Navodaya Vidyalaya Samithi, Noida

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E-Content of Class XI

Subject : Chemistry

Chapter-2 Structure of Atom

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Prepared By Dr. R. Sudhir Kumar

PGT Chemistry

JNV Guntur

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Structure of Atom Introduction

Democritus 460 B.C was the first to

theorize that matter was made of small

pieces.

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Leucippus was the first to use the term

atom (atomon), which meant "indivisible"

in Greek.

atom

Matter consists of tiny particles

Structure of Atom

The existence of atoms has been proposed since the time of early Indian and Greek philosophers (400 B.C.) who were of the view that atoms are the fundamental building blocks of matter. According to them, atoms are indivisible.

The word ‘atom’ has been derived from the Greek word ‘a-tomio’ which means ‘uncut-able’ or ‘non-divisible’.

Dalton’ atomic theory

Dalton’ atomic theory

The atomic theory of matter was first proposed on a firm scientific basis by John Dalton, a British school teacher in 1808.

Dalton’s atomic theory was able to explain the

law of conservation of mass, law of constant composition and law of multiple proportion very successfully.

Failed to explain the results of many experiments, for example, it was known that substances like glass or ebonite when rubbed with silk or fur get electrically charged.

�Atoms are made of sub-atomic particles, �i.e., electrons, protons and neutrons�

Experiment No.1 Discovery of Electron (1897) J J Thomson

When sufficiently high voltage is applied through an inert gas (He, Ar) across the electrodes, current starts flowing through a stream of particles moving in the Cathode ray discharge tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles.

�Cathode ray discharge tube experiment :�Discovery of an Electron�

Properties of Cathode Rays

1. Cathode rays travel in a straight line.
2. Cathode rays produces mechanical effect, because they rotate a light paddle wheel placed in their path.
3. Cathode rays produces Heating effect when they hit a heavy metal.
4. Cathode rays produce flourescent effect on fluorescent material.

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Properties of Cathode Rays

6. Cathode rays deflect towards a positive terminal in an

electric field.

7. Cathode rays deflect towards the direction determined by

Fleming’ left hand rule.

8. Cathode rays are Negatively charged.

8. Cathode rays can ionize gasses.

9. Cathode rays can produce X rays.

10. Cathode rays do not depend upon the nature of the gas

and material.

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Charge to mass (e/m) ratio determination of an electron

• This experiment measures e/m, the charge to mass ratio of the electron.

This ratio was first measured by J. J. Thomson in 1897. He won a Nobel

prize for his study of electrons.

Procedure :

• (i) In the present experiment a beam of electrons is accelerated through a

known potential, so the velocity of the electrons is known.

• (ii) A pair of Helmholtz coils produces a uniform and measurable magnetic field at right

angles to the electron beam. This magnetic field deflects the electron beam in a

circular path. By measuring the accelerating potential, the current to the Helmholtz

coils, and the radius of the circular path of the electron beam, the ratio e/m is

calculated.

In 1897, British physicist J.J. Thomson measured the ratio of electrical charge (e) to the mass of electron (m_e ) by using cathode ray tube and applying electrical and magnetic field perpendicular to each other as well as to the path of electrons.

Arguements :

Thomson argued that the amount of deviation of the particles from their path in the presence of electrical or magnetic field depends upon:

1. the magnitude of the negative charge on the particle, greater the

magnitude of the charge on the particle, greater is the interaction

with the electric or magnetic field and thus greater is the

deflection.

(ii) the mass of the particle — lighter the particle, greater the

deflection.

(iii) the strength of the electrical or magnetic field — the deflection of

electrons from its original path increases with the increase in the

voltage across the electrodes, or the strength of the magnetic field.

Conclusion :

By carrying out accurate measurements on the amount of deflections observed by the electrons on the electric field strength or field strength,

Thomson was able to determine the value of e/m_e as:

e/m_e = 1.758820 × 10¹¹ C kg^–1

Where m_e is the mass of the electron in kg and e is the magnitude of the charge on the electron in coulomb (C). Since electrons are negatively charged, the charge on electron is – e.

