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 ⁻²⁰J. B)1.36 × 10 ⁻¹⁹J. C)2.42 × 10 ⁻¹⁹J. D)1.55 × 10 ⁻¹⁹J. E)1.09 × 10 ⁻¹⁸J.

Question

Quizplus · Accepted Answer

The energy difference between two energy levels in the hydrogen atom is given by the formula:
ΔE = -Rh[(1/nf^2) - (1/ni^2)]
where Rh is the Rydberg constant, nf and ni are the final and initial energy levels, respectively.
For this problem, we have:
ΔE = -Rh[(1/5^2) - (1/3^2)]
Substituting the values of Rh and simplifying, we get:
ΔE = 1.55 × 10^-19 J

The Bohr Theory of the Hydrogen Atom Predicts the Energy