The Bohr theory of the hydrogen atom predicts the energy difference (in J) between the n = 3 and the n = 5 state to be A) 8.72 × 10^-20 J. B) 1.36 × 10^-19 J. C) 2.42 × 10^-19 J. D) 1.55 × 10^-19 J. E) 1.09 × 10^-18 J.

Question

Quizplus · Accepted Answer

The energy difference between two energy levels in the Bohr model is given by the formula ΔE = -Rh[(1/n₂²) - (1/n₁²)], where Rh is the Rydberg constant (2.18 x 10^-18 J), and n₁ and n₂ are the initial and final energy levels, respectively. Substituting n₁ = 3 and n₂ = 5, we get:
ΔE = -Rh[(1/5²) - (1/3²)] = 1.55 x 10^-19 J. Therefore, the correct answer is option D.

The Bohr Theory of the Hydrogen Atom Predicts the Energy