Charge of an electron (1909)�(Millikan oil drop experiment)

• In 1909, Robert Millikan and Harvey Fletcher conducted the oil drop experiment to determine the charge of an electron.
• They suspended tiny charged droplets of oil between two metal electrodes by balancing downward gravitational force with upward drag and electric forces. The density of the oil was known, so Millikan and Fletcher could determine the droplets’ masses from their observed . Using the known electric field and the values of gravity and mass, Millikan and Fletcher determined the charge on oil droplets in mechanical equilibrium.
• They calculated this value to be 1.5924 × 10⁻¹⁹Coulombs (C), which is within 1% of the currently accepted value of -1.602176487 × 10⁻¹⁹ C.

At the time of Millikan and Fletcher’s oil drop experiments, the existence of subatomic particles was not universally accepted.

George FitzGerald and Walter Kaufmann found similar results.

In 1923, Millikan won the Nobel Prize in physics in part because of this experiment.

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Experiment No.2 : Discovery of Proton (1919) Eugene Goldstein

• Eugene Goldstein noted stream of particles in Cathode rays in 1886. These particles move in opposite direction to Cathode rays are called Canal rays because they passed through holes drilled through a negative plate (Cathode)
• When sufficiently high voltage is applied through an inert gas (He or Ar) at low pressure across the electrodes, he observed a new type of rays carrying a positive charge streaming behind the cathode moving from the positive electrode (Anode) to the negative electrode (cathode). These were called Anode rays .

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�Anode ray discharge tube experiment :�Discovery of an Proton�

Properties of Anode Rays

1. Anode rays travel in a straight line.
2. Anode rays produces mechanical effect, because they rotate a light paddle wheel placed in their path.
3. Anode rays produces Heating effect when they hit a heavy metal.
4. Anode rays produce flourescent effect on fluorescent material.
5. Anode rays are Positively charged.

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Properties of Anode Rays

6. Anode rays deflect towards a Negative terminal in an electric

field.

7. Anode rays deflect towards the direction determined by

Fleming’ left hand rule in magnetic field.

8. Anode rays can ionize gasses.

9. Anode rays do not depend upon the nature of the gas and

material, but mass of positively charged particles depends

upon the nature of gas present in the cathode ray tube.

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Experiment.3 :Discovery of Neutron (1932)

The British Physicist Sir James Chadwick smashed alpha particles into Beryllium, a rare metallic element, allowed the radiation that was released to hit another target paraffin wax, This led to the production of an uncharged, penetrating radiation. the unusually penetrating radiation consisted of uncharged particles having (approximately) the same mass as a proton. These particles were later termed ‘neutrons’.

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Characteristics of sub atomic particles

Atomic models

The structure of an atom, theoretically consisting of a positively charged nucleus surrounded and neutralized by negatively charged electrons revolving in orbits at varying distances from the nucleus, the constitution of the nucleus and the arrangement of the electrons differing with various chemical elements.

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Atomic model no.1 (1904)

Shortcomings and achievements

An important feature of this model is that the mass of the atom is assumed.

• It failed to explain the stability of an atom because his model of atom failed to explain how a positive charge holds the negatively charged electrons in an atom.
• Thomson’s model failed to explain the scattering of alpha particles by thin metal foils.
• Thomson’ model does not accout for the existence of nucleus.
• No experimental evidence.

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J.J.Thomson was awarded the Nobel prize in 1906 for discovery of electron. He also received Knighthood from British Empire.

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Rutherford’ α-scattering experiment(1911)

Objective:

To demonstrate the scattering of alpha particles by gold foil.

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Ernest Rutherford was interested in knowing how the electrons are arranged within an atom. In this experiment, fast moving alpha (α)-particles were made to fall on a thin gold foil.

He selected a gold foil because he wanted as thin a layer as possible of about 1000 atoms thick, around it a circular fluorescent ZnS screen is present.

α-particles are doubly-charged helium ions (He⁺² ) having a mass of 4µ, the fast-moving α-particles have a considerable amount of energy. 

It was expected that α-particles would be deflected by the sub-atomic particles in the gold atoms. Since the α-particles were much heavier than the protons, he did not expect to see large deflections. 

�Observations of Rutherford's scattering experiment�

1.Most of the fast moving α-particles passed straight through the gold foil.

2.Some of the α-particles were deflected by the foil by small angles.

3.Surprisingly one out of every 20,000 alpha particles appeared to rebound.

