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Structure of Atom

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Chapter 2 : Structure of Atom

2.1 Sub-Atomic Particles arrow_upward

  • Electron, proton and neutron are sub-atomic particles.

  • 2.1.1 Discovery of Electron

  • In 1850, Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes.
  • A cathode ray tube is made of glass containing two thin pieces of metal, called electrodes, sealed in it.
  • The electrical discharge through the gases could be observed only at very low pressures and at very high voltages. The pressure of different gases could be adjusted by evacuation.
  • When sufficiently high voltage is applied across the electrodes, current starts flowing through a stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles.
  • The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide. When these rays, after passing through anode, strike the zinc sulphide coating, a bright spot on the coating is developed.
  • Results of the Experiment
  • The results of these experiments are summarized below.
  • The cathode rays start from cathode and move towards the anode.
  • These rays themselves are not visible but their behavior can be observed with the help of certain kind of materials (fluorescent or phosphorescent) which glow when hit by them.
  • In the absence of electrical or magnetic field, these rays travel in straight lines

  • 2.1.2 Charge to Mass Ratio of Electron

  • J.J. Thomson measured the ratio of electrical charge (e) to the mass of electron (me ) by using cathode ray tube.
  • Thomson was able to determine the value of e/me as:
  • Where me is the mass of the electron in kg and e is the magnitude of the charge on the electron in coulomb (C).

  • 2.1.3 Charge on the Electron

  • R.A. Millikan devised a method known as oil drop experiment, to determine the charge on the electrons. He found that the charge on the electron to be – 1.6 × 10–19 C.
  • The present accepted value of electrical charge is – 1.6022 × 10–19 C.

  • 2.1.4 Discovery of Protons and Neutrons

  • Electrical discharge carried out in the modified cathode ray tube led to the discovery of particles carrying positive charge.
  • The smallest and lightest positive ion was obtained from hydrogen and was called proton.
  • Neutrons:
  • Chadwick bombarded a thin sheet of beryllium by .
  • When electrically neutral particles having a mass slightly greater than that of the protons was emitted.
  • He named these particles as neutrons.

  • 2.2 Atomic Models arrow_upward

  • An atomic model is a model such that the complete type of every tuple is axiomatized by a single formula. Such types are called principal types, and the formulas that axiomatize them are called complete formulas.

  • 2.2.1 Thomson Model of Atom

  • Also known as Plum Pudding Model.
  • It can be visualised as a pudding or watermelon of positive charge with plums or seeds (electrons) embedded into it.

  • 2.2.2 Rutherford’s Nuclear Model of Atom

  • A stream of high energy  from a radioactive source was directed at a thin foil (thickness ) of gold metal.
  • The thin gold foil had a circular fluorescent zinc sulphide screen around it. Whenever α–particles struck the screen, a tiny flash of light was produced at that point. It was observed that: 
    • Most of the  passed through the gold foil undeflected.
    • A small fraction of the  was deflected by small angles.
    • A very few  (1 in 20,000) bounced back, that is, were deflected by nearly 180°. 

  • On the basis of above observations and conclusions, Rutherford proposed the nuclear model of atom (after the discovery of protons). According to this model:
    • 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.
    • The nucleus is surrounded by electrons that move around the nucleus with a very high speed in circular paths called orbits. Thus, Rutherford’s model of atom resembles the solar system in which the nucleus plays the role of sun and the electrons that of revolving planets.
    • Electrons and the nucleus are held together by electrostatic forces of attraction.

    2.2.3 Atomic Number and Mass Number

    Atomic Number:
  • The presence of positive charge on the nucleus is due to the protons in the nucleus.
  • The number of protons present in the nucleus is equal to atomic number (Z).
  • For example, the number of protons in the hydrogen nucleus is 1, in sodium atom it is 11.
  • Mass Number:
  • The mass of the nucleus, due to protons and neutrons.
  • Protons and neutrons present in the nucleus are collectively known as nucleons.
  • The total number of nucleons is termed as mass number (A) of the atom.
  •      Mass number (A) = Number of protons (Z ) + Number of neutrons (n)

    2.2.4 Isobars and Isotopes


  • Isobars are the atoms with same mass number but different atomic number for example,  and.

