atomic structure 2011

Unit- structure of atomPaper A Class 11th 1 | P a g e B y : A l t a f

IntroductionThe word atom is a Greek word meaning indivisible, i.e., an ultimate particle which cannot be further subdivided. The idea that all matter ultimately consists of extremely small particles was conceived by ancient Indian and Greek philosophers. The old concept was put on firm footing by John Dalton in the form of atomic theory which he developed in the years 1803–1808. This theory was a landmark in the history of chemistry. According to this theory, atom is the smallest indivisible part of matter which takes part in chemical reactions. Atom is neither created nor destroyed. Atoms of the same element are similar in size, mass and characteristics; however, atoms of different elements have different size, mass and characteristics. In 1833, Michael Faraday showed that there is a relationship between matter and electricity. This was the first major break-through to suggest that atom was not a simple indivisible particle of all matter but was made up of small particles. Discovery of electrons, protons and neutrons discarded the indivisible nature of the atom proposed by John Dalton. Discharge tube (Discovery of electron) It is a tube filled with low-pressure gas that glows when it conducts electricity at a given voltage. It is used in neon & fluorescent lights. Construction A discharge tube is a long glass tube G closed at both ends. Two circular metal plates A & B, called electrodes are sealed at the two ends of the tube. These are connected to a source of electrical power such as an induction coil which can supply very high voltage. The plate A connected to the negative terminal of the source is called cathode whereas the plate B connected to the positive terminal of the source is called anode. A side tube S is also fused to the tube G & can be connected to a vacuum pump to suck out the air or gas present inside the tube to reduce the pressure inside the tube.

WorkingOn applying high voltage (about 10,000 volts) between the electrodes, the results observed at different pressures of the air or gas inside the tube are as follows (i) at ordinary pressure, no current flows through the air between the electrodes. This is because air or any gas at this pressure is a poor conductor of electricity.(ii) If the air inside the tube is sucked out by the vacuum pump so that the pressure falls to about 1 mm of mercury the entire discharge tube begins to glow uniformly with magenta-red color. (The color emitted depends upon the nature of the gas taken in the tube) The study with different gases was made by Crookes. That is why these discharge tubes are also called Crookes tubes. (iii) If more air from inside the tube is sucked out so that pressure falls further the glow is intercepted by dark bands at right angle to the axis of the tube.(iv) When the pressure of the air or the gas inside the tube falls to about 0.001 mm, the discharge completely disappears, i.e., there is no light emitted by the air. The tube appears completely dark. However, the glass wall of the tube exactly opposite to the cathode glows with a greenish-yellow fluorescent light. Some sort of invisible rays moved from the negative electrode to the positive electrode Since the negative electrode is referred to as cathode, these rays were called cathode rays. (fluorescence The emission of electromagnetic radiation, especially light, by an object or substance exposed to radiation or bombarding particles is k/as fluorescence.) Television picture tube is a cathode ray tube in which picture is produced on the television screen. Similarly,


