Modern Physics

# Bohr’s atomic model: characteristics and postulates

The Bohr model is a representation of the proposed atom by the Danish physicist Niels Bohr (1885-1962). The model claims that the electron travels in orbit at a fixed distance around the atomic nucleus, describing a uniform circular motion. The orbits – or energy levels, as he called them – are of different energy.

Each time the electron changes its orbit, it emits or absorbs energy in fixed quantities called “quanta”. Bohr explained the spectrum of light emitted (or absorbed) by the hydrogen atom. When an electron moves from one orbit to another towards the nucleus, energy is lost and light is emitted, with a characteristic wavelength and energy.

Bohr numbered the energy levels of the electron, considering that the closer the electron is to the nucleus, the lower its energy state. So the further the electron is from the nucleus, the higher the energy level number and therefore the higher energy state.

## Main features

The characteristics of the Bohr model are important because they set the path for the development of a more complete atomic model. The main ones are:

### It is based on other models and theories of the time.

Bohr’s model was the first to incorporate quantum theory based on Rutherford’s atomic model and ideas drawn from Albert Einstein’s photoelectric effect. In fact, Einstein and Bohr were friends.

### experimental evidence

According to this model, atoms absorb or emit radiation only when electrons bounce between allowed orbits. German physicists James Franck and Gustav Hertz obtained experimental evidence for these states in 1914.

### Electrons exist at energy levels

Electrons surround the nucleus and exist at certain energy levels, which are discrete and are described in quantum numbers.

The energy value of these levels exists as a function of a number n, called the principal quantum number, which can be calculated with equations that will be detailed below.

### No energy, no electron movement

The illustration above shows an electron that makes quantum leaps.

According to this model, without energy there is no movement of the electron from one level to another, just as without energy it is not possible to lift a dropped object or separate two magnets.

Bohr suggested the quantum as the energy required by an electron to pass from one level to another. He also established that the lowest level of energy an electron occupies is called its “ground state”. The “excited state” is a more unstable state, resulting from the passage of an electron into a higher energy orbital.

### Number of electrons in each shell

The electrons that fit into each shell are calculated with 2n 2

The chemical elements that are part of the periodic table and that are in the same column have the same electrons in the last shell. The number of elecrons in the first four layers would be 2, 8, 18 and 32.

### Electrons rotate in circular orbits without radiating energy

According to Bohr’s First Postulate, electrons describe circular orbits around the atom’s nucleus without radiating energy.

### orbits allowed

According to Bohr’s second postulate, the only orbits allowed for an electron are those for which the angular momentum L of the electron is an integer multiple of Planck’s constant. Mathematically, it is expressed like this:

### Energy emitted or absorbed in leaps

According to the third postulate, electrons emitted or absorbed energy when jumping from one orbit to another. In the jump in orbit, a photon is emitted or absorbed, whose energy is mathematically represented:

## Bohr’s atomic model postulates

Bohr continued the planetary model of the atom, in which electrons revolved around a positively charged nucleus, as did planets around the sun.

However, this model challenges one of the postulates of classical physics. According to him, a particle with an electrical charge (such as an electron) that moves in a circular path must continuously lose energy emitting electromagnetic radiation. When losing energy, the electron would have to follow a spiral until it lands in the nucleus.

Bohr then assumed that the laws of classical physics are not the most appropriate for describing the stability observed in atoms and expounded the following three postulates:

### first postulate

The electron rotates around the nucleus in orbits that draw circles, without radiating energy. In these orbits, the angular orbital momentum is constant.

For the electrons of an atom, only orbits of certain radii are allowed, corresponding to certain defined energy levels.

### second postulate

Not all orbits are possible. But once the electron is in an allowed orbit, it is in a specific, constant state of energy and does not emit energy (stationary energy orbit).

For example, in the hydrogen atom, the allowable energies for the electron are given by the following equation:

In this equation, the value -2.18 x 10–18 is the Rydberg constant for the hydrogen atom and en = quantum number can take values ​​from 1 to ∞.

The electron energies of a hydrogen atom that are generated from the above equation are negative for each of the values ​​of n. As n increases, the energy is less negative and therefore increases.

When n is large enough – for example, n = ∞ – the energy is zero and represents that the electron has been released and the atom ionized. This zero energy state harbors greater energy than negative energy states.

### third postulate

An electron can change from one stationary energy orbit to another by emitting or absorbing energy.

The energy emitted or absorbed will be equal to the difference in energy between the two states. This energy E is in the form of a photon and is given by the following equation:

E = h ν

In this equation, E is the energy (absorbed or emitted), h is Planck’s constant (its value is 6.63 x 10-34 joule-seconds [Js]) and ν is the frequency of light, whose unit is 1 / s

## Diagram of energy levels of hydrogen atoms

Bohr’s model was able to satisfactorily explain the spectrum of the hydrogen atom. For example, in the visible light wavelength range, the emission spectrum of the hydrogen atom is as follows:

Let’s see how you can calculate the frequency of some of the observed light bands; for example, the one with the color red.

Using the first equation and substituting n by 2 and 3, the results shown in the diagram are obtained.

To mean:

For n = 2, E 2 = -5.45 x 10 -19 J

For n = 3 and 3 = -2.42 x 10 -19 J

It is then possible to calculate the energy difference for the two levels:

ΔE = E 3 – E 2 = (-2.42 – (- 5.45)) x 10 – 19 = 3.43 x 10 – 19 J

According to the equation explained in the third postulate ΔE = h ν. So, you can calculate ν (frequency of light):

ν = ΔE / h

To mean:

ν = 3.43 x 10–19 J / 6.63 x 10 -34 Js

ν = 4.56 x 10 14 s -1 or 4.56 x 10 14 Hz

Where λ = c / ν, and the speed of light c = 3 x 10 8 m / s, the wavelength is given by:

λ = 6.565 x 10 – 7 m (656.5 nm)

This is the wavelength value of the red band observed in the spectrum of the hydrogen lines.

## The three main limitations of the Bohr model

1- Fits the spectrum of the hydrogen atom, but not the spectra of other atoms.

2- The undulating properties of the electron are not represented in its description as a small particle that revolves around the atomic nucleus.

3- Bohr fails to explain why classical electromagnetism does not apply to his model. That is, why electrons do not emit electromagnetic radiation when they are in a stationary orbit.

## articles of interest

Schrödinger Atomic Model.

Broglie’s atomic model.

Heisenberg Atomic Model.

Perrin atomic model.

Thomson Atomic Model.

Dalton Atomic Model.

Atomic model of Dirac Jordan.

Atomic model of Democritus.