5.1. Light http://www.ck12.org
Bohr’s model explains the spectral lines of the hydrogen atomic emission spectrum. While the electron of the atom
remains in the ground state, its energy is unchanged. When the atom absorbs one or more quanta of energy, the
electron moves from the ground state orbit to an excited state orbit that is farther away. Energy levels are designated
with the variablen. The ground state isn= 1, the first excited state isn= 2, and so on. The energy that is gained by
the atom is equal to the difference in energy between the two energy levels. When the atom relaxes back to a lower
energy state, it releases energy that is again equal to the difference in energy between the two orbits (Figure5.10).
FIGURE 5.10
Bohr model of the atom: an electron is shown transitioning from then= 3
energy level to then= 2 energy level. The photon of light that is emitted
has a frequency that corresponds to the difference in energy between the
two levels.The change in energy,∆E, is converted from potential energy within the atom to emitted light, which has a frequency
that can be determined using the equation∆E=hν. Recall that the atomic emission spectrum of hydrogen has
spectral lines at four different visible frequencies, but these lines are not equally spaced. This can be explained by
the Bohr model if we assume that the energies of various electron orbits are also not equally spaced. As the electron
gets farther and farther from the nucleus, the differences in energy between successive orbits get smaller and smaller.
Based on the wavelengths of the spectral lines, Bohr was able to calculate the energies that the hydrogen electron
would have in each of its allowed energy levels. He then mathematically showed which energy level transitions
corresponded to the spectral lines in the atomic emission spectrum (Figure5.11).
FIGURE 5.11
This electron energy level diagram for
the hydrogen atom shows various pos-
sible electron transitions, some of which
are classified as the Lyman, Balmer,
Paschen, and Brackett series. Bohr’s
atomic model mathematically accounted
for the atomic emission spectrum of hy-
drogen. The four visible lines in the
atomic emission spectrum of hydrogen
correspond to the first four lines in the
Balmer series; all other transitions pro-
duce photons that are outside of the visi-
ble spectrum.