photon energy is written as N ÷ 100 eV, find N to the nearest integer.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A hydrogen atom has its electron initially in the third Bohr orbit. The electron makes a direct transition to the second orbit and emits a single photon. If the photon energy is written as N ÷ 100 eV, find N to the nearest integer.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For hydrogen, Eₙ = −13.6 ÷ n² eV. Initial energy: E₃ = −13.6 ÷ 9. Final energy: E₂ = −13.6 ÷ 4. Photon energy is the magnitude of the energy decrease: E(γ) = 13.6[(1 ÷ 4)−(1 ÷ 9)]. Now, (1 ÷ 4)−(1 ÷ 9) = 5 ÷ 36. Therefore, E(γ) = 13.6×5 ÷ 36 ≈ 1.8889 eV. Thus, E(γ) ≈ 189 ÷ 100 eV. Hence N = 189.