Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

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ATOMIC STRUCTURE

Dalton’s Theory of Atom

John Dalton developed his atomic theory. According to this theory the Atom is considered to be hard, dense and smallest particle of matter, which is indivisible, the atoms belonging to a particular element, is unique. The properties of elements differ because of the uniqueness of the atoms belonging to particular elements. This theory provides a satisfactory basis for the laws of chemical combination. The atom can neither be created nor be destroyed i.e., it is indestructible.

Drawbacks: It fails to explain why atoms of different kinds should differ in mass and valency etc.

Sub-Atomic Particles: The discovery of various sub-atomic particles like electrons, protons etc. during late 19th century led to the ideal that the atom was no longer an indivisible and the smallest particle of the matter.

Characteristics of the three fundamental particles are:

 

Electron

Proton

Neutron

Symbol

e or e–1

P

n

Approximate relative mass

1/1836

1

1

Approximate relative charge

–1

+1

No charge

Mass in kg

9.109 × 10–31

1.673 × 10–27

1.675 × 10–27

Mass in amu

5.485 × 10–4

1.007

1.008

Actual charge (coulomb)

1.602 × 10–19

1.602 × 10–19

0

Actual charge (e.s.u.)

4.8 × 10–10

4.8 × 10–10

0

The atomic mass unit (amu) is 1/12 of the mass of an individual atom of 6C12, i.e., 1.660 × 10h – 27 kg. The neutron and proton have approximately equal masses of 1 amu and the electron is about 1836 times lighter. Its mass can sometimes be neglected as an approximation.

The electron and proton have equal, but opposite, electric charge while the neutron is not charged.

Models of Atom

Thomson’s Model: Putting together all the facts known at that time, Thomson assumed that an atom is a sphere of positive charges uniformly distributed, with the electrons scattered as points throughout the sphere. This was known as plum-pudding model at that time. However this ideal was dropped due to the success of a-particle scattering experiments studied by Rutherford and Mardson.

Rutherford’s Model: a-particle emitted by radioactive substance were shown to be dipositive Helium ions (He++) having a mass of 4 units and 2 units of positive charge.

Rutherford allowed a narrow beam of α-particles to fall on a very thin gold foil of thickness of the order of 4 × 10–4 cm and determined the subsequent path of these particles with the help of a zinc sulphide fluorescent screen. This zinc sulphide screen gives off a visible flash of light when struck by an α-particle, as ZnS has the remarkable property of converting kinetic energy of particle into visible light.

 

Observation: 

  • Majority of the α-particles pass straight through the gold strip with little with little or no deflaction.
  • Some-particles are deflected from their path and diverge.
  • Very few-particles are deflected backwards through angles greater than 90°
  • Some were ever scattered in the opposite direction at an angle of 180°

Conclusion:

  • The fact that most of the a-particles passed straight through the metal foil indicates the most part of the atom is empty.
  • The fact that few a-particles are deflected at large angles indicates the presence of a heave positively charged body i.e., for such large deflections to occur a-particles must have some closer to or collided with a massive positively charged body, and he named it nucleus.
  • The fact that one in 20,000 have deflected at 180° backwards indicates that volume occupied by this heavy positively charged body is very small in comparison to total volume of the atom

Drawbacks of Rutherford’s Atomic Model  

  • Position of electrons: The exact positions of the electrons from the nucleus are not mentioned.
  • Stability of the atom: Neils Bohr pointed out that Rutherford’s atom should be highly unstable. According to the law of electro-dynamics, the electron should therefore, continuously emit radiation and lose energy. As a result of this a moving electron will come closer and closer to the nucleus and after passing through a spiral path, it should ultimately fall into the nucleus.

It was calculated that electron should fall into the nucleus in less than 10–8 sec. But it is known that electrons keep moving outsided the nucleus.

To solve this problem Neils Bohr proposed an improved form of Rutherford’s atomic model.

Before going into the details of Neils Bohr model we would like to inctroduce you some important atomic terms.

Atomic Structure:

If the atom gains energy the electron passes from a lower energy level to a higher energy level, energy is absorbed that means a specific wave length is absorbed. Consequently, a dark line will appear in the spectrum. This dark line constitutes the absorption spectrum.

