Chapter 12: ATOMS 

Atomic Spectra

ALPHA-PARTICLE SCATTERING AND RUTHERFORD’S NUCLEAR MODEL OF ATOM

Rutherford proposed a new model of the atom based on Alpha-Particle Scattering experiment.In 1911, Ernst Rutherford suggested some experiments to H. Geiger and E. Marsden. Both scientists performed an experiment whose schematic diagram is shown in the figure given. Alpha-Particle scattering and Rutherford’s Nuclear Model of Atom They directed a beam of 5.5 MeV α-particles emitted from a radioactive source at a thin metal foil made of gold. The beam was allowed to fall on a thin foil of gold thickness 2.1 × 10-7 m.

 

The scattered alpha-particles were observed through a rotatable detector consisting of zinc sulphide screen and a microscope. The scattered alpha-particles on striking the screen produced brief light flashes or scintillations. These flashes may be viewed through a microscope and the distribution of the number of scattered particles may be studied as a function of angle of scattering

Observation of the Alpha (α) scattering Experiment

Many of the α-particle pass through the foil which means that they do not suffer any collisions. Approximately 0.14% of the incidents α-particles scatter by more than 10 and about 1 in 8000 deflect by more than 900.

  • Scattering of alpha particle is due to columbic force between positive charge of α particle and positive charge of atom.
  • Rutherford’s experiments suggested the size of the nucleus to be about 10–15 m to 10–14 m.
  • The electrons are present at a distance of about 10,000 to 100,000 times the size of the nucleus itself.
  • Atom has a lot of empty space and the entire mass of the atom is confined to very small central core also known as nucleus.

ATOMIC SPECTRA

Atoms have an equal number of negative and positive charges. Atoms were described as a spherical cloud of positive charges with embedded electrons in Thomson’s concept. In Rutherford’s model, one tiny nucleus carries the majority of the atom’s mass, as well as its positive charges, and the electrons orbit it.

The study of the electromagnetic radiation received or emitted by atoms is known as atomic spectroscopy. There are three different forms of atomic spectroscopy:

The transfer of energy from the ground state to an excited state is the subject of atomic emission spectroscopy. Atomic emission can explain the electronic transition.

Atomic absorption spectroscopy: For absorption to occur, the lower and higher energy levels must have equivalent energy differences. The notion that free electrons created in an atomizer can absorb radiation at a given frequency is used in the atomic absorption spectroscopy principle. The absorption of ground-state atoms in the gaseous state is measured.

Atomic fluorescence spectroscopy combines atomic emission and atomic absorption since it uses both excitation and de-excitation radiation.

THE LINE SPECTRA OF THE HYDROGEN ATOM

A hydrogen atom is made up of several line spectrum series, including:

1.Pfund Series

2.Brackett Series

3.Paschen Series

4.Balmer Series

5.Lyman Series

RIES:

  1. Balmer Series:

First scientist to discover a spectral series of hydrogen atom

It consist of visible radiation spectrum

Experimentally, he found that these spectral lines could be expressed mathematically in the form of wavelength as:


Here R= Rhydberg constant = 109677cm-1(found experimentally), n= 3, 4, 5…… (higher discrete energy state from which electron jumps to 2nd energy state thus emitting radiation)

         λ = wavelength of emitted radiation in (cm)

For maximum wavelength(λmax) in the Balmer series, n=3 (has to be minimum):

For minimum wavelength (λmin) in the Balmer series, n=∞(has to be minimum):

  1. Lyman Series:

Spectral series when radiation emitted is due to jumping of electron from higher energy states to ground state

Mathematically expressed as

Here n= 2, 3, 4…

For maximum wavelength  in the Lyman series, n=2 (has to be minimum):

λmax = 4/3R

For minimum wavelength in the Lyman series, n=∞(has to be minimum):

λmin = 1/R

Similarly, all other series could be expressed as:

  1. Paschen Series:

Mathematically expressed as

Here n= 4, 5, 6…

  1. Bracket Series:

Mathematically expressed as


Here n= 5, 6, 7…

  1. PfundSeries:

Mathematically expressed as


Here n= 6, 7, 8…

THE LINE SPECTRA OF THE HYDROGEN ATOM

Bohr’s model of the hydrogen atom is the very first model of atomic structure that correctly explained the radiation spectra of atomic hydrogen. The model has a special place in the history of physics because it introduced an early quantum theory, which brought about new developments in scientific thought and later culminated in the development of quantum mechanics. To understand the specifics of Bohr’s model, we must first review the nineteenth-century discoveries that prompted its formulation.


An empirical formula to describe the positions (wavelengths) lambda of the hydrogen emission lines in this series was discovered in 1885 by Johann Balmer. It is known as the Balmer formula

The constant  is called the Rydberg constant for hydrogen. In (Figure), the positive integer n takes on values n=3,4,5,6 for the four visible lines in this series. The series of emission lines given by the Balmer formula is called the Balmer series for hydrogen. Other emission lines of hydrogen that were discovered in the twentieth century are described by the Rydberg formula, which summarizes all of the experimental data

DE BROGLIE’S EXPLANATION OF BOHR’S SECOND POSTULATE OF QUANTISATION


The  particle waves can be viewed analogously to the waves travelling on a string. Particle waves can lead to standing waves held under resonant conditions. When a stationary string is plucked, a number of wavelengths are excited. On the other hand, we know that only those wavelengths survive which form a standing wave in the string, that is, which have nodes at the ends.

2πrk = kλ

Let this be equation (1).

Λ = h/p

P is electron’s momentum

 

H = Planck’s constant

Λ = h/mvk

Let this be equation (2).

Where mvk is the momentum of an electron revolving in the kth orbit. Inserting the value of λ from equation (2) in equation (1) we get,

2πrk = kh/mvk

Mvkrk = kh/2π