Conclusions of Rutherford's scattering experiment :

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• Most of the space inside the atom is empty because most of the α-particles passed through the gold foil without getting deflected.
• Very few particles were deflected from their path, indicating that the positive charge of the atom occupies very little space.
• A very small fraction of α-particles were deflected by very large angles, indicating that all the positive charge and mass of the gold atom were concentrated in a very small volume within the atom called nucleus.
• From the data he also calculated that the radius of the nucleus (10^–15 ) is about 10⁵ times less than the radius of the atom (10^-10 m)

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Rutherford’ Nuclear model of an atom

On the basis of above observations and conclusions, Rutherford proposed the nuclear model of atom.

According to this model:

(i) Atom is assumed to be hollow sphere.

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(ii) The positive charge and most of the mass of the

atom was densely concentrated in extremely small

region. This very small portion of the atom was

called nucleus by Rutherford.

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Rutherford’ Nuclear model of an atom

(iii)The nucleus is surrounded by electrons that move around the nucleus with a very high speed in circular paths called orbits, like the planets revolve around the Sun in Solar family.

(iv) Electrons and the nucleus are held together by electrostatic forces of attraction.

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Drawbacks of Rutherford’ atomic model

1. Rutherford could not explain the stability of an atom.

According to the electromagnetic theory of Maxwell, charged particles when accelerated should emit electromagnetic radiation . The energy carried by radiation comes from electronic motion. The orbit will thus continue to shrink and ultimately electron fall into the ground of Nucleus.

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Drawbacks of Rutherford’ atomic model

2.If the electron loss energy continuously the observed

spectrum should be continuous, but the actual observed

spectrum consists of well defined lines of definite

frequencies (i.e. discontinuous).

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3. Rutherford model failed to say nothing about distribution of

the electrons around the nucleus and the energies of these

electrons.

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4. Line spectra of atoms

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Atomic number

The number of protons in the nucleus of an atom, which is characteristic of an chemical element and determines its place in the periodic table.  It was discovered by This was Henry Gwyn-Jefferies Moseley's. Or

The number of positive charges or protons in the nucleus of an atom of a given element, and therefore also the number of electrons normally surrounding the nucleus. It is represented by the letter “Z.” The atomic number symbol, Z, stands for “Zahl,” meaning German number.

Mass number

Mass number is an integer (whole number) equal to the sum of the number of protons and neutrons of an atomic nucleus.

In other words, it is the sum of the number of nucleons in an atom. It is represented by the letter “A.” Symbol A, from the German word Atomgewicht [atomic weight]

• In 1913 radio chemist Frederick Soddy while experimenting with the products of radioactive decay discovered that there appeared to be more than one element at each position on the periodic table.

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• The term isotope was coined by Margaret Todd.
• Experimental evidence: J.J.Thomson conducted an experiment in which he channeled a stream of Neon ions through magnetic and electric fields, striking a photographic plate at the other end. He observed two glowing patches on the plate, which suggested two different deflection trajectories.

Thomson concluded this was because some of the Neon ions had a different mass.

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Isotopes

Isotopes are the atoms of same element have same atomic number, but have different mass numbers. They have same chemical properties as they have same electron and proton number.

An important point to mention regarding isotopes is that chemical properties of atoms are controlled by the number of electrons, which are determined by the number of protons in the nucleus. Number of neutrons present in the nucleus have very little effect on the chemical properties of an element.

Isobars

Isobars are the atoms of different elements with same mass number, but have different atomic numbers. They have different chemical properties as they have different electron and proton number.

The name was given by Alfred Walter Stewart in 1918. It is originally taken from the combination of Greek words- isos means equal and bar means weight.

Examples

₁₈Ar⁴⁰ ₁₉K⁴⁰ ₂₀Ca⁴⁰ ₃₂ Ce⁷⁶, ₃₄Se⁷⁶

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₁₁Na²⁴ ₁₂Mg²⁴ ₂₆Fe⁵⁸, ₂₇ Ni⁵⁸ 

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�DEVELOPMENTS LEADING TO THE BOHR’S MODEL OF ATOM�

Two developments played a major role in the formulation of Bohr’s model of atom. These were:

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1. Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties.

