Bohr’s model

Introduction

Niels Henrik David Bohr, a great name in physics, was the first one who explained quantitatively the general features of the structure of hydrogen atoms and their spectrum. In 1912, Bohr joined Ernest Rutherford’s group, which was at Manchester, England, where he began to work on the atomic theory. When Bohr was working in England in 1913, he established this atomic model. 

One of the earliest models of the atom was the planetary model, as proposed by Rutherford. Although useful, it was partly inaccurate as it did not incorporate the quantum theory and could not explain why atoms produced discrete spectral lines.

To include the quantum theory, Niels Bohr proposed his own model for the structure of the atom called Bohr’s model.

The Bohr atomic model modified the older Rutherford model, so it is also called the Rutherford–Bohr model. Bohr suggested that if we make certain assumptions, the puzzle of the hydrogen spectra may be solved. Bohr used Planck’s quantization of energy concept in his theory called Bohr’s theory.

Bohr made the following assumptions in his theory:

• An atom consists of a nucleus, which contains protons and neutrons, and hence, most of the mass and positive charge is concentrated there. Electrons move around the nucleus in some circular orbits.
• The electrons revolve only in certain non-radiating orbits called stationary orbits. Bohr found that electrons can occupy those orbits where the angular momentum of a moving electron is an integral multiple of h÷2π where h is Planck’s constant and is given by the equation:

       mvr = nh÷2π

Here m is mass of electron

v  = angular velocity of electron

r = radius of the orbit 

n = principle quantum number

• The electron in an atom shifts from a lower energy level to a higher energy level by obtaining the required energy, and it moves from a higher energy level to a lower energy level by losing energy in the form of radiation. The amount of energy that an electron releases or absorbs is the difference between the two orbit’s energies.

hv = E2 – E1 = hc÷λ

Here v = frequency of the radiation

E1  and E2 are energy of lower level and higher level respectively 

The different energy levels or orbits are defined in two ways, such as 1, 2, 3, 4…or;  K, L, M, N, … shells. The orbit closest to the nucleus has the lowest energy level, and electrons in this orbit are said to be in the ground state,

• The first orbit (energy level) is defined as a K shell, and can hold up to 2 electrons.
• The second orbit (energy level) is defined as an L shell, and can hold up to 8 electrons.
• The third orbit (energy level) is defined as an M shell, and can contain up to 18 electrons.
• Similarly, the fourth orbit (energy level) is defined as an N Shell, and can hold a maximum of 32 electrons.

These orbits continue to increase similarly.

Distribution of electrons in orbits or shells:

The electronic distribution of various energy levels or orbits can be calculated by the 2n2 formula. Here, ‘n’ indicates the number of orbits. 

• The number of electrons in the K shell (i.e., the first orbit) can be calculated by 2n2= 2 x 12 = 2. Thus, the maximum number of electrons in the first orbit is 2.
• Similarly, the number of electrons in the L shell (i.e., second orbit) can be calculated by 2n2=  2 x 22 = 8. Thus, the maximum number of electrons in the second orbit is 8.

We can calculate the maximum number of electrons in each orbit or shell in the same manner.

Energy of electrons through Bohr model:

The energy that an electron has in an orbit is known as an energy level or energy state of an electron. The orbit closest to the nucleus has the lowest energy level and electrons in this orbit are said to be in the ground state. Electrons higher up are said to be in an excited state.

The electric potential energy is given as: 

E = q1q2÷4πε0r

Here q1 and q2 are charges of two different electrons

r is the distance between two electrons.

An electron found in the ground state is assigned negative energy. To move an electron further from the nucleus, energy must be imputed. Hence, energy becomes less negative as the electron is moved away. The minimum energy required to move an electron infinitely from the atom is the ionization energy.

Key points of the Bohr model:

An atom’s nucleus consists of protons and neutrons, and these have a net positive charge. Electrons have a negative charge and orbit the nucleus. Electron orbits are circular in shape, but not all the electrons orbit in the same plane (the way planets orbit around a star), which results in spheres or shells where an electron may be found. While gravity defines the orbits of planets around stars, electrostatic forces (Coulomb force) cause electrons to orbit around the nucleus. The lowest energy for an electron (which is the most stable state) is in the smallest orbit, which is very close to the nucleus. When an electron moves from one orbit to another, energy is absorbed (i.e., moving from lower to higher orbit) or emitted (i.e., moving from higher to lower orbit).

Limitations of Bohr’s model:

1. The Bohr model could not explain the spectrum of atoms containing multiple electrons.
2. Bohr’s atomic theory failed to explain the fine structure of spectral lines.
3. The Bohr atomic model of an atom failed to explain the Zeeman effect (the effect of magnetic field on the spectra of atoms).
4. Bohr’s atomic model also failed to explain the Stark effect (the effect of electric field on the spectra of atoms).
5. The Bohr model of an atom could also not explain Heisenberg’s uncertainty principle.
6. Bohr’s atomic theory has no explanation for elliptical orbits.
7. This theory failed to explain the ability of atoms to form molecules by chemical bonds.

Improvements to Bohr’s model: 

The Bohr–Sommerfeld model greatly expanded on the original Bohr model by describing elliptical electron orbits instead of circular orbits. This allowed the Bohr–Sommerfeld model to describe atomic effects, such as the Stark effect in the splitting of spectral lines. Nevertheless, the Sommerfeld model couldn’t accommodate the magnetic quantum number. In 1925, Wolfgang Pauli’s atomic model replaced the Bohr model and all those models which were based on it. Pauli’s model was based purely on quantum mechanics, so it described more phenomena than the Bohr model. In 1926, Erwin Schrodinger’s equation came with wave mechanics, leading to the modifications of Pauli’s model that are used presently.

Conclusion

This model accurately fits the quantised energy levels of the hydrogen atom and predicates only certain allowed circular orbits for the electrons.

When the electrons are more deeply bound, their energy becomes more negative as compared to the zero-energy reference state.

When the electron is put closer to the nucleus, energy is released from the system.

The energy levels obtained by Bohr closely agreed with the values calculated from the hydrogen emission spectrum but are not well applicable to other atoms