  • Isotopes:

  • Atoms with identical atomic number but different atomic mass number are known as Isotopes.
  • For example, Protium  and Deuterium .

  • 2.2.5 Drawbacks of Rutherford’s Model

  • Rutherford model cannot explain the stability of an atom.
  • It says nothing about the electronic structure of atoms i.e., how the electrons are distributed around the nucleus and what are the energies of these electrons.


  • Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and
  • Experimental results regarding atomic spectra which can be explained only by assuming quantized electronic energy levels in atoms.

  • 2.3.1 Wave Nature of Electromagnetic Radiation

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

  • Properties:

  • The oscillating electric and magnetic fields produced by oscillating charged particles are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.
  • Unlike sound waves or water waves, electromagnetic waves do not require medium and can move in vacuum.
  • There are many types of electromagnetic radiations, which differ from one another in wavelength (or frequency). These constitute what is called electromagnetic spectrum.
  • Different kinds of units are used to represent electromagnetic radiation.
  • These radiations are characterized by the properties, namely, frequency  and wavelength.

  • 2.3.2 Particle Nature of Electromagnetic Radiation: Planck’s Quantum Theory

  • Planck suggested that atoms and molecules could emit (or absorb) energy only in discrete quantities and not in a continuous manner, a belief popular at that time.
  • Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation.
  • The energy (E) of a quantum of radiation is proportional to its frequency  and is expressed by the following equation

  • The proportionality constant, ‘h’ is known as Planck’s constant and has the value 6.626 × 10–34 J s.
  • With this theory, Planck was able to explain the distribution of intensity in the radiation from black body as a function of frequency or wavelength at different temperatures.

  • Photoelectric Effect arrow_upward

  • 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.
  • This phenomenon is known as Photoelectric effect.
  • The results observed in this experiment were:

  • The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of light beam and the ejection of electrons from the metal surface.
  • The number of electrons ejected is proportional to the intensity or brightness of light.
  • For each metal, there is a characteristic minimum frequency, (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency, the ejected electrons come out with certain kinetic energy. The kinetic energies of these electrons increase with the increase of frequency of the light used.

  • Einstein’s Explanation:

  • Photon a particle representing a quantum of light or other electromagnetic radiation.
  • 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.
  • Since the striking photon has energy equal to  and the minimum energy required to eject the electron is, then the difference in energy  is transferred as the kinetic energy of the photoelectron.
  • Following the conservation of energy principle, the kinetic energy of the ejected electron is given by the equation:


  • Where me is the mass of the electron and v is the velocity associated with ejected electron.

  • Dual Behavior of Electromagnetic Radiation

  • Light has dual behaviour. Depending on the experiment, we find that light behaves either as a wave or as a stream of particles.
  • Whenever radiation interacts with matter, it displays particle like properties in contrast to the wavelike properties (interference and diffraction), which it exhibits when it propagates.

  • Emission and Absorption Spectra arrow_upward

  • 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”.
  • An absorption spectrum is like the photographic negative of an emission spectrum.

  • Spectroscopy

  • The study of emission or absorption spectra is referred to as spectroscopy.
  • The spectrum of the visible light, was continuous as all wavelengths (red to violet) of the visible light are represented in the spectra.

  • Line Spectra

  • The emission spectra of atoms in the gas phase, do not show a continuous spread of wavelength from red to violet, rather they emit light only at specific wavelengths with dark spaces between them. Such spectra are called line spectra or atomic spectra because the emitted radiation is identified by the appearance of bright lines in the 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. The hydrogen spectrum consists of several series of lines named after their discoverers.
  • Balmer showed 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:
  • Where n is an integer equal to or greater than 3.

  • The series of lines described by this formula are called the Balmer series.
  • The Balmer series of lines are the only lines in the hydrogen spectrum which appear in the visible region of the electromagnetic spectrum.
  • Rydberg, noted that all series of lines in the hydrogen spectrum could be described by the following expression:
  • The value 109,677 cm–1 is called the Rydberg constant for hydrogen.

  • 2.3.3 Evidence for the Quantized Electronic Energy Levels: Atomic Spectra

  • The speed of light depends upon the nature of the medium through which it passes.
  • The beam of light is deviated or refracted from its original path as it passes from one medium to another.
  • When a ray of white light is passed through a prism, the wave with shorter wavelength bends more than the one with a longer wavelength.