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(ii) Experimental results regarding atomic spectra.

1. Dual nature of electromagnetic radiation

Introduction

James Maxwell (1870) was the first to give a comprehensive explanation about the interaction between the charged bodies and the behaviour of electrical and magnetic fields on macroscopic level.

He suggested that when electrically charged particle moves under accelaration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the forms of waves called electromagnetic waves or electromagnetic radiation.

Dual nature of electromagnetic radiations

Electromagnetic radiation is a form of energy that is transmitted through space in the form of a wave. It can be treated as discrete packets of energy or particles called photons or quanta.

Light is the form of radiation known from early days and it was supposed to be made of particles (corpuscules) by Newton.

Maxwell was again the first to reveal that light waves are associated with oscillating electric and magnetic character.

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Electromagnetic radiation wave

General properties of electromagnetic radiation

1. The oscillating electric and magnetic fields produced

by oscillating charged particles are perpendicular to

each other and also perpendicular to the direction

of propagation of the wave.

2. Electromagnetic waves are transverse.

3. Unlike sound waves or water waves, electromagnetic waves do not require medium and

can travel in vacuum.

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General properties of electromagnetic radiation

4. Electromagnetic waves can travel at the speed of

light in vaccum.

5. Electromagnetic waves can bounce off from a

surface.(i.e reflected)

6. Electromagnetic waves can change direction (i.e. can

be refracted)

7. Electromagnetic waves can spread around

corners.(i.e. diffracted)

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Electromagnetic spectrum

Electromagnetic spectrum consists of different electromagnetic radiations which are arranged in the increasing order of their wavelengths and decreasing order their frequencies.

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Characteristics of a wave�1.Wavelength

Wavelength can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave. Wavelength is represented by the Greek letter lambda (λ).

Units : Wavelength can be measured in meters, centimeters, or nanometers (1 m = 10⁹ nm)

2. Frequency

Wave frequency is the number of waves that pass a fixed point in a given amount of time.

SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second.

A higher-frequency wave has more energy than a lower-frequency wave with the same amplitude.

3. Amplitude

The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. or

The amplitude of a wave is the maximum disturbance or displacement of the medium from the equilibrium (rest) position.

The SI unit of amplitude is the metre (m).

4. Wavenumber

Wavelength is defined as the number of wavelengths per unit length.

The wavenumber (k) is simply the reciprocal of the wavelength, given by the expression. k = 1 / λ The wavenumber (k) is therefore the number of waves or cycles per unit distance.

Units for wavenumber are (1/distance), such as 1/m, 1/cm or 1/mm.

Drawbacks of the Wave nature of Electromagnetic radiations

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1. Black body radiation
2. Photoelectric effect
3. Heat capacity of solids as a function of temperature
4. Line spectra of atoms

2.Particle nature of Electromagnetic radiation�Black body Radiation

Black body :

An object that absorbs all radiation falling on it, at all wavelengths, is called a black body.

Black body radiation :

When a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation.

Or

An ideal body, which emits and absorbs radiations of all frequencies uniformly, is called a black body and the radiation emitted by such a body is called black body radiation.

Example of a Black body

Carbon black approximates fairly closely to black body. A good physical approximation to a black body is a cavity with a tiny hole, which has no other opening. Any ray entering the hole will be reflected by the cavity walls and will be eventually absorbed by the walls.

A black body is also a perfect radiator of radiant energy.

Planck’ quantum theory

1. Matter radiate or absorb energy in discrete quantities .

discontinuously in the form of small packets or bundles called

‘quanta’. In case of light, a quantum light radiation is called ‘photon’.

2. The energy of the quantum absorbed or emitted is directly proportional to the frequency of the light radiation.

The energy of radiation is expressed in terms of frequency as,

E = h ν

Where,

E = Energy of the radiation

h = Planck’s constant (6.626×10^–34 J.s)

ν= Frequency of radiation

3. A body or matter radiate or absorb energy in whole number multiples of a quantum as nhʋ. Where n is a positive integer. So energy can be absorbed or radiated as hʋ, 2hʋ, 3hʋ, 4hʋ -------- etc.

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�Evidences in support of Planck’ quantum theory :�

• A prism can separate the light accordinig to their wavelengths. If light behaves only as a wave, then a prism should give a continuous rainbow, but in reality it does not.
• Emission spectrum of nitrogen gas.