Fluorescent light tubes are cathode ray tubes coated inside with suitable material (called phosphor) which produce visible light when hit by cathode rays. Origin of cathode rays Cathode rays are a stream of electrons emitted from a cathode in a vacuum(discharge)tube. The cathode rays are first produced from the material of the cathode. These then hit the gas atoms present in the discharge tube & knock out electrons (from the gas atoms). These electrons travel towards the oppositely charged anode in the form of cathode rays. This shows that all materials used as cathode as well as all gases contain electrons. Hence, we conclude that electrons are constituents of all atoms. Properties of cathode rays1. Cathode rays travel in straight lines. A shadow of metallic object placed in the path is cast on the wall opposite to the cathode.2. . Cathode rays carry negative charge. When the rays are passed between two electrically charged plates, these are deflected towards the positively charged plate. They discharge a positively charged gold leaf electroscope. It shows that cathode rays carry negative charge.4. They produce green fluorescence on the glass walls of the discharge tube as well as on certain substances such as zinc sulphide.5. Cathode rays produce heating effect. Thus, as they strike a metal foil, it becomes hot.6. They possess kinetic energy. It is shown by the experiment that when a small pin wheel is placed in their path, the blades of the wheel are set in motion. Thus, the cathode rays consist of material particles which have mass and velocity. These particles carrying negative charge were called negatrons by Thomson. The name `negatron' was changed to `electron' by Stoney.7. Cathode rays produce X-rays. When these rays fall on material having high atomic mass like tungsten, molybdenum etc., new type of penetrating rays of very small wavelength are emitted which are called X-rays. 8.These rays affect the photographic plate.9.These rays can penetrate through thin foils of solid materials and cause ionisation in gases through which they pass.10.The nature of the cathode rays is independent of- the nature of the cathode and the gas in the discharge tube. Electrons An electron can, thus,be defined as a sub-atomic particle which carries charge -1.602×10-19coulomb, i.e., one unit negative charge and has mass 9.11 × 10-31Kg, i.e., nearly 1/1840th of an atom of hydrogen. As charge on the electron is —l unit & mass is negligible, it is represented by the symbol O-1e.Discovery of electron J.J. Thomson in 1897 carried out discharge tube experiments & showed that Cathode rays were made up of negatively charged particles called electrons. It was also found that, whatever the nature of the gas or the material of the cathode, the electrons had the same charge to mass (e/m) ratio. Anode rays:- (Discovery of Proton) These are the positively charged radiations that travel from anode to cathode in a discharge tube containing a gas under low pressure, when a high potential difference is applied between the electrodes. They are also known as Canal rays or Positive rays. The existence of positively charged particles (now k/as protons) in an atom was shown by Goldstein in 1886 with discharge tube experiments. He took a discharge tube with a perforated cathode. On applying high voltage b/w the anode & the cathode, he observed that besides the fluorescence at E due to cathode rays coming from the cathode, fluorescence is also observed on the glass wall of the tube at F. This shows that some passed through the holes or canals (T/F also k/as “canal rays”) in the cathode & struck the glass wall of the tube at F. Since these rays are coming from the side of the anode, therefore, they are called “anode rays”.


Further, their deflection in an electric field shows that they carry positive charge. Hence they are also called “positive rays”.Origin of Anode rays Anode rays do not originate from the anode. They are produced in the space between the anode & the cathode. It is believed that gas atoms which are bombarded have their electrons knocked out in the form of cathode rays. The remaining parts of these atoms become positively charged particles that travel as a beam of anode rays towards the negatively charged cathode. Properties of anode rays 1. They travel in straight lines. 2. They are made up of material particles. 3. They carry positive charge. 4. Their charge/mass (e/m) ratio is not constant but depends upon the nature of the gas taken in the discharge tube.5. Mass of these positively charged particles also depends upon the nature of the gas & is found to be nearly equal to the mass of the atom of the gas.6. Charge on the positively charged particles constituting the anode rays is also found to depend upon the nature of the gas & the voltage applied. However, the charge is found to be a whole number multiple of the charge present on the electron. It may be + 1, + 2 or + 3 units depending upon the number of electrons knocked out of the gaseous atom.ProtonA proton is a sub-atomic elementary particle which carries one unit positive charge & has a mass nearly equal to that of a hydrogen atom. As charge on the Proton is +l unit & mass is 1 amu or u, it is represented by the symbol 1

1p. A proton is in fact an ionized hydrogen atom, i.e., it is obtained by the removal or loss of the only electron present in hydrogen atom. The number of protons in the nucleus of an atom determines what kind of a chemical element it is. Discovery of Neutron The discovery of neutron was actually made about 20 years after the structure of atom was elucidated by Rutherford. Atomic masses of different atoms could not be explained if it was accepted that atoms consisted only of protons and electrons. Thus, Rutherford (1920) suggested that in an atom, there must be present at least a third type of fundamental particles which should be electrically neutral and possess mass nearly equal to that of proton. He proposed the name for such fundamental particle as neutron. In 1932, Chadwick bombarded beryllium with a stream of α-particles. He observed that penetrating radiations were produced which were not affected by electric and magnetic fields. These radiations consisted of neutral particles, which

were called neutrons. The nuclear reaction can be shown as:

