Introduction

In this chapter, we will study various atomic models. Initially, J.J. Thomson proposed an atomic model in which he thought of as electrons embedded in between protons. In 1911, his student Earnest Rutherford proposed a nuclear model, on the basis of a scattering experiment. In spite of strong experimental evidence, Rutherford’s model of the atom was rejected on the ground of the classical theory of electromagnetism.

So in order to rectify the shortcomings of Rutherford’s model, in 1913, Niels Bohr combined the classical and early quantum concepts of Einstein and Plank to explain the stability of an atom.

Thomson Model

According to Thomson, “An atom consists of positively charged matter, into which negatively charged particles are embedded randomly”. But this model did not last long as it could not explain the observations of Rutherford’s alpha-particle scattering experiment.

Alpha-Particle Scattering

In 1911, Rutherford, along with his assistants, H. Geiger and E. Marsden, performed the Alpha Particle scattering experiment, which led to the birth of the ‘nuclear model of an atom’.

They took a thin gold foil having a thickness of 2.1×10^-7 m and placed it in the center of a rotatable detector made of zinc sulfide and a microscope. Then, they directed a beam of 5.5MeV alpha particles emitted from a radioactive source at the foil. Lead bricks collimated these alpha particles as they passed through them.

After hitting the foil, the scattering of these alpha particles could be studied by the brief flashes on the screen. Rutherford and his team expected to learn more about the structure of the atom from the results of this experiment.

Observations

Here is what they found:

1. Most of the alpha particles passed through the foil without suffering any collisions
2. Around 1 in 8000 alpha particles deflected by more than 90^o

Rutherford’s Nuclear Model

In 1912, Rutherford proposed his nuclear model of the atom. It is also known as Rutherford’s planetary model of the atom. Salient features of Rutherford’s atom model are as follows :

1. Every atom consists of a tiny central core, named nucleus, in which the entire positive charge and the almost whole mass of the atom are concentrated. The size of the nucleus is typically 10^-4 times the size of an atom.
2. Most of an atom is empty space.
3. In free space around the nucleus, electrons would be moving in orbits just as the planets do around the sun. The centripetal force needed for the orbital motion of electrons is provided by electrostatic attractive forced experience by electrons due to a positively charged nucleus.
4. An atom as a whole is electrically neutral. Thus, the total positive charge of the nucleus is exactly equal to the total negative charge of all the electrons orbiting in an atom.

Bohr Model of the Hydrogen Atom

It was Niels Bohr (1885-1962) who used the concept of quantized energy and explained the model of a hydrogen atom in 1913. Bohr combined classical and early quantum concepts and proposed a theory in the form of three postulates. These postulates are:

1. Postulate I: An electron in an atom could revolve in certain stable orbits without emitting radiant energy. Each atom has certain definite stable orbits. Electrons can exist in these orbits. Each possible orbit has definite total energy. These stable orbits are called the stationary states of the atom.
2. Postulate II: An electron can revolve around the nucleus in an atom only in those stable orbits whose angular momentum is the integral multiple of h/2π (where h is Planck’s constant). Therefore, the angular momentum (L) of the orbiting electron is quantized.mvr=nh2πmvr=nh2π  where, n = 1, 2, 3, …..
3. Postulate III: An electron can make a transition from its stable orbit to another lower stable orbit. While doing so, a photon is emitted whose energy is equal to the energy difference between the initial and final states. Therefore, the energy of photon is given by,hυ = E_i – E_fwhere E_i and E_f are the energies of the initial and final states.

Ground State and the Excited States

The lowest energy level of an atom is called the “ground state” and higher levels are called “excited states”. The H-atom has the lowest energy in the state for the principal quantum number n = 1. and all other states (i.e, for n = 2, 3, 4…) are excited states. Thus E₂, E₃, E₄ …are called the first, the second, and the third …excited states respectively.

Ionisation Energy and Ionisation Potential

The minimum energy needed to ionize an atom is called “ionisation energy”. The potential difference through which an electron should be accelerated to acquire this much energy is called “ionisation potential”. Hence, ionisation energy of H-atom in the ground state is 13.6 eV and ionisation potential is 13.6 V.

Binding Energy

The binding energy of a system is defined as the minimum energy needed to separate its constituents over large distances. This may also be defined as the energy released when its constituents are brought from infinity to form the system. The binding energy of H-atom in the ground state is 13.6 eV which is the same as its ionization energy.

Excitation Energy and Excitation Potential

The energy needed to take an atom from its ground state to an excited state is called the “excitation energy” of that excited state. The potential through which an electron should be accelerated to acquire this energy is called the “excitation potential”.

The Line Spectra of the Hydrogen Atom

Bohr’s model explains the spectral lines of the hydrogen atomic emission spectrum. While the electron of the atom remains in the ground state, its energy is unchanged. When the atom absorbs one or more quanta of energy, the electron moves from the ground state orbit to an excited state orbit that is further away. When the atom relaxes back to a lower energy state, it releases energy that is again equal to the difference in energy of the two orbits.

Based on the wavelengths of the spectral lines, Bohr was able to calculate the energies that the hydrogen electron would have in each of its allowed energy levels. He then mathematically showed which energy level transitions corresponded to the spectral lines in the atomic emission spectrum.

The general formula for wavelength of emitted radiation is given by

1λ=R(1n21−1n22)1λ=R(1n12-1n22)

where n₂ = 2, 3, 4, …. and n₂ > n₁

R = 1.01 x 10⁷ m^-1 = Rydberg constant

He found that the four visible spectral lines corresponded to transitions from higher energy levels down to the second energy level (n = 2). This is called the Balmer series. Transitions ending in the ground state (n = 1) are called the Lyman series, but the energies released are so large that the spectral lines are all in the ultraviolet region of the spectrum. The transitions called the Paschen series and the Brackett series both result in spectral lines in the infrared region because the energies are too small.

de-Broglie’s Explanation of Bohr’s Second Postulate

de-Broglie explained the second postulate of Bohr’s atomic model by assuming an electron to be a particle wave. Therefore, it should form standing waves under resonance conditions.

According to de-Broglie, for an electron moving in n^th circular orbit of radius r,

2πr = nλ     n = 1, 2, 3, …..

i.e., the circumference of the orbit should be an integral multiple of the de-Broglie wavelength of an electron moving in n^th orbit. As we know that de-Broglie wavelength,

λ=hmvλ=hmv

2πr=nhmv2πr=nhmv

mvr=nh2π