Science, Tech, Math › Science Bohr Atom Energy Change Example Problem Finding Energy Change of an Electron in a Bohr Atom Share Flipboard Email Print Getty Images / lpsumpix Science Chemistry Basics Chemical Laws Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Todd Helmenstine Todd Helmenstine is a science writer and illustrator who has taught physics and math at the college level. He holds bachelor's degrees in both physics and mathematics. our editorial process Todd Helmenstine Updated August 20, 2018 This example problem demonstrates how to find the energy change that corresponds to a change between energy levels of a Bohr atom. According to the Bohr model, an atom consists of a small positive charged nucleus that is orbited by negatively charged electrons. The energy of an electron's orbit is determined by the size of the orbit, with the lowest energy found in the smallest, innermost orbit. When an electron moves from one orbit to another, energy is absorbed or released. The Rydberg formula is used to find the atom energy change. Most Bohr atom problems deal with hydrogen because it is the simplest atom and the easiest to use for calculations. Bohr Atom Problem What is the energy change when an electron drops from the n=3 energy state to the 𝑛=1 energy state in a hydrogen atom? Solution: E = hν = hc/λ According to the Rydberg Formula 1/λ = R(Z2/n2) whereR = 1.097 x 107 m-1Z = Atomic number of the atom (Z=1 for hydrogen) Combine These Formulas E = hcR(Z2/n2)h = 6.626 x 10-34 J·sc = 3 x 108 m/secR = 1.097 x 107 m-1hcR = 6.626 x 10-34 J·s x 3 x 108 m/sec x 1.097 x 107 m-1hcR = 2.18 x 10-18 JE = 2.18 x 10-18 J(Z2/n2)En=3E = 2.18 x 10-18 J(12/32)E = 2.18 x 10-18 J(1/9)E = 2.42 x 10-19 JEn=1E = 2.18 x 10-18 J(12/12)E = 2.18 x 10-18 JΔE = En=3 - En=1ΔE = 2.42 x 10-19 J - 2.18 x 10-18 JΔE = -1.938 x 10-18 J Answer The energy change when an electron in the n=3 energy state to the n=1 energy state of a hydrogen atom is -1.938 x 10-18 J.