The mass of the neutron was determined. It was 1.675 × 10-27Kg, i.e., nearly equal to the mass of proton. Thus, a neutron is a sub-atomic particle which has a mass 1.675 × 10-27 Kg, approximately 1u, or nearly equal to the mass of proton or hydrogen atom and carrying no electrical charge.The e/m value of a neutron is thus zero. As charge on neutron = 0 & mass = 1 u, therefore, it is represented by the symbol, 1

on. The main


characteristics of the three fundamental particles, i.e., electron, proton & neutron are given in the Table below:

Atomic modelsObservations obtained from the experiments suggested that Dalton’s indivisible atom is composed of sub-atomic particles carrying positive and negative charges. Different atomic models were proposed to explain the distributions of these charged particles in an atom. Thomson Model of AtomJ. J. Thomson, in 1898, proposed that an atom possesses a spherical shape (radius approximately 10–10 m) in which the positive charge is uniformly distributed. The electrons are embedded into it in such a manner as to give the most stable electrostatic arrangement. Many different names are given to this model, for example, plum pudding, raisin pudding or watermelon. This model can be visualised as a pudding or watermelon of positive charge with plums or seeds (electrons) embedded into it. An important feature of this model is that the mass of the atom is assumed to be uniformly distributed over the atom. Although this model was able to explain the overall neutrality of the atom, but was not consistent with the results of later experiments.( Thomson was awarded Nobel Prize for physics in 1906, for his theoretical and experimental investigations on the conduction of electricity by gases.)Rutherford’s Nuclear Model of Atom:

In 1911, Rutherford (and his students Hans Geiger and Ernest Marsden) performed α-ray scattering experiment to know about the position of the two fundamental particles – electrons and protons in an atom.

In the experiment a stream of very highly energetic alpha particles from a radio active source (Ra or Po) placed in a lead box with a hole in it was directed at a thin foil (≈ 100 nm thick) of gold metal. The alpha particles coming out of the thin gold foil were then detected by scintillation s. Whenever, alpha particles struck the screen, a tiny flash of light was produced at that point.Rutherford noticed the following experimental observations :


1. Most of the alpha particles (nearly 99%) passed through the foil without being deviated from their paths.

2. A small fraction of the alpha particles was deflected by small angles. 3. A very few alpha particles (≈ 1 in 20,000) were bounced back that is were deflected by

nearly 1800. Rutherford drew the following conclusions regarding the structure of atom.

1) Since most of the alpha particles passed through the foil undeflected, it indicates that the most of the space in an atom is empty.

2) A few positively charged α-particles were deflected. The deflection must be due to enormous repulsive force showing that the positive charge of the atom is not spread through out the atom as Thomson had presumed. The positive charge has to be concentrated in a very small volume that repelled and deflected positively charged α-particles.

3) α-particles which make head on collision with heavy positive charge centre are deflected through large angles.

On the basis of above observations and conclusions Rutherford proposed the nuclear model of atom. According this model :

1) Most of the mass and all positive charge of an atom is concentrated in a very small region called nucleus. Size of the nucleus is extremely small as compared with the size of the atom.

2) The radius of the atom is of the order of 10 -10m whereas radius of nucleus is of the order of 10-15m.

3) The positive charge of the nucleus is due to protons. The magnitude of the charge of nucleus is different for atoms of different elements.

4) The nucleus is surrounded by electrons which are revolving around it at very high speeds. The electrostatic force of attraction between electrons and the nucleus is balanced by the centrifugal force acting on revolving electrons.

