Assignment:
Calculate the visible lines that should be seen with a spectroscope. This must correspond to lines in which the final bound energy level is N = 2.
Then, compare the observed lines to the ones that I calculate.
The observed, recorded wave length lines were:
RED = 650 nanometers
TURQUOISE = 490 nanometers
VIOLET 1 = 435 nanometers
VIOLET 2 = 405 nanometers
(The lines above were observed by looking at the line spectra from hydrogen gas being placed in an electrical discharge tube.)
The energy of an electron bound to a proton for the Hydrogen atom as a function of energy level number N is given by:
E (N) = -13.6 / N2
Where E(N) is given in electron volts (eV). And that one eV = 1.6 * 10-19 Joules. This energy is negative indicating that the electron is bound to the proton by at least 13.6 eV when N = 1, and that this is the most the electron can be bound by.
Einstein proved that the energy of the photon is related to it’s frequency with:
E = h f
Where h = Planck’s constant of (6.63 * 10-34 J.sec) or (4.135 * 10-15 eV) and f is the frequency of the light being given off.
The first excited state (n=2) of the hydrogen atom has an energy of –(13.6/22) eV, or -3.40 eV.