Bohr Model Calculator

Table of contents:
The Bohr Model was the first theory used to correctly describe the structure of hydrogen, the simplest atom. It was introduced by Niels Bohr in 1913 to show a positively charged nucleus (where the protons and neutrons reside) surrounded by an electron cloud with a negative charge. The model is similar to the position of the planets (the electrons) around the sun (the nucleus). While recent discoveries show a more accurate portrayal of the anatomy of an atom, the Bohr Model is still widely used to determine the energy levels in electrons.

The Bohr Model has four important points:

First, the electrons of an atom are in a circular orbit surrounding the nucleus. They stay in place because of Coulomb’s force. This is the force between two or more charged bodies. If these charged bodies (electrons, protons, and neutrons) have the same charge (all positive or all negative), they will repel each other. On the other hand, if they have opposite charges, they will attract each other.

Second, an electron can only have specific energies on its orbital. This is expressed in the fact that an electron’s angular momentum is restricted by different variables including the energy level of its orbital.

Third, electrons can continue to orbit without losing energy. However, the electron can only do this on a specific set of distances from the nucleus.

Lastly, electrons can jump between energy levels without absorbing electromagnetic radiation (photon). The energy of the electron is determined by the difference between its initial and final energy levels.

Keep in mind that the Bohr model is a simplified theory that describes an atom with only one electron orbiting its nucleus. These atoms are called hydrogen-like atoms because hydrogen only has one electron. However, other atoms with single electrons that orbit the nucleus at different distances also exist. So the Bohr model equation can also apply to them.

Using the Bohr Model Calculator

The Bohr Model Calculator allows you to determine the energy difference between an electron’s initial energy and its final energy in electron volts or eV. It also determines the frequency of the electron in terahertz or THz.

The calculator uses the following formula:

Change in Energy = Initial Energy Level of the Electron – Final Energy Level of the Electron = Planck’s Constant x Frequency of the Absorbed or Emitted Electromagnetic Wave

If the final energy of the electron is smaller than its initial energy, the electron will emit an electromagnetic wave. Likewise, if the final energy of the electron is larger than its initial energy, it will absorb the electromagnetic wave.

Let’s try an example:

The initial energy of a given electron is 12 eV and its final energy is 30 eV.

Using the formula:

Change in Energy = 12 eV – 30 eV = 6.62607004 × 10^-34 m2 kg/s x Frequency
Change in Energy = -18 eV = 6.62607004 × 10^-34 x Frequency
Frequency = -18 eV / 6.62607004 × 10^-34
Frequency = -4,352 THz

Since the final energy of the electron (30 eV) is larger than its initial energy (12eV), the electron will absorb the electromagnetic wave.

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