How did Neil Bohr explained the Stability of Atom?

Bohr model of the atom was explained by Neil Bohr in 1915. It came into existence with the modification of Rutherford’s model of the atom. Rutherford’s model introduces the nuclear model of the atom, in which he explained that a nucleus (positively charged) is surrounded by negatively charged electrons. Bohr modified his atomic structure model by explaining that electrons move in fixed orbitals (shells) and not anywhere in between and he also explained that each orbit (shell) has fixed energy levels. Rutherford basically explained the nucleus of an atom and Bohr modified that model into electrons and energy level. Bohr model consists of a small nucleus (positively charged) surrounded by negative electrons moving around the nucleus in orbits. Bohr found that electron located away from nucleus has more energy, and electrons close to the nucleus have less energy.

Neil Bohr proposed the stability of the atoms through the concept of the revolution of electrons in different energy levels. The change in energy of an electron occurs when it jumps from a lower energy level to a higher energy level or vice versa.

Postulates of Bohr Model of an atom

• In an atom, electrons (negatively charged) revolve around a positively charged nucleus in a definite circular path called orbits or shells.
• Each orbit or shell has fixed energy & these circular orbits are known as orbital shells.
• The energy levels are represented by an integer (n = 1, 2, 3…) known as a quantum number. This range of quantum numbers starts from the nucleus side with n=1 having the lowest energy level. The orbits n=1, 2, 3, 4… assigned as K, L, M, N…. shells and when the electron attains the lowest energy level, it is said to be in the ground state.
• The electron in an atom moves from a lower energy level to a higher energy level by gaining the required energy and the electron moves from a higher energy level to a lower energy level by losing energy.

Atomic models

Various atomic models were proposed to show the arrangements and distribution of particles [electrons, protons and neutrons] within an atom

1. Thomson’s Atomic Model: The first simple model of the atom was proposed by J.J Thomson. according to Thomson, an atom is a positively charged uniform sphere of radius 10^-8 cm in which electrons are embedded in such a way that the negative charge is equal to the positive charge.  This model is also called the plum pudding model and watermelon model.
2. Rutherford’s Atomic model (1912): This model was based upon ∝-particle scattering experiment. The ∝-particle scattering experiments performed by rutherfords are concerned with the discovery of the nucleus.
3. Neils Bohr’s Atomic model(1913): Neils Bohrs proposed this atomic model which is based upon Planck’s quantum theory of radiation.

Planck’s quantum theory

This theory was proposed by Max Planck. The main postulates of this theory are as follows:

• The energy emitted or absorbed by the atoms and molecules will be in the form of discrete packets of energy called quanta.
• The energy of quanta (E) is proportional to its frequency (v).

E ∝ v or  E=hv

where h is the Planck’s Constant (6.626 × 10^-34 Js)

• The energy of quanta is quantised, thus, E=hv.

Bohr’s Atomic Model(1913)  

The electron in an atom revolve around the nucleus only in certain selected circular paths called orbits each orbit have a definite amount of energy. electron in the particular orbits does not lose or gain energy. only those orbits are permitted in which the angular momentum (mvr) of the electron is the whole number multiple of h/2π (‘h’ is a Planck’s constant i.e. mvr=nh/2π  where n=1,2,3……….)

the energy is emitted when an electron jumps from a higher energy level and energy is absorbed when an electron jumps from a lower energy level to higher energy levels. the frequency of radiation absorbed or emitted when the transition occurs between two different energy levels or states is given by                                                                 v = ΔE/h = (E₂-E₁)/h

where E₁ and E₂ are the energies of lower and higher energy states.

• The energy of electron residing in a particular energy level(n) is given by,

E_n = -21.8× 10^-12×Z²/n² erg atom^-1 =  -13.6 × z²/n² eV atom^-1

and 

E_n =  hc/λ_n = -R_H (1/n₂² -1/n₁¹)Z²

• Radius of nth orbit (r_n) = 0.53n²/Z  Å.
• Velocity of electron in nth orbit = 2.18×10⁸ Z / n  cm/s.

Achievements Of Bohr’s  Model Of Atom

Bohr’s theory has explained the stability of an atom:: According to Bohr’s theory, the electron present in a particular energy level cannot lose the energy of its own it can do so when jumps from a higher energy level to a lower energy level. Thus, in its stationary state, the electrons keep on revolving in the same circular orbit and do not come closer to the nucleus as suspected by the radiation theory. thus accounts for the stability of atoms.

• Bohr’s theory has been used to derive Balmer’s formulae: According to Bohr’s theory, 

E_n=-R_H(1/n²)  and  ΔE=E_F-E_i  

where E_f is the energy associated with the final state while E_i is the energy of the initial state. 

ΔE = (-R_H/n_f²) – (-R_H/n_i²)   or   R_H(1/n_i²  –  1/n_f²) 

Here n_f and n_i  represent final and initial electron orbits

ΔE =(21.8 × 10^-18 J ) (1/n_i²  –  1/n_f²)

• The frequency (v) for the absorption and emission of the photon can be calculated as follows:

v =  ΔE/h  =  R_H/h × (1/n_i²  –  1/n_f²) 

   = 3.29 × 10¹⁵ (1/n_i² -1/n_f²) s^-1                                                                                                                                                                

• Bohr’s theory has helped in calculating the energy of electrons in the hydrogen atom and one electron species: Based upon the postulates of Bohr’s theory, it is possible to calculate the energy of the hydrogen electron and also one-electron species (He⁺, Li²⁺ etc.). The mathematical expression for the energy in the nth orbit is, 

E_n = -2π² k²m_e e⁴ z² /  n² h²

Bohr’s Atomic model

Limitations of Bohr’s Model of an Atom

• Bohr’s model of atoms failed to explain the Zeeman Effect (effect of magnetic field on spectra of atoms).
• It also failed to explain the Stark effect (effect of electric field on spectra of atoms).
• It disobeys Heisenberg Uncertainty Principle.
• It could not explain spectra obtained from larger atoms.

Sample Questions

Question 1: What are the features of Bohr’s atomic model?

Answer:  

Salient features of Bohr’s atomic model are: Electrons revolve around the nucleus in stable orbits without emission of radiant energy. An orbit or energy level is assigned as K, L, M, N shells. An electron emits or absorbs energy when it jumps from one orbit or energy level to another.  

Question 2: The maximum number of emission lines noticed when the electron jumps from the nth shell to the ground state is?

Answer: 

The maximum number of emission lines noticed when the electron jumps from the nth shell to the ground state due to all possible jumps is n (n-1)/2.

Question 3: Protons and neutrons are bound in a nucleus by?

Answer: 

Protons and neutrons are bound in a nucleus by short-range ‘strong interaction’ force.

Question 4: Neutrons are present in all atoms except?

Answer: 

Neutrons are present in all atoms except hydrogen (H). Hydrogen is the lightest element. It exists as the stable isotope Deuterium and the unstable, radioactive isotope Tritium. Hydrogen (H) is a colourless, odourless, tasteless, flammable gas.            

Question 5: The atom of an element contains 2 electrons in its M shell. What the element is?

Answer: 

The atom of an element contains 2 electrons in its M shell. The element is Magnesium (Mg).

Question 6: How to calculate the number of electrons in an atom?

Answer: 

The number of electrons is equal to the atomic number of an atom. e.g. The atomic number of O is 8 and numbers of electrons present in oxygen atoms are also 8.