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Photoelectric efffect

In 1887, H. Hertz performed a very interesting experiment in which electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc.) were exposed to a beam of light. The phenomenon is called Photoelectric effect.

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Threshold energy

“The minimum amount of energy, that is required to eject an electron from the surface of a metal is called threshold energy or photoelectric work function".

Although the work function specifically refers to the energy that needs to be put in, and the threshold energy refers to the frequency required to eject an electron, they are the same thing when calculating with the equation.

Threshold frequency

Threshold frequency is the minimum frequency of incident light which can cause emission of photo-electrons from the metal surface.

Photo-emission of electrons is not possible below threshold frequency.

V ˃ V₀

Photoelectric effect explanation

When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy instantaneously to the electron during the collision and the electron is ejected without any time lag or delay.

Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron.

In other words, kinetic energy of the ejected electron is proportional to the frequency of the electromagnetic radiation.

K E of the ejected electron

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hv = Energy of the striking photon

hv₀ = threshold energy

hv - hv₀ = Kinetic energy of the photoelectron

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Atomic Spectrum

Meaning : The spectrum is the range of different colours which is produced when light passes through a glass prism or through a drop of water. A rainbow shows the colours in the spectrum.

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Atomic spectra is the study of atoms (and atomic ions) through their interaction with electromagnetic radiation. 

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Absorption spectrum

A spectrum of electromagnetic radiation transmitted through a substance, showing dark lines or bands due to absorption at specific wavelengths.

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Formation of Absorption spectrum

Emission spectrum

The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be “excited”.

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Formation of Emission spectra

�Line spectrum of Hydrogen :�

When an electric discharge is passed through gaseous hydrogen, the H₂ molecules dissociate and the energetically excited hydrogen atoms produced emit electromagnetic radiation of discrete frequencies.

Balmer showed in 1885 on the basis of experimental observations that if spectral lines are expressed in terms of wavenumber , then the visible lines of the hydrogen spectrum obey the following formula:

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Rydberg’ formula

The Swedish spectroscopist, Johannes Rydberg, noted that all series of lines in the hydrogen spectrum could be described by the following expression :

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The value 109,677 cm–1 is called the Rydberg constant for hydrogen.

The first five series of lines that correspond to n1 = 1, 2, 3, 4, 5 are known as Lyman, Balmer, Paschen, Bracket and Pfund series, respectively.

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Emission spectrum and Spectral lines of Hydrogen

�Electron transitions in the Hydrogen atomic spectrum :�

BOHR’S MODEL OF ATOM:-

1. The electrons in Hydrogen atom revolve around the nucleus only in certain selected circular paths of fixed radius and definite energy. These paths are called orbits or energy shells or energy levels.

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1. The energy of an electron in the orbit does not change with time. As long as electron remains in a particular orbit, it does not lose or gain energy. Therefore these orbits are called “Stationary states”.

APPLICATIONS

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Explanation of Line Spectrum of Hydrogen Atom

WAVE PARTICLE DUALITY

Wave Nature of light:

• Diffraction
• Interference

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Particle nature of light:

• Photoelectric effect
• Scattering of light

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Thus light has a dual nature possessing the properties of both wave and a particle.

h is known as Planck’s constant and its value is 6.626 × 10^-34 js.�p = mv is the linear momentum of the particle.

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• The de Broglie wavelength of a body is inversely proportional to its momentum. Since the magnitude of h is very small, the wavelength of the objects of our everyday world would be too small to be observed.

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HEISENBERG’S UNCERTAINTY PRINCIPLE

QUANTUM MECHANICAL MODEL OF ATOM

• Erwin Schrodinger and Heisenberg developed the quantum mechanical model of an atom in 1926.
• Erwin described the wave motion of electron in three dimensional space around the nucleus by a mathematical equation known as Schrodinger wave equation.

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QUANTUM MECHANICAL MODEL OF ATOM

• In short the wave equation may be written as:

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• The wave function ψ is a solution of the Schrodinger equation and describes the behavior of an electron in a region of space called the atomic orbital.
• We can find energy values that are associated with particular wave functions.

