According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is A) 2.18 × 10^-18 J. B) 1.64 × 10^-18 J. C) 5.45 × 10^-19 J. D) 3.03 × 10^-19 J. E) None of these choices are correct.

Question

Quizplus · Accepted Answer

The minimum energy required to ionize a hydrogen atom from the n = 2 state is equal to the difference in energy between the n = 2 and n = ∞ states. According to the Bohr theory, the energy of a hydrogen atom in the nth state is given by:

E = -13.6/n^2 eV

Converting this to joules and using n = 2 for the initial state and n = ∞ for the final state, we get:

E = (-13.6/2^2 + 13.6/∞^2) × 1.602 × 10^-19 J/eV
E = (13.6/4) × 1.602 × 10^-19 J
E = 3.40 × 10^-19 J

Therefore, the minimum energy required to ionize a hydrogen atom from the n = 2 state is 3.40 × 10^-19 J, which is closest to option C.

According to the Bohr Theory of the Hydrogen Atom, the Minimum