5) Total negative charge on the electrons is equal to the total positive charge on the nucleus so that atom on the whole is electrically neutral.

6) Most of the space inside an atom is empty. 7) The limitations of Rutherford's model are as follows:

1) According to the 'Classical Theory of Electromagnetism', whenever a charged body is subjected to an acceleration around an opposite charge, it emits radiation continuously. Hence, the electron in Rutherford's atom will lose energy and will not be able to stay in a circular path around the nucleus and will ultimately go into spiral motion. Such an electron will fall into the nucleus. This, of course, does not happen for electrons in an atom and this discrepancy could not be explained at that time.

8) 2) Rutherford's model could not explain the emission of various spectral lines (Lyman, Balmer, Paschen, Brackett, and Pfund series) in the emission spectrum of hydrogen.

9) 3) It could not suggest the discontinuous spectrum of hydrogen, which is in the form of characteristic line wavelengths.

Atomic number ( Z )


{Moseley devised an experiment to find out positive charge on the nucleus .He calculated the charge on the nucleus from the frequencies or wave lengths of X-rays emitted by different elements. The number of unit-positive charges on the nucleus of the atom of the element is called atomic number of the element. The positive charge on the nucleus is due to protons and each proton carries one unit positive charge. Atomic number of an element is equal to the number of protons in the nucleus of its atom. Further in an atom the number of protons is equal to the number of electrons. Hence atomic number is also equal to the number of electrons in an atom of the element. Thus atomic number of an element is equal to the number of protons in the nucleus of its atom or the number of extra-nuclear electrons. Generally it is denoted by the letter Z.Atomic number Z = Number of protons = Number of electrons.Mass number (A)Mass of an atom is mainly concentrated in the nucleus. In the nucleus there are protons and neutrons. The mass of an atom is mainly due to protons and neutrons. The number of protons and neutrons in the nucleus is called mass number of the atom. It is generally represented by the letter A .Mass number = Number of protons + Number of neutrons = Number of nucleons. From the knowledge of atomic number and mass number of an element, it is possible to calculate , the number of electrons, protons and neutrons in an atom of the element. For example, atomic number and mass number of sodium are 11 and 23 respectively. Number of electrons, protons and neutrons in an atom of it can be calculated as under :Number of protons = Atomic number = 11Number of electrons = Atomic number = 11Number of neutrons = (Mass number) − (Atomic number) = 23 − 11 = 12 In case of ions, the number of protons and neutrons remain the same as in atoms, however, the number of electron changes. This is due the reason that an ion is formed either by addition or by removal of one or more electrons from the neutral atom.For example, Mg2+ ion has two electrons less than the number of electrons in Magnesium atom. Knowing that the atomic number and mass number of Magnesium as 12 and 24 respectively, the number of electrons , protons and neutrons in i Mg2+ons may be calculated as under :Number of protons = Atomic number = 12Number of electrons = Atomic number − 2 = 12 − 2 = 10Number of neutrons = 24 − 12 = 12Similarly, a negative ion is formed by a addition of one or more electrons to the neutral atom. For example, P3− ion (phosphide ion) is formed by the addition of three electrons to a phosphorus atom.P + 3 e− → P3−

Knowing the atomic number of phosphorus ( Z = 15 ) , and mass number ( A = 31 ) , the number of electrons , protons and neutrons in phosphide ion may be calculated as under :Number of protons = Atomic number = 15Number of electrons = Atomic number + 3 = 18Number of neutrons = Mass number − Atomic number = 31 − 15 = 16IsotopesAtoms of the same element having the same atomic number but different mass number are called isotopesFor example , there are three isotopes of hydrogen having mass numbers , 1, 2 and 3 respectively and each of them having atomic number equal to 1. They are represented as 1

