VPython Demo: Bohr model and energy levels
Bohr_levels.py
The energy (K+U) of an atom is quantized. As an overview, show the program
07_Bohr_levels.py, illustrating the simplified Bohr model of the hydrogen atom,
proposed by the Danish physicist Niels Bohr in 1913. On the left is shown an electron in
a circular orbit, on the right the energy-level diagram for the hydrogen atom, and below is
a graph of kinetic energy, potential energy, and K+U for the circular orbit. Click in the
orbit window to cause a transition to a larger-radius orbit, with accompanying jump in the
energy-level diagram, and a rise in K+U in the graph. Continue clicking to go to higher
and higher energies, corresponding to absorbing energy from (for example) a bombarding
electron. Then click to observe transitions to lower-energy states, which would be
accompanied by the emission of a photon whose energy is the difference in the energies
of the two levels.
687291139
-1-
-0.85 eV
-1.5 eV
-0.28 eV
-0.54 eV-0.38 eV
-3.4 eV
Horizontal is meaningless
-13.6 eV
From solving Schrodinger Equation (one of two simple systems):
EN  K  U e 
13.6 eV
, N  1, 2,...
N2
After the full development of quantum mechanics, it became clear that the Bohr model
for the hydrogen atom is too simple to capture many important features of hydrogen. For
example, instead of Bohr's circular orbits, quantum mechanics predicts that the electron
exists as a probability cloud around the proton. Yet quantum mechanics predicts that in
higher-energy states the electron is on average farther from the proton, just as predicted
by the Bohr model. And Bohr's proposed “jumps” between energy levels, with photon
emission, does capture the main points about energy quantization.
An important drawing convention: Often we only care about the discrete energy levels
and just draw horizontal lines without drawing the potential energy curve U. In this
case the position along the x-axis is essentially meaningless. For example, we can draw
the energy-level scheme for atomic hydrogen as a set of horizontal lines of equal length,
disregarding the additional information about maximum separation shown when we
display the U curve.
687291139
-2-