Bohr’s model

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

One of the earliest models of the atom was the planetary model proposed by Rutherford; although helpful, it was partly inaccurate because it did not incorporate the quantum theory and could not explain why atoms produced discrete lines of spectra.

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

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

Bohr made the following assumptions in his theory:

• (a)An atom consists of a nucleus that contains protons and neutrons, and hence most of the mass and positive charge is concentrated. Electrons move around the nucleus in some circular orbits.
• (b)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.

       mvr = nh/2π

• (c)The electron in an atom shifts from a lower energy level to a higher energy level by obtaining the required energy and an electron moves from higher energy level to lower energy level by losing energy in the form of radiation and vice versa. The amount of energy which an electron releases or absorbs is the difference in the energies of the two orbits.

hv = E2 – E1 = hc/λ

The different energy levels or orbits are defined in two ways like  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 it can hold up to 2 electrons.
• The second orbit (energy level) is defined as an L shell, and it can hold up to 8 electrons.
• The third orbit (energy level) is defined as an M shell containing 18 electrons.
• Similarly, the fourth orbit (energy level) is defined as N Shell, and it can contain a maximum of 32 electrons.

These orbits continue to increase similarly.

Distribution of Electrons in Orbits

According to Bohr’s Atomic model, the number of electrons that an orbit or shell can hold can be calculated using the formula: 2n2. Note- ‘n’ is the number of the orbit or shell. For K-shell n=1, for L-shell n=2, for M-shell n=3, and so on.

The K-shell can hold a maximum of 2 electrons, the L-shell can hold a maximum of 8 electrons, and so on.

The energy of electrons through Bohr model:

An electron’s energy at some orbit is known as the electron’s energy level or energy state. 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 excited.

The electric potential energy is given as 

E = q1q2/4πε0r

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

Limitations of Bohr’s Model:

1. The Bohr model could not explain the spectrum of atoms containing more than 1 electron or multi 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 atomic model of an atom also failed to explain the stark effect (which is the effect of electric field on the spectra of atoms)
5. The Bohr model of an atom also could 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.

Conclusion

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

When the electrons come more deeply bound, their energy becomes more damaging than 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 agree with the values calculated from the hydrogen emission spectrum but are not applied well to other atoms. Bohr’s model is fundamentally incorrect. Still, it is essential historically because it anticipated our current theory of atomic structure.