  • 2.4 Bohr’s Model for Hydrogen Atom arrow_upward

  • Bohr’s model for hydrogen atom is based on the following postulates:
    • The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus.
    • The energy of an electron in the orbit does not change with time. However the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state.
    • The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by , is given by :

    • The angular momentum of an electron in a given stationary state can be expressed as:

  • According to Bohr’s theory for hydrogen atom:
    • The stationary states for electron are numbered n = 1, 2, 3.......... These integral numbers are known as Principal quantum numbers.
    • The radii of the stationary states are expressed as:

            rn = n2 a0

    • Where a0 = 52.9 pm. Thus the radius of the first stationary state, called the Bohr orbit, is 52.9 pm. normally the electron in the hydrogen atom is found in this orbit (that is n=1). As n increases the value of r will increase. In other words the electron will be present away from the nucleus.
    • The most important property associated with the electron, is the energy of its stationary state. It is given by the expression.

    • Where RH is called Rydberg constant and its value is 2.18 × 10-18 J.
    • The energy of the lowest state also called the ground state is:

    • The energy of the stationary state for n = 2 will be:

    • Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom. For example, He+ , Li2+ etc. The energies of the stationary states associated with these kinds of ions are given by the expression.

    2.4.1 Explanation of Line Spectrum of

  • 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.

  • 2.4.2 Limitations of Bohr’s Model

  • It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques.
  • This model is also unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which possesses only two electrons.
  • Further, Bohr’s theory was also unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman Effect) or an electric field (Stark effect).
  • It could not explain the ability of atoms to form molecules by chemical bonds.

  • 2.5.1 Dual Behavior of Matter arrow_upward

  • De Broglie proposed that matter, like radiation, should also exhibit dual behavior i.e., both particle and wavelike properties.
  • This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, de Broglie, from this analogy, gave the following relation between wavelength  and momentum (p) of a material particle.
  • Where m is the mass of the particle, v its velocity and p its momentum.
  • De Broglie’s prediction was confirmed experimentally when it was found that an electron beam undergoes diffraction, a phenomenon characteristic of waves.

  • 2.5.2 Heisenberg’s Uncertainty Principle arrow_upward

  • It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.
  • Mathematically, it can be given as in equation:
  • Where  is the uncertainty in position, (or ) is the uncertainty in momentum (or velocity) of the particle.

  • Significance of Uncertainty Principle

  • It rules out existence of definite paths or trajectories of electrons and other similar particles.
  • The effect of Heisenberg Uncertainty Principle is significant only for motion of microscopic objects and is negligible for that of macroscopic objects.
  • In dealing with milligram-sized or heavier objects, the associated uncertainties are hardly of any real consequence.
  • The precise statements of the position and momentum of electrons have to be replaced by the statements of probability, that the electron has at a given position and momentum.

  • 2.6 Quantum Mechanical Model of Atom

  • The branch of science that takes into account this dual behavior of matter is called quantum mechanics.
  • Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties. It specifies the laws of motion that these objects obey.
  • The fundamental equation of quantum mechanics was developed by Schrödinger.
  • The Schrödinger equation is written as:
    • Where  is a mathematical operator called Hamiltonian.

    2.6.1 Orbitals and Quantum Numbers

  • Atomic orbitals are precisely distinguished by quantum numbers.
  • Each orbital is designated by three quantum numbers labelled as n, l and ml .

    Principal Quantum Number (n)
  • The principal quantum number ‘n’ is a positive integer with value of n = 1, 2, 3....... .
  • The principal quantum number determines the size and to large extent the energy of the orbital.
  • The principal quantum number also identifies the shell. With the increase in the value of ‘n’, the number of allowed orbital increases and are given by ‘n2 ’.  
  • All the orbitals of a given value of ‘n’ constitute a single shell of atom and are represented by the following letters

  • N










    Azimuthal quantum number ‘l’:
  • Azimuthal quantum number ‘l’ is also known as orbital angular momentum or subsidiary quantum number.
  • It defines the three dimensional shape of the orbital. For a given value of n, l can have n values ranging from 0 to n – 1. For example, for n = 3, the possible l values are 0, 1 and 2.
  • Each shell consists of one or more subshells or sub-levels. The number of subshells in a principal shell is equal to the value of n. For example, there are two sub-shells (l = 0, 1) in the second shell (n = 2).
  • Sub-shells corresponding to different values of l are represented by the following symbols:

