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

According to the Bohr theory, the energy difference between two energy levels can be calculated using the formula:
ΔE = -Rhc/ni² + Rhc/nf²
where R is the Rydberg constant, h is Planck's constant, c is the speed of light, ni and nf are the initial and final energy levels (in this case, n=3 and n=5).
Plugging in the values:
ΔE = -Rhc/3² + Rhc/5² = -13.6 eV * (1.6 × 10^-19 J/eV) * (2.998 × 10^8 m/s) / 3² + 13.6 eV * (1.6 × 10^-19 J/eV) * (2.998 × 10^8 m/s) / 5²
ΔE = 1.55 × 10^-18 J, which is answer choice D.

The Bohr Theory of the Hydrogen Atom Predicts the Energy