Bohr Orbit Definition

The Bohr model proposed that the electrons present in atoms revolve around the nucleus in a fixed path termed as bohr orbits or energy shells.

In atomic physics, an atom is defined by the Bohr model as a small, positively charged nucleus that is surrounded by negatively charged particles called electrons.

Overview of the Bohr Model

Niels Bohr projected the Bohr Model of the Atom in the year 1915. The Bohr Model has some drawbacks but this model is vital to study because it describes most of the accepted features of atomic theory without the high-level math of the modern version.

The Bohr Model also describes the Rydberg formula for the spectral emission lines of atomic hydrogen. Bohr model of atom described the planetary model which states that the negatively charged electrons revolve around a positively charged nucleus like the planets orbit the sun. The gravitational force of the solar system is scientifically similar to the electrical ( or Coulomb ) force between the nucleus and electrons.

The Bohr model was the modification of the earlier cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and lastly the Rutherford model (1911).

The Rydberg formula for the spectral emission lines of atomic hydrogen was successfully explained by Bohr. Apart from this, the Bohr model also explained the structure of the Rydberg formula, he also justified its experimental results in terms of fundamental physical constants.

Bohr Model of Hydrogen

The simplest example used to explain the Bohr Model is the model of a hydrogen atom (Atomic number or Z= 1) or for a hydrogen-like ion (Z > 1), in which a negatively charged particle termed as electron revolve around a positively charged nucleus. Electromagnetic energy is either absorbed or emitted when an electron jumps from one orbit to another.

Methodically, the value of the atomic radius is as follows:

r(n)=n²×r(1)

Where,

• n signifies a positive integer

• r(1) signifies the value of the smallest allowed radius for the hydrogen atom also termed as Bohr’s radius.

Important Equations

The equation used to find the Radii of Bohr’s stationary orbits is;

r_n = n² (h²ε_o/πmZe²)

• n denotes integer

• r_n denotes the radius of the nth orbit

• h denotes Planck’s constant

• ε₀ signifies the Electric constant

• m signifies the mass of the electron

• Z signifies the Atomic number of the atom

• e signifies Elementary charge

The equation used to find the velocity of Electron in Bohr’s Stationary orbit is;

v_n = (Ze²/2hε_o)(1/n)

ε₀, h, and e are the constants and for a hydrogen atom, Z or atomic number is 1 Hence, r_n α (1/n)

Total Energy of Electron in Bohr’s Stationary Orbits is;

E_n = -(me⁴/8ε₀²h²)(Z²/n²)

E_n = -13.6(Z²/n²)eV

The negative sign indicates that the electron is bound to the nucleus. The energy therefore obtained is always a negative number.

Bohr Model for Heavier Atoms

Heavier atoms comprises of more protons in the nucleus as compared to a hydrogen atom( as atomic number = 1). So, more number of electrons were required to cancel out the positive charge of these protons. Bohr stated that each electron orbit or shell could only hold a fixed number of electrons. Once this energy level is filled, then additional electrons would jump to the next level. Therefore, the Bohr model for heavier atoms explained electron shells. This model also explained some of the atomic properties of heavier atoms.

Properties of Electrons under the Bohr Model

In 1913, Bohr proposed that electrons could only have certain standard motions:

1. Electrons (negatively charged particles) present in atoms orbit the nucleus.

2. The electrons can only revolve in a certain orbit, at a discrete distance from the nucleus. These orbits are linked with certain energies and are also termed as energy shells or energy levels.

3. Electrons can only absorb or emit energy by jumping from one orbit to another orbit.

Merits of Bohr Model

1. The Bohr model was the primary model to suggest the quantization of electron orbits in atoms. Hence, it specifies an early quantum theory that also gave a way to the development of modern quantum theory. It also presented the concept of a quantum number to explain the atomic states of an atom.

2. Bohr also described the stability of atoms.

3. He described the spectrum of hydrogen and he also calculated the size of an atom.

Limitations of Bohr Model

• The Bohr Model was unable to explain the fine structure and hyperfine structure in the spectral lines.

• The Bohr atomic model theory correctly described the structure of small-sized atoms for instance – hydrogen, but for larger atoms, poor spectral predictions are attained. Therefore, Bohr failed to explain the structure of large-sized atoms.

• The Zeeman effect (which states that the spectral line usually splits into several components in the presence of a magnetic field) could not be described by Bohr.

• The Stark effect(which further states that the spectral line generally splits into fine lines in the presence of an electric field) could not be explained by Bohr.

• Bohr model of the atom was unable to predict the relative intensities of several spectral lines.

The Bohr model explained the structure of hydrogen atom and other single-electron structures. Unfortunately, he failed to explain the spectra of more complex atoms. Furthermore, the Bohr model also failed to explain why some spectral lines are more intense as compared to other lines or why some spectral lines split into numerous other lines in the presence of a magnetic or electric field.

This phenomenon of splitting of spectral lines in presence of a magnetic field is termed as the Zeeman effect and the splitting of spectral lines in presence of an electric field is termed as the stark effect. In the following decades, several theories were proposed by different scientists such as Erwin Schrödinger stated that electrons can be assumed to behave like waves as well as particles.

This further means that it is not possible to know an electron’s location in space as well as its velocity at the same time, a concept that is described by Heisenberg.