A wavelength of 434.1 nm is emitted by the hydrogen atoms in a high-voltage disc
ID: 2202901 • Letter: A
Question
A wavelength of 434.1 nm is emitted by the hydrogen atoms in a high-voltage discharge tube. What are the (a) initial and (b) final values of the quantum number n for the energy level transition that produces this wavelength?
(a) Number Units No unitsExplanation / Answer
One of the Balmer series, level 5 (initial) to level 2 (final). This comes from a data generator I made that spits out all the transition energies over a specified range of N-values. If one chose to start from scratch (going from specified wavelength to N-values), one would first find the photon energy: Ep = hc/lambda = 4.5760090E-19 J, 2.8561204 eV and then exhaustively search the values of N1 and N2 (>N1) to find a transition energy E = E(ground)*Z^2*(1/N1^2-1/N2^2) close to Ep (where E(ground) = 2.17987197E-18 J-N^2, 13.60569193 eV-N^2). One quickly finds that N1=3 is starting too high, since E(3) = -2.442E-19 J, not negative enough for any downward transition to it to have sufficient energy. However E(2) = -5.450E-19 J, a sufficient value, so the search starts here and thus is blessedly short.