Hydrogen atom: If an electric discharge is passed through hydrogen gas taken in a discharge tube under low pressure, and the emitted radiation is analyzed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and Ir regions. This series of lines is knows as line or atomic spectrum of hydrogen. The lines in the visible region can be directly seen on the photographic film.

Each line of the spectrum corresponds to a light of definite wavelength. The entire spectrum consists of six series of lines each, known after their discoverer as the Balmer, Paschen, Lyman, Brackett, Pfund and Humphrey series. The wavelength of all these series can be expressed by a single formula.

                                                        Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

                                                          Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev   = wave number

                                                            l = wave length

                                                            R = Rydberg constant (109678 cm–1)

                                                            n1 and n have integral values as follows

Series

n1

n2

Main spectral lines

Lyman

1

2, 3, 4, etc.

Ultra-vio

Balmer

2

3, 4, 5, etc.

Visible

Paschen

3

4, 5, 6, etc.

Infra-red

Brackett

4

5, 6, 7, etc.

Infra-red

Pfund

5

6, 7, 8, etc.

Infra-red

Types of emission spectra

  • Continuous spectra: When white light from any source such As sun or bulb is analyzed by passing through a prism, it splits up into seven different wide bands of colour from violet to red (like rainbow). These colour also continuous that each of them merges into the next. Hence the spectrum is called as continuous spectrum.
  • Line spectra: When as electric discharge is passed through a gas at low pressure light is emitted. If this light is resolved by a spectroscope, it is found that some isolated coloured lines are obtained on a photographic plate separated from each other by dark spaces. This spectrum is called line spectrum. Each line in the spectrum corresponds to a particular wavelength. Each element gives its own characteristic spectrum.

Planck’s Quantum Theory

When a black body is heated, it emits thermal radiations of different radiations of different wavelengths or frequency. To explain these radiations, Max Planck put forward a theory known as Planck’s theory. The main points of quantum theory are:

  • Substances radiate or absorb energy discontinuously in the form of small packets or bundles of energy.
  • The smallest packet of energy is called quantum. In case of light the quantum is known as photon.
  • The energy of a quantum is directly proportional to the frequency of the radiation. E∝ ν ( or E= hv where v is the frequency of radiation and h is Planck’s constant having the value 6.626 × 10–27 erg-sec or 6.626 × 10–34 J-sec.
  • A body can radiate or absorb energy in whole number multiple of a quantum hv, 2hv, 3hv, nhν where n is the positive integer. Nelis Bohr used this theory to explain the structure of atom.

Bohr’s Atomic Model

Bohr developed a model for hydrogen and hydrogen like atoms one-electron species (hydrogenic species). He applied quantum theory in considering the energy of an electron bond to the nucleus.

Important postulates: An atom consists of a dense nucleus situated at the center with the electron revolving around it in circular orbitals without emitting any energy. The force of attraction between the nucleus and an electron is equal to the centrifugal force of the moving electron.

Of the finite number of circular orbits possible around the nucleus, the electron can revolve only in those orbits whose angular momentum (mvr) is an integral multiple of factor h/2p.

            Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

            Where, m = mass of the electron

            v = velocity of the electron

            n = orbit number on which electron is present

            r = radius of the orbit

As long as an electron is revolving in a orbit it neither loses nor gains energy. Hence these orbits are called stationary states. Each stationary state is associated with a definite amount of energy and it is also known as energy levels. The greater the distance of the energy level form the nucleus, the more is the energy associated with it. The different energy levels are numbered as 1, 2, 3, 4 (from nucleus onwards) or K, L, M, N etc.

Ordinarily an electron continues to move in a particular stationary state without losing energy. Such a stable state of the atom is called as ground state or normal state.

If energy is supplied to an electron, it may jump (excite) instantaneously from lower energy (say 1) to higher energy level (say 2, 3, 4, etc) by absorbing one quantum of energy. This new state of electron is called as excited state. The quantum of energy absorbed is equal to the difference in energies of the two concerned levels. Since the excited state is less stable, atom will lose it’s energy and come back  to the ground state.

Energy absorbed or released in an electron jump, (ΔE) is given by

                                                            ΔE = E2 – E1 = hv

Where E2 and E1 are the energies of the electron in the first and second energy levels, and v is the frequency of radiation absorbed or emitted.

