Bohr Atom Energy Level Example Problem

This example problem demonstrates how to find the energy that corresponds to an energy level of a Bohr atom. Problem: What is the energy of an electron in the 3 energy state of a hydrogen atom? Solution: E hÃŽ ½ hc/ÃŽ » According to the Rydberg formula: 1/ÃŽ » R(Z2/n2) where R 1.097 x 107 m-1Z Atomic number of the atom (Z1 for hydrogen) Combine these formulas: E hcR(Z2/n2) h 6.626 x 10-34 JÂ ·sc 3 x 108 m/secR 1.097 x 107 m-1 hcR 6.626 x 10-34 JÂ ·s x 3 x 108 m/sec x 1.097 x 107 m-1hcR 2.18 x 10-18 J E 2.18 x 10-18 J(Z2/n2) E 2.18 x 10-18 J(12/32)E 2.18 x 10-18 J(1/9)E 2.42 x 10-19 J Answer: The energy of an electron in the n3 energy state of a hydrogen atom is 2.42 x 10-19 J.