1 H, 21H and 3

1H and named as protium (H), deuterium(D) and tritium (T)respectively. Ordinary hydrogen is protium. Isotopes of other elements do not have special names. They are represented by simply indicating the values of A on the symbol. For example, isotopes of chlorine are written as 35Cl and 37Cl.ISOBARS Atoms of the different elements having the same mass number but different atomic number are called isobarse.g. 40

18Ar , 4019K, 40

20CaISOTONESAtoms of different elements which contain the same number of neutrons are called isotones . e.g.14

6C, 157N, 16

8O.ISOSTERS


These are molecules of different substances which contain the same number of atoms and same total number of electrons which leads to similarity in their physical properties. The phenomenon is called isosterism. For example, carbon dioxoide CO2and nitrous oxide, N2O are isosters.IsodiaphersIsodiapheres are the atoms having the same difference of neutron and proton or same isotopic number. Nuclides and its decay product after the emission of an α -particle are called isodiapheres. e.g. . U -235 and Th- 231 are isodiaphers 143 - 92 and 141-90 = 51 in both

Dual nature of electromagnetic radiation({☺During the period of developments of new models and to improve Rutherford’s model of an atom,two developments played a major role. These are: (i) Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and(ii) Experimental results regarding atomic spectra which can be explained only by assuming quantized (fixed) electronic energy levels in atoms.})wave nature of electromagnetic radiationNewton (17 th century) : - Suggested that light has a corpuscular (or particle) nature i.e. it consists of a stream of energetic particles. The particle nature of light explained some of the experimental laws like reflection and refraction of light. However, it failed to explain the phenomena of interference and diffraction.James Maxwell (19 th Century): - suggested that light waves are electromagnetic in nature i.e. they are oscillations of electric and magnetic filed in space. This theory could explain clearly optical phenomena such as interference, refraction, diffraction, polarization etc. but failed to explain black body radiations (radiations which are emitted by hot bodies) and photoelectric effect (ejection of electrons when light is incident on metal surfaces). characteristics of electromagnetic waves (i) 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.(ii) In vaccum all types of electromagnetic radiations, regardless of wavelength, travel at the same speed, i.e., 3.0 x 108 m s-1 (2.997925 x 108 m s-1, to be precise). This is called speed of light and is given the symbol ‘c’. The frequency (ν ), wavelength (λ) and velocity of light (c) are related by the equation c = ν λ (iii) Electromagnetic waves do not require medium and can move in vacuum. Particle Wave

1. A particle occupies a well-defined position in space i.e. a particle is localized in space 2. When a particular space is occupied by one particle, the same space cannot be occupied simultaneously by any other particle. In other words, particles do not interfere. 3. When a number of particles are present in a given region of space, their total value is equal to their sum i.e. it is neither less nor more.

1. A wave is spread out in space. i.e, delocalized in space. 2. Two or more waves can coexist in the same region of space and hence interfere. 3. When a number of waves are present in a given region of space, due to interference, the resultant wave can be larger or smaller than the individual waves i.e. interference may be constructive or destructive.


PARTICLE NATURE OF ELECTROMAGNETIC RADIATION – Some of the experimental phenomena such as diffraction and interference can be explained by the wave nature of the electromagnetic radiation. However, experimental observations such as emission of radiation from a hot body and photoelectric effect cannot be explained on this basis.Black body radiation The ideal body , which emits and absorbs all frequencies(which is a perfect absorber and perfect radiator of energy), is called black body and the radiation emitted by this body is called black body radiation. If any substance with high melting point (e.g, an iron bar) is heated, it first becomes red, then yellow------ white and finally blue as temperature becomes very high. According to electromagnetic wave theory, the energy is emitted or absorbed continuously. Hence, the energy of any electromagnetic radiation is proportional to its intensity i.e. a square of amplitude and is independent of its frequency or wavelength. Thus, according to the wave theory, the radiation emitted by the body being heated should have the same colour, although its intensity may vary as the heating is continued. In terms of frequency, it means that the radiation emitted goes on from a lower frequency to a higher frequency as the temperature increases. The red colour lies in the lower frequency region , while blue colour belongs to the higher frequency region of the electromagnetic spectrum. The exact frequency distribution of the emitted radiation (i.e., intensity versus frequency curve of the radiation ) from a black body depends upon its temperature. At a given temperature, intensity of radiation emitted increases with decrease of wave length, reaches a maximum value at a given wave length and then starts decreasing with further decrease of wave length, as shown .The above experimental results cannot be explained on the basis of the wave theory of light. Explanation of Black Body Radiation. When some solid substance is heated, the atoms of the substance are set into oscillation and emit radiation of frequency, . Now, as heating is continued, more and more energy is being absorbed by the atoms and they emit radiations of higher and higher frequency. As red light has minimum frequency, yellow has higher frequency, therefore, the body on heating becomes first red, then yellow and so on.