  • Value of l:






    Notation for sub-shell






    Magnetic orbital quantum number ‘ml ’:
  • Magnetic orbital quantum number ‘ml ’ gives information about the spatial orientation of the orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’ value) 2l+1 values of ml are possible and these values are given by:
  •     ml = -l, - (l - 1), - (l - 2)…. 0, 1…… (l - 2), (l - 1), l

    Electron Spin:
  • An electron spins around its own axis.
  • An electron has, besides charge and mass, intrinsic spin angular quantum number. Spin angular momentum of the electron — a vector quantity, can have two orientations relative to the chosen axis.
  • These two orientations are distinguished by the spin quantum numbers ms which can take the values of +­ or –­. These are called the two spin states of the electron and are normally represented by two arrows,  (spin up) and  (spin down).
  • An orbital cannot hold more than two electrons and these two electrons should have opposite spins.

  • 2.6.2 Shapes of Atomic Orbitals

  • According to the German physicist, Max Born, the square of the wave function  at a point gives the probability density of the electron at that point.
  • For 1s orbital the probability density is maximum at the nucleus and it decreases sharply as we move away from it.
  • On the other hand, for 2s orbital the probability density first decreases sharply to zero and again starts increasing. After reaching small maxima it decreases again and approaches zero as the value of r increases further.
  • The region where this probability density function reduces to zero is called nodal surfaces or simply nodes.
  • In general, it has been found that ns-orbital has (n – 1) nodes, that is, number of nodes increases with increase of principal quantum number n.

  • Boundary surface diagrams

  • In this type of representation, a boundary surface or contour surface is drawn in space for an orbital on which the value of probability density  is constant.
  • Boundary surface diagram of constant probability density is taken to be good representation of the shape of the orbital which encloses a region or volume in which the probability of finding the electron is very high, say, 90%.

    Boundary surface diagram for s orbital:
  • For a s orbital it is actually a sphere centered on the nucleus. In two dimensions, this sphere looks like a circle.
  • In reality all the s-orbitals are spherically symmetric, that is, the probability of finding the electron at a given distance is equal in all the directions.
  • It is also observed that the size of the s orbital increases with increase in n, that is, 4s > 3s > 2s > 1s and the electron is located further away from the nucleus as the principal quantum number increases.
  • Boundary surface diagrams for p orbitals
  • Each p orbital consists of two sections called lobes that are on either side of the plane that passes through the nucleus.
  • The probability density function is zero on the plane where the two lobes touch each other. The size, shape and energy of the three orbitals are identical.
  • They differ however, in the way the lobes are oriented. Since the lobes may be considered to lie along the x, y or z axis, they are given the designations 2px , 2py , and 2pz .
  • Boundary surface diagrams for d orbitals:
  • There are five d-orbitals and are designated as dxy , dyz , dxz ,  and. The shapes of the first four d-orbitals are similar to each other, where as that of the fifth one, , is different from others, but all five 3d orbitals are equivalent in energy. The d orbitals for which n is greater than 3 (4d, 5d...) also have shapes similar to 3d orbital, but differ in energy and size.
  • The boundary surface diagrams of d orbitals are shown below:
  • Besides the radial nodes, the probability density functions for the np and nd orbitals are zero at the plane (s), passing through the nucleus (origin). For example, in case of pz orbital, xy-plane is a nodal plane, in case of dxy orbital, there are two nodal planes passing through the origin and bisecting the xy plane containing z-axis.
  • The total number of nodes are given by (n – 1), i.e., sum of l angular nodes and (n – l – 1) radial nodes.