QUANTUM MECHANICAL MODEL OF ATOM

• The solutions of wave equation gives the possible energy levels the electron can occupy.
• The quantized energy states and corresponding wave functions are characterized by three quantum numbers:

1) Principle quantum number (n)

2) Azimuthal quantum number (l)

3) Magnetic quantum number ( m_l)

ORBITAL AND QUANTUM NUMBERS

• Principle Quantum number (n ) : This quantum number determines the size and energy of the orbital. It also identifies the shell.

With the increase in the value of “n” the number of allowed orbitals

increases. Size of an orbital also increases with increase of “n”.

The number of orbitals = n² ,where n = 1,2,3,4,…………( non zero integer)

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“n value” and shell designation:

ORBITAL AND QUANTUM NUMBERS

• Azimuthal Quantum Number (l) : This quantum number defines the three dimensional shape of the orbital.

For a given value of n, l can have values ranging from 0 to n-1.

so possible values of l = 0,1,2,3,………….(n-1)

This quantum number thus tells us about the no. of subshells or sub levels

in a given shell.

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ORBITAL AND QUANTUM NUMBERS

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ORBITAL AND QUANTUM NUMBERS

• Magnetic Orbital Quantum Number ( m_l ): It describes the behavior of electron in a magnetic field.

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Under the applied magnetic field, electrons in a given subshell orient

themselves in certain preferred regions of space around the nucleus.

These are called orbitals.

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For any sub-shell, 2l+1 values of m_l are possible.

so for a given value of l, m_l can have values ranging from –l to +l.

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m_l = -l………..0…………..+l

ORBITAL AND QUANTUM NUMBERS

ORBITAL AND QUANTUM NUMBERS

IMPORTANT POINTS

• No. of subshells in nth shell = n

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• No. of orbitals in a subshell = 2l + 1

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• No. of electrons in a subshell = 2 (2l + 1) = 4l + 2

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SHAPES OF ATOMIC ORBITALS

SHAPES OF ATOMIC ORBITALS

SHAPES OF D-ORBITALS

NODES IN ATOMIC ORBITALS

• Nodes are the positions where the probability of finding the electron is zero.

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• Total no. of nodes = n-1
• Angular nodes = l
• Radial nodes = n-l-1

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ELECTRONIC CONFIGURATION

• The distribution of electrons in different orbitals is known as electronic configuration.

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Aufbau Principle: “In the ground state of the atoms, the orbitals are filled in order of their increasing energies”.

The orbital energy is defined by a rule known as Bohr-Bury Rule or (n+l) rule.

• Rule 1: An orbital with a lower value for (n + l) has lower energy.
• For example,
• The 4s orbital (n + l = 4+0 = 4) will be filled before a 3d orbital (n + l = 3 + 2 = 5).
• Rule 2: If the value of (n + l) is same for two orbitals then the orbital with lower value of n will be filled first.
• For example, the 3d orbital (n + l = 3+2=5) will be filled before a 4p orbital (n + l = 4 + 1 =5).

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ELECTRONIC CONFIGURATION

• The energies of different orbitals thus

follows the order

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1s<2s<2p<3s<3p<4s<3d<4p<5s……..

and so on.

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PAULI’S EXCLUSION PRINCIPLE

HUND’S RULE OF MAXIMUM MULTIPLICITY

• According to this Rule, "Electron pairing will not take place in orbitals of same energy (same subshell) until each orbital is singly filled”.

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• For example: The six electrons in Carbon atom are distributed as 1s²2s²2p_x¹2p_y¹ not as 1s²2s²2p_x² as shown in figure below.

ELECTRONIC CONFIGURATION OF ELEMENTS

Exceptional configuration of Chromium and Copper

• Chromium (atomic no. 24) :

expected configuration = 1s²2s²2p⁶3s²3p⁶4s²3d⁴

actual configuration = 1s²2s²2p⁶3s²3p⁶4s¹3d⁵

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• Copper (atomic no. 29) :

expected configuration = 1s²2s²2p⁶3s²3p⁶4s²3d⁹

actual configuration = 1s²2s²2p⁶3s²3p⁶4s¹3d¹⁰

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STABILITY OF COMPLETELY FILLED AND HALF FILLED SUBSHELLS�

• Symmetry of Orbital

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• Exchange energy

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