When a black body is heated, it emits thermal radiations of different wavelengths or frequency. To explain these radiations,Planck's quantum theory of radiation The main features of Planck's quantum theory of radiation are:(i) Radiant energy is emitted or absorbed, not continuously but discontinuously, in discrete units or packets of energy called quanta. (ii) Each packet of energy or quantum has a definite amount of energy. In the case of light, the quantum of light energy is called a photon. (iii) The magnitude of energy (E), associated with a quantum of radiation, is proportional to the frequency of radiation.

where the proportionality constant 'h', is a universal constant known as Planck's constant. It has a value of 6.626 10-34 J s or 6.626 10-27erg s. This relation was found to be valid for all types of electromagnetic radiations. (iv) The gain or loss of radiant energy involves discrete energy changes that must be a whole number multiple of the quantum i.e.E = nh ; where n is an integer such as 1, 2, 3...


Thus, a body can emit or absorb energy equal to or any other integral multiple

of . But it cannot absorb energy equal to or any other fractional value of . Neil Bohr used this theory to explain the structure of atom. Photoelectric EffectIn 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 . When radiations with certain minimum frequency strike the surface of a metal, the electrons are ejected from the surface of the metal . This phenomenon is called photoelectric effect. The electrons emitted are called photo-electrons.

Equipment for studying Photoelectric effect.

The results observed in this experiment were:(i) 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.(ii) The number of electrons ejected is proportional to the intensity or brightness of light.(iii) For each metal, there is a characteristic minimum frequency, ν0 (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency ν >ν0, 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. The above observations cannot be explained by the Electromagnetic wave theory. According to this theory, since radiations are continuous, therefore it should be possible to accumulate energy on the surface of the metal, irrespective of its frequency and thus radiations of all frequencies should be able to eject electrons.Similarly, according to this theory, the energy of the electrons ejected should depend upon the intensity of the incident radiation.. Explanation of Photoelectric effect. Einstein (1905) was able to explain the photoelectric effect using Planck’s quantum theory of electromagnetic radiation as a starting point.Explanation of the different points of the photoelectric effect as under :(i) When light of some particular frequency falls on the surface of metal, the photon gives its entire energy to the electron of the metal atom. The electron will be dislodged or detached from the metal atom only if the energy of the photon is sufficient to overcome the force of attraction of the electron by the nucleus. That is why photo-electrons are ejected only when the incident light has a certain minimum frequency (threshold frequency ν0 ).(ii) If the frequency of the incident light (ν) is more than the threshold frequency (ν0 ), the excess energy (hν – hν0 ) is imparted to the electron as kinetic energy. i.e. K.E. of the

ejected electron = . Hence greater is the frequency of the incident light, greater is the kinetic energy of the emitted electron.