    2.6.3 Energies of Orbitals

  • The energy of an electron in a hydrogen atom is determined solely by the principal quantum number.
  • Thus the energy of the orbitals increases as follows:
  •     1s < 2s = 2p < 3s = 3p = 3d <4s = 4p = 4d = 4f <

  • The 1s orbital in a hydrogen atom corresponds to the most stable condition and is called the ground state and an electron residing in this orbital is most strongly held by the nucleus. An electron in the 2s, 2p or higher orbitals in a hydrogen atom is in excited state.
  • The energy of an electron in a multi-electron atom depends not only on its principal quantum number (shell), but also on its azimuthal quantum number (subshell). That is, for a given principal quantum number, s, p, d, f ... all have different energies.
  • The main reason for having different energies of the subshells is the mutual repulsion among the electrons in a multi-electron atom.
  • Rule:
  • The lower the value of (n + l) for an orbital, the lower is its energy. If two orbitals have the same value of (n + l), the orbital with lower value of n will have the lower energy.
  • This rule is depicted in the table given below:

  • 2.6.4 Filling of Orbitals in Atom arrow_upward

  • The filling of electrons into the orbitals of different atoms takes place according to the aufbau principle which is based on the Pauli’s exclusion principle, the Hund’s rule of maximum multiplicity and the relative energies of the orbitals.
  • Aufbau Principle:
  • In the ground state of the atoms, the orbitals are filled in order of their increasing energies.
  • In other words, electrons first occupy the lowest energy orbital available to them and enter into higher energy orbitals only after the lower energy orbitals are filled.
  • The order in which the energies of the orbitals increase and hence the order in which the orbitals are filled is as follows:
  •     1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s .........

  • The order may be remembered by using the method given in the figure given below.
  • Starting from the top, the direction of the arrows gives the order of filling of orbitals that is starting from right top to bottom left.
  • Pauli Exclusion Principle
  • No two electrons in an atom can have the same set of four quantum numbers. Pauli exclusion principle can also be stated as:
  • “Only two electrons may exist in the same orbital and these electrons must have opposite spin.”
  • This means that the two electrons can have the same value of three quantum numbers n, l and ml , but must have the opposite spin quantum number.
  • This principle helps in calculating the capacity of electrons to be present in any subshell.
    • The maximum number of electrons in the shell with principal quantum number n is equal to 2n2 .
    Hund’s Rule of Maximum Multiplicity
  • This rule deals with the filling of electrons into the orbitals belonging to the same subshell (that is, orbitals of equal energy, called degenerate orbitals).
  • It states: pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied.
  • Since there are three p, five d and seven f orbitals, therefore, the pairing of electrons will start in the p, d and f orbitals with the entry of 4th, 6th and 8th electron, respectively.
  • It has been observed that half-filled and fully filled degenerate set of orbitals acquire extra stability due to their symmetry.

  • 2.6.5 Electronic Configuration of Atoms

  • The distribution of electrons into orbitals of an atom is called its electronic configuration.
  • The electronic configuration of different atoms can be represented in two ways:
    • sa pb dc notation
    • Orbital diagram

  • The hydrogen atom has only one electron which goes in the orbital with the lowest energy, namely 1s. The electronic configuration of the hydrogen atom is 1s1 meaning that it has one electron in the 1s orbital.
  • The second electron in helium (He) can also occupy the 1s orbital. Its configuration is, therefore, 1s2 .
  • The third electron of lithium (Li) is not allowed in the 1s orbital because of Pauli exclusion principle. It, therefore, takes the next available choice, namely the 2s orbital. The electronic configuration of Li is 1s2 2s1 .
  • The electronic configuration of other elements are as follows:
  • Be = 1s2 2s2

        B = 1s2 2s2 2p1

        C = 1s2 2s2 2p2

        N = 1s2 2s2 2p3

        O = 1s2 2s2 2p4

        F = 1s2 2s2 2p5

        Ne = 1s2 2s2 2p6

    2.6.6 Stability of Completely Filled and Half Filled Subshells arrow_upward

  • The ground state electronic configuration of the atom of an element always corresponds to the state of the lowest total electronic energy.
  • The electronic configurations of most of the atoms follow the basic rules. However, in certain elements such as Cu, or Cr, where the two subshells (4s and 3d) differ slightly in their energies, an electron shifts from a subshell of lower energy (4s) to a subshell of higher energy (3d), provided such a shift results in all orbitals of the subshell of higher energy getting either completely filled or half filled.
  • The valence electronic configurations of Cr and Cu, therefore, are 3d5 4s1 and 3d10 4s1 respectively and not 3d4 4s2 and 3d9 4s2 . It has been found that there is extra stability associated with these electronic configurations.

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