Bohr’s Theory of Hydrogen-Like Atoms

Rutherford’s planetary model of the atom was immediately adopted by Niels Bohr (1885–1962), a prominent Danish physicist. Bohr felt convinced of its veracity and spent a year at Rutherford’s laboratory in 1912. He began publishing his idea of the simplest atom, hydrogen, based on the planetary model of the atom in 1913, after returning to Copenhagen. Many questions about atomic properties have been asked for decades. Much was known about atoms, from their sizes to their spectra, but little had been explained in terms of physical rules. Bohr’s model of the hydrogen atom clarified the atomic spectrum of hydrogen and created new, widely applicable quantum mechanics principles.

Bohr’s Solution for Hydrogen

Using fundamental physics, the planetary model of the atom, and some very important new proposals, Bohr established the formula for the hydrogen spectrum. His first proposal is that only certain orbits are permitted: we refer to electron orbits in atoms as quantised. Each orbit has distinct energy, and electrons can absorb energy to travel to a higher orbit or emit energy to fall to a lower orbit. The energy absorbed or released is quantised when the orbits, resulting in discrete spectra.

The major mechanisms of moving energy into and out of atoms are photon absorption and emission. The photons’ energies are quantised, and their energy is calculated as the change in energy of the electron as it goes from one orbit to the next. It is written as ΔE = hf = Ei – Ef in equation form.

Five concentric rings depict the orbits of Bohr’s correspondence principle planetary model of an atom. From the innermost to the outermost circles, the radii of the circles grow. Labels E sub one, E sub-two, and up to E sub, I are marked on the circles.

The orbits of the electrons are quantised in Bohr’s modified planetary model of the atom. Only a limited number of orbits are permitted, explaining why atomic spectra are discrete (quantised). The energy taken away from an atom by a photon is quantised and comes from an electron dropping from one allowable orbit. It is also true for photon absorption at the atomic level.

The energy difference between the starting and final orbits is ΔE, and the energy of the absorbed or emitted photon is hf. Energy is involved in shifting orbits, which is rational (predicted from our everyday experience). To climb to a higher orbit, the space shuttle, for example, requires an explosion of energy. The quantisation of atomic orbits, on the other hand, is not expected. On the other hand, satellites and planets can have an orbit if they have enough energy.

Properties of Electrons under the Bohr Model

Bohr proposed in 1913 that electrons could only move in particular classical ways:

• Atomic electrons orbit the nucleus.
• Only specific orbits (named “stationary orbits” by Bohr) at a fixed range of distances from the nucleus allow electrons to orbit stably without radiating. These orbits, also known as energy shells or energy levels, are connected with specific energies. The acceleration of an electron in these orbits does not cause radiation or energy loss, as required by classical electromagnetic theory.
• Electrons can only gain or lose energy by jumping from one authorised orbit to another, absorbing or imparting electromagnetic radiation at a frequency (v) set by the energy difference between the levels, according to the Planck relation.

Triumphs and Limits of the Bohr Theory

No one had ever been able to accomplish what Bohr had. He not only explained the hydrogen spectrum, but he also properly computed the atom’s size using simple physics. Some of his concepts can be applied to a wide range of situations. All atoms and molecules have quantised electron orbital energies. The electrons do not flow into the nucleus as expected by conventional wisdom. These are significant achievements.

However, Bohr’s model of the hydrogen atom has limitations. It can’t be used on multielectron atoms, even if they’re as simple as helium atoms with two electrons. The model proposed by Bohr is classified as semiclassical. The orbits are quantised (nonclassical), although basic circular trajectories are assumed (classical). It became obvious as quantum mechanics progressed that there are no well-defined orbits but rather clouds of probability. According to Bohr’s theory of hypothesis, when viewed attentively, some spectral lines are doublets (split into two). Bohr took significant steps forward to pursue knowledge, laying the groundwork for all subsequent atomic physics.

Conclusion

A hydrogen-like atom consists of a positively charged nucleus and an electron in a stable circular orbit around the nucleus. By incorporating ideas from the recently developing Quantum theory, Bohr’s theory model of the hydrogen atom aims to fill in some of the gaps identified by Rutherford’s model. Bohr proposed that electrons in an atom might orbit in stable orbits without producing radiant energy.