Merits of Bohr’s theory:

  • The experimental value of radii and energies in hydrogen atom are in good agreement with that calculated on the basis of Bohr’s theory.
  • Bohr’s concept of stationary state of electron explains the emission and absorption spectra of hydrogen like atoms.
  • The experimental values of the spectral lines of the hydrogen spectrum are in close agreement with the calculated by Bohr’s theory.

Limitations of Bohr’s Theory

  • It does not explain the spectra of atoms or ions having more than one electron.
  • Bohr’s atomic model failed to account for the effect of magnetic field (Zeeman effect) or electric field (Stark effect) on the spectra of atoms or ions. It was observed that when the source of a spectrum is placed in a strong magnetic or electric filed, each spectral line further splits into a number of lines. This observation could not be explained on the basis of Bohr’s model.
  • De-Broglie suggested that electrons like light have dual character. It has particle and wave character. Bohr treated the electron only as particle.
  • Another objection to Bohr’s theory came from Heisenberg’s Uncecrtainty Principle. According to this principle “it is impossible to determine simultaneously the exact possible and momentum of a small moving particle like an electron”. The postulate of Bohr, that electrons revolve in well defined orbits around the nucleus with well defined velocities is thus not attainable.

 

By Bohr’s theory

  • Radius and Energy levels of hydrogen atom: Consider an electron of mass ‘m’ and charge ‘e’ revolving around a nucleus of charge Ze (where, Z = atomic number and e is the charge of the proton) with a tangential velocity v.r is the radius of the orbit in which electron is revolving.

    By Coulomb’s Law, the electrostatic force of attraction between the moving electron and nucleus is

Coulombic force = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev (where ε0 is permittivity of free space)

K = 9 × 109 Nm2C–2

In C.G.S units, value of K = 1 dyne cm2 (esu)–2

The centrifugal force acting on the electron is  Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Since the electrostatic force balance the centrifugal force, for the stable electron orbit.

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev   ...............(i)

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev ...............(ii)

According to Bohr’s postulate of angular momentum quantization, we have

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev
Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev   ............ (iii)

Equating (ii) and (iii)

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Solving for r we get  r = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Where n = 1, 2, 3, ………….∞

Hence only certain orbits whose radii are given by the above equation are available for the electron. The greater the value of n, i.e., farther the level from the nucleus the greater is the radius.

The radius of the smallest orbit (n = 1) for hydrogen atom (Z = 1) is 

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

r0 = 0.529 Å

Radius of nth orbit for an atom with atomic number Z is simply written as

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Illustration: Calculate the ratio of the radius of Li+2 ion in 3rd energy level to that of He+ ion in 2nd energy level:

Solution: 

            Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev
            Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

            n1 = 3

            n2 = 3

            z1 = 3                                       (for Li2+)

            z2 = 2                                       (for He+)

            Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

  • Energy level of Hydrogen atom: The total energy, E of the electron is the sum of kinetic energy and potential energy. Kinetic energy of the electron = 1/2 mv2
    • Potential energy = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev
    • Total energy = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev                   ………..(4)

            From equation (1) we known that

                    Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev
Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Substituting this in equation (4)

            Total energy (e) 

            Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev
Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Substituting for r, gives us

  E  Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev        where n 1, 2, 3.........

This expression shows that only certain energies are allowed to the electron. Sin e this energy expression consists so many fundamental constant, we are giving you the following, simplified expressions.

E = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduReverg per Atom

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

(1 eV = 3.83 × 10–23 Kcal)

(1 eV = 1.602 × 10–12 erg)

(1 eV = 1.602 × 10–19 J)

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev kcal/mole (1cal = 4.18 J)

The energies are negative since the energy of the electron in the atom is less than the energy of a free electron (i.e., the electron is at infinite distance from the nucleus) which is taken as zero. The lowest energy level of the atom corresponds to n = 1, and as the quantum number increases, E become less negative.

When n = ∞, E = 0 which corresponds to an ionized atom i.e., the electron and nucleus are infinitely separated.

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

  • Velocity of electron:

We know that,  mvr = Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

By substituting for r we are getting

Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Where excepting n and z all are constant, v =Introduction to Atomic Structure - Atomic Structure Chemistry Notes | EduRev

Further application of Bohr’s work was made, to other one electron species (Hydrogenic ion) such as He+ and Li2+. In each case of this kind, Bohr’s prediction of the spectrum was correct.

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