Energy graphs and the Bohr model

Allison Fain Fall 2021

The Main Idea

Energy graphs and the Bohr model.

This page gives a more in-depth explanation of how to use energy graphs to comprehend the Bohr model. It specifically explains how to illustrate the various aspects such as excited states and photon emissions or absorptions on the energy graphs as well as what each component corresponds to.

A Mathematical Model

The Bohr Model, as explained in more detail on the Bohr Model wiki, page depicts the atom as a small, positively charged nucleus surrounded by electrons which can only be at certain different distances from the proton to which it is bound. Energy is quantized which means that only orbits with certain radii are allowed.[1] These levels are labeled with integer N, known as quantum number, where the lowest energy state is the ground state. Beyond an energy called the ionization potential the single electron of the hydrogen atom is no longer bound to the atom. The Bohr model works well for very simple atoms such as hydrogen.

Electronic Energy levels of a Hydrogen Atom

E = K + Uelectric

1) [math]\displaystyle{ E = {\frac{mv^2}{2}} - {\frac{{\frac{1}{2}}*{\frac{1}{4π ε0}}*{\frac{me^2}{h*}}}{N^2}} }[/math]

2) [math]\displaystyle{ E = {\frac{13.6 eV}{N^2}} }[/math] where N = 1,2,3

A Computational Model

Visualize this topic given this glow script written by matter and interactions Bohr Model Glowscript [3]

Examples

Simple

This Bohr model picture helps you visualize the orbit radii of the different excited states of the hydrogen atom described in the Bohr model. It displays how the distances in orbit radii get increasingly larger. This also means that due to the fact that the distance from the center is much larger, the ionization energy is much less. [2] The Bohr model shows us that electron orbits aren't equally spaced and that as you get farther from the nucleus (as your get more energy), the spacing between these levels decreases.

]

This visualization of the orbitals in a more graphical way shows that as the distance from the center becomes larger, the ionization energy is much less. [2]

Middling

This graph explains in more detail how each level corresponds to less energy. If the energy reached zero, the electron would be free from the hydrogen nucleus because no energy is holding it on. The levels get exponentially closer as they approach the ionization energy

Difficult

When energy is added, the electron moves up to the next orbital. This is called atomic excitation. This energy is released as a photon (light energy) and the electron moves back down.

Hydrogen specifically gives of lightwaves with the wavelengths that correspond to red, glue green, and violet.

Connectedness

Though it is not related to my major, one of my favorite classes I took at Georgia Tech was Earth and Atmospheric Sciences. I found it immensely fascinating when I realized that the same ideology is used as described here as is used to determine the composition of things in space. These emission spectra can be utilized to determine the type of elements that are in stars. Without this method, we would not know what stars are composed of. The ability to study the emission spectra gives us the capabilities to understand where stars come from as well as ideas of the origins of our universe. [4]

History

Ernest Rutherford created the Rutherford Model in 1911 which consisted of a planetary-model atom. His model had flaws including the fact that he thought the electron would lose energy gradually causing it to spiral inwards. However, in 1913 Niehls Bohr proposed the Bohr Model which suggested new ideas regarding the motion of electrons. These new ideas fixed the flaws in the Rutherford Model but are oversimplifications of reality. In 1925, a more accurate model of electron motion was proposed by Werner Heisenberg called quantum mechanics. Today, the Bohr model is taught as a simplified way to understand the mechanics of electrons and can be used fairly accurately in simply elements such as hydrogen, consisting of one single electron. A more complete history can be found on the main Bohr Model page.

Spectral Lines of Hydrogen Application

[5]

See also

Bohr Model Main Page

External links

[1][1]

References

1. http://csep10.phys.utk.edu/astr162/lect/light/bohr.html

2. http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

3. http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/08-Bohr-levels

4. http://skyserver.sdss.org/dr1/en/proj/advanced/spectraltypes/lines.asp

5. https://courses.lumenlearning.com/cheminter/chapter/spectral-lines-of-hydrogen/