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(iii) Increasing the intensity of light of a given frequency increases the number of photons but does not increase the energies of photons. Hence, when the intensity of light is increased, more electrons are ejected but the energies of these electrons are not altered.If kinetic energy of the emitted photo-electrons is plotted against the frequency of the absorbed photons, a straight line of slope h is obtained . Dual Behaviour of Electromagnetic RadiationLight has been regarded as wave to explain the phenomena of interference and diffraction and as particle to explain the phenomena of Black body radiation & photoelectric effect. Thus it may be concluded that light possesses both particle and wave-like properties, i.e., light has dual behaviour. Depending on the experiment, 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. ELECTROMAGNETIC SPETCRUM Various types of electromagnetic radiation having different wave lengths (or frequency). are known. They constitute the electromagnetic spectrum. The arrangement of different types of electromagnetic radiations in the order of increasing wave lengths (or decreasing frequencies) is known as Electromagnetic Spectrum. The complete electromagnetic spectrum is shown .

Different regions of spectrum are identified by different names .Some important electromagnetic radiations in the decreasing order of their wave lengths are :Radio waves > Microwaves > Infrared (IR) > Visible >Ultra violet (UV) > X-rays > Gamma rays > Cosmic rays{(☺SOURCES OF ELECTROMAGNETIC RADIATIONSRadio waves (ν = 10 6 Hz) are generated from alternating electric currents of high frequencies. These are used in broadcasting.Microwaves (ν = 10 10 Hz) are produced by special generators, e.g., Klystron tube. These are used in telephone transmission and radar. These are also absorbed by food molecules and hence are used to cook food.IR radiations (ν = 10 13 Hz) are emitted by incandescent objects. These produce high thermal effect and is heat radiation. These are used in physiotherapy. A plot of the frequencies of IR radiations versus the intensities of radiations absorbed is called infrared spectrum and used to identify a substance because each substance has a characteristic infra-red spectrum.Visible light radiations (ν = 3.95 x 10 14 – 7.9 x 10 14 Hz ) are produced from stars, arc lamps, hot filaments as of tungsten in an electric bulb.Ultra-violet radiations (ν = 10 16 Hz) are present in sun's rays. In the laboratory these can be produced from the arc lamps containing mercury vapour, xenon or hydrogen gas.X-rays (ν = 10 19 Hz) are produced when a stream of electrons strike a heavy metal target. These are used in radiotherapy.Cosmic rays (ν = 3 x 10 20 Hz to infinity) originate from the outer space and continously fall on the earth due to their great penetrating power. )}


Emission And Absorption SpectraElectromagnetic spectrum consists of radiations of different wave lengths and frequencies. An instrument used to separate the radiations of different wavelengths (or frequencies) is called spectroscope or a spectrograph. A spectroscope consists of a prism or a diffraction grating for the dispersion of radiations and a telescope to examine the emergent radiations with the human eye. However, if in a spectroscope, the telescope is replaced by a photographic film, the instrument is called a spectrograph and the photograph (or the pattern) of the emergent radiation recorded on the film is called a spectrogram or simply a spectrum of the given radiation.Depending upon the source of radiation, the spectra are broadly classified into (i) Emission spectra and (ii) Absorption spectra. These are briefly explained below :–1. Emission spectra. When the radiation emitted from some source e.g. from the sun or by passing electric discharge through a gas at low pressure or by heating some substance to high temperature etc. is passed directly through the prism and then received on the photographic plate, the spectrum obtained is called ‘Emission spectrum’.The emission spectra are mainly of two types:(i) Continuous spectra. When white light from any source such as sun, a bulb or any hot glowing body is analysed by passing through a prism, it is observed that it splits up into seven different wide bands of colours from violet to red, (like rainbow), as shown in Figure. These colours are so continuous that each of them merges into the next. Hence the spectrum is called continuous spectrum.(ii) Line spectra. When some volatile salt (e.g., sodium chloride) is placed in the Bunsen flame or an electric discharge is passed through a gas at low pressure, light is emitted. If this light is resolved in a spectroscope, it is found that no continuous spectrum is obtained but some isolated coloured lines are obtained on the 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. Further it is observed that each element gives its own characteristic spectrum, differing from those of all other elements. For example, sodium always gives two yellow lines (corresponding to wavelengths 5890 and 5896 Å). Hence the spectra of the elements are described as their finger prints differing from each other like the finger prints of the human beings. Several elements including Rubidium (Rb) Caesium (Cs),thallium(Tl) Indium (In) and gallium (Ga) were discovered in this way.Alkali metals like Na and K and alkaline earth metals like Ca, Sr and Ba are detected in qualitative analysis by flame test.

The element helium (He) was first discovered in the sun spectroscopically.The line spectra are obtained as a result of absorption and subsequent emission of energy by the electrons in the individual atoms of the element. Hence the line spectrum is also called atomic spectrum.


2. Absorption spectra. when white light from any source is first passed through the solution or vapours of a chemical substance and then analysed by the spectroscope, it is observed that some dark lines are obtained in the otherwise continuous spectrum . These dark lines are supposed to result from the fact that when white light (containing radiations of many wavelengths) is passed through the chemical substance, radiations of certain wavelengths are absorbed, depending upon the nature of the element. Further it is observed that the dark lines are at the same place where coloured lines are obtained in the emission spectra for the same substance. This shows that the wavelengths absorbed were same as were emitted in the emission spectra. The spectrum thus obtained is, therefore, called ‘absorption spectrum’.

Line Spectrum of HydrogenWhen 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 in 1885 on the basis of experimental observations that if spectral lines are expressed in terms of wavenumber (ν ), then the visible lines of the hydrogen spectrum obey the following formula :

where n is an integer equal to or greater than 3 (i.e., n = 3,4,5,….)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. The Swedish spectroscopist, Johannes Rydberg, noted that all series of lines in the hydrogen spectrum could be described by the following expression :

where n1 = 1,2……..n2 = n1 + 1, n1 + 2………..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, Of all the elements, hydrogen atom has the simplest line spectrum. Line spectrum becomes more and more complex for heavier atom. There are however certain features which are common to all line spectra, i.e., (i) line spectrum of element is unique and (ii) there is regularity in the line spectrum of each element.

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Bohr’s model of atom:-To overcome the shortcomings of Rutherford’s model and to account for the line spectra of hydrogen. Neil Bohr (Danish physicist) in 1913 put forward his model of atom. Bohr proposed his model on the basis of Planck’s quantum theory. The main postulates of the Bohr's model are: -

1) The electrons in an atom revolve around the nucleus in certain specific orbits. These orbits are associated with definite amounts of energy and are called energy levels or energy shells. These orbits are arranged concentrically around the nucleus. The energy levels are designated as K, L, M, N, O, P, Q or numbered as 1, 2, 3, 4, 5, 6, 7 starting from the nucleus.

2) The electron can revolve around the nucleus only along those circular orbits for which the angular momentum of an electron is an integral multiple of the quantity h/2. That ismvr = nh/2

Where m = mass of the electronv = velocity of the electronr = radius of the orbit

n= an integer (1, 2, 3,----)h = Planck’s constant.

This postulate implies that the angular momentum of an electron revolving around the nucleus is quantised. 3) The energy of an electron revolving in a particular orbit is given by the expressionEn = - Z 2 e 4 m

8ε02 n2h2

where m = Mass of the electrone = charge of the electron

h = Planck’s constantn = number of orbitε0 = permitivity constant

When values are substituted in the above expression, the energy of an electron in the nth orbit comes out i.e be

En = -1312 kjmol-1

n2

Thus an electron cannot radiate energy if no lower energy level is available.4) As long as the electron stays in a particular orbit, its energy remains constant i.e.

electron can have acceleration and yet not radiate energy.5) Energy given out or absorbed is not continuous but is quantized i.e. in separate packets

of energy called quanta represented by h where h is Planck’s constant and is the frequency of radiation.

6) When an electron accepts a quantum of energy, it jumps from a lower