How Electrons Move in Bohr’s Model of An Atom

In 1915, a Danish physicist named Neils Bohr came up with the Bohr atomic model. He resolved the issues and constraints that arose from Rutherford’s model of an atom. 

Rutherford had discovered that the core of the atom is positively charged and encircled by electrons (negatively charged particles). He also postulated that electrons move in predictable orbits and that each orbital shell had a fixed energy level. Bohr took these aspects of Rutherford’s model and improved on them. He came up with a model that would explain the nature of electrons and the different energy levels related to them.

What is Bohr’s Model of an Atom?

• The atomic model proposed by Bohr indicates that negatively charged electrons orbit a tiny, positively charged core in fixed circular paths.  
• He found out that the energy of an electron was determined by how far it was from the nucleus. The farther away from the nucleus the electron was, the more energy it had. 
• Similarly, electrons would have less energy the closer they are situated to the nucleus.

Electron Distribution in the Orbital Shells

• The energy level of each shell can be determined with the formula 2n2, where ‘n’ is the level of the shell. Thus, 
  • The energy level of the first orbit is represented as a K-shell and can contain up to 2 electrons. 
  • The energy level of the second orbit is represented as an L-shell and can contain up to 8 electrons. 
  • The energy level of the third orbit is represented as an M-shell and can contain up to 18 electrons. 

The energy levels of each orbit increase in a similar fashion.

• The outermost shell can always only have 8 electrons (the Octet rule).

Properties of Electrons in the Bohr Atomic Model

Bohr proposed a model of an atom in 1915, where:

• Electrons orbit around the nucleus. 
• The acceleration of an electron in these orbits produces no radiation or loss of energy as required by classical electromagnetic theory. 
• Electrons can circulate stably and without radiation only on certain orbits, which are termed discrete orbits.
• Electrons can only gain or lose energy by jumping from one orbit to another. 
• They absorb or emit electromagnetic radiation with a frequency (v) that is determined by Planck’s formula.

The Behaviour of Electrons

Bohr’s model is revolutionary because the laws of traditional mechanics apply to the electron’s movement around the core only when limited by a quantum rule. 

• Bohr stated that the angular momentum of an electron in any orbit could only have specific values that are determined by the formula:

L=nh/2π

where ‘n’ is the energy level and ‘h’ is Planck’s constant. 

• The lowest n can go is 1, which gives the orbital range 0.0529 nm, also known as the Bohr range.
• After an electron reaches this orbit, it can draw no closer to the proton. Using the precise force quantum rule, Bohr determined the energies of the permitted orbits of the hydrogen molecule.

Energy of An Electron in Bohr’s Orbit:

• The energy absorbed or discharged by an atom would be based on the difference between the energy levels of the orbits based on this equation:

∆E=Ef–Ei=hv=hc

Here, ‘h’ is Planck’s constant, and Ei and Ef are the initial and final orbital energies, respectively. Since frequencies are always positive, the modulus function is used when finding the difference between any two energy levels. 

• Bohr also found the formula for finding the energies of these electron orbitals:

En=-kn2,

where ‘k’ is a steady constant of the value 2.179 × 10–18 J and ‘n’ is the energy level of the shell. 

• Substituting the formula for the energy of an orbit in the formula for ΔE gives

∆E=k1n12–1n22=hc

OR

1=khc1n12–1n22,

which is almost identical to the Rydberg formula, where R=khc. 

• Since the Rydberg equation was widely accepted at the time, this concurrence was what strengthened Bohr’s findings in the scientific community.
• Since Bohr’s model included just a solitary electron, it could likewise be applied to the single atoms like He+, Li2+, Be3+, etc., since these atoms only differ from hydrogen in their atomic charges. The energy levels of hydrogen-like atoms can be found using the formula given below, where Z is the atomic charge (+1 for hydrogen, +2 for He, +3 for Li, etc.).

En=-kZ2n2

Conclusion

Neils Bohr proposed the Bohr atomic model in 1915, based on the hydrogen (or hydrogen-like) atoms. This model resolved the drawbacks of the Rutherford model of an atom and presented some important discoveries on the nature of atoms and electrons.

Bohr applied the rules of mechanics instead of electromagnetics and discovered that an electron moved around the nucleus in a specific orbit with a very specific angular momentum. The model figured out how an atom absorbs or emits radiation when electrons on the subatomic stage soar between the discrete orbits and other orbits.