## 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.

Thomson atomic model |

## 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.

## Recommended Books

- NCERT Textbook For Class 12 Physics Part 1 & 2
- CBSE All In One Physics Class 12 2022-23 Edition
- Oswaal CBSE Chapterwise Question Bank Class 12 Physics Book
- Modern's abc Plus of Physics for Class-12 (Part I & II)

**Read also:** Nuclei Class 12 Physics Notes Chapter 13

### Observations

Here is what they found:

Most of the alpha particles passed through the foil without suffering any collisions

Around 0.14% of the incident alpha particles scattered by more than 1

^{o}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 :

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.Most of an atom is empty space.

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.

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**.

Rutherford's Atom Model |

**Read also:** Aldehydes, Ketones and Carboxylic Acids Chemistry Class 12 Notes Chapter 12

## 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:

**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.**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=\frac{nh}{2\pi}` where, n = 1, 2, 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_{f}where 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 E_{2}, E_{3}, E_{4} …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.

**Read also:** Conceptual Questions for Class 12 Physics Chapter 12 Atoms

## 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

`\frac{1}{λ}=R(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}})`

where n_{2} = 2, 3, 4, .... and n_{2} > n_{1}

R = 1.01 x 10^{7} 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=\frac{h}{mv}`

`2\pi r=\frac{nh}{mv}`

`mvr=\frac{nh}{2\pi}`

## Summary

**Impact parameter:**Perpendicular distance of initial velocity vector of α-particles from the center of the nucleus.**Distance of closest approach:**Distance of a point from the nucleus at which α-particle is nearest to the center of the nucleus.**Bohr radius:**The first orbit of a hydrogen atom is called the**Bohr radius**.**Ground state:**Lowest state of an atom, called the**ground state**, is the state in which the electron revolves in the orbit of the smallest radius, the Bohr radius, a_{0}.**Ionization energy:**Minimum energy required to free an electron from the ground state of a hydrogen atom is called the**ionization energy**.The first atomic model was proposed by J.J. Thomson in 1898, according to this model the positive charge of the atom was uniformly distributed throughout the volume of the atom and negatively charged electrons are embedded in it like seeds in watermelon.

**Rutherford’s nuclear model:**Entire positive charge and most of the mass of an atom are concentrated in a small volume called the**nucleus**, with electrons revolving around the nucleus just as planets revolve around the sun. This model could not explain**(i)**Stability of atom,**(ii)**The line spectra of atoms.**Bohr’s model of hydrogen atom:**Bohr proposed a model for hydrogen and hydrogen-like atom, which explained the line spectra emitted by atoms, according to this model only those orbits are stable for which angular momentum of the electron is an integral multiple of h/2π.**de-Broglie’s explanation to Bohr’s postulate of quantization:**He assumed electrons to be particle waves, therefore, the circumference of the stable orbit should be an integral multiple of the wavelength of the wave associated with the electron.Atom, as a whole, is electrically neutral and therefore contains an equal amount of positive and negative charges.

In

**Thomson’s model**, an atom is a spherical cloud of positive charges with electrons embedded in it.In Rutherford’s model, most of the mass of the atom and all its positive charge is concentrated in a tiny nucleus and the electrons revolve around it.

Atoms of each element are stable and emit a characteristic spectrum. The spectrum consists of a set of isolated parallel lines termed a

**line spectrum**. It provides useful information about the**atomic structure**.The atomic hydrogen emits a line spectrum consisting of various series. As Lyman series, Balmer series, Paschen series, Brackett series, Pfund series.

de Broglie’s hypothesis that electrons have a wavelength λ = h/mv gave an explanation for Bohr’s quantized orbits by bringing in the wave-particle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

**Bohr’s model**is applicable only to hydrogenic (single electron) atoms. It cannot be extended to even two-electron atoms such as helium. This model is also unable to explain the relative intensities of the frequencies emitted even by hydrogenic atoms.