Using eV nm, a classmate finds the photon energies of the first two Balmer lines of…
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Line spectra, the Bohr atom and the old quantum theory
Problem
Using hc=1240 eV nm, a classmate finds the photon energies of the first two Balmer lines of hydrogen: 1240/656=1.89 eV for the 656 nm line and 1240/486=2.55 eV for the 486 nm line, then argues:"Bohr's model gives the energy of each photon, so it predicts the brightness of each line. Since 2.55/1.89=1.35, the 486 nm line should appear 1.35 times as bright as the 656 nm line."In a real hydrogen discharge the 656 nm line is observed to be several times brighter than the 486 nm line. Which one of the following is the correct assessment? (a) The photon energies are miscalculated; done properly, they give the observed brightness ratio. (b) The photon energies are right, but Bohr's postulates fix only which jumps occur and with what energy, not how often a jump happens, so the model makes no prediction of brightness at all. (c) Bohr's model does predict brightness through the postulate hν=En2−En1; the disagreement shows the discharge tube is faulty. (d) Sommerfeld's rule ∮pdq=nh, applied to elliptical orbits, supplies the missing brightness prediction, so that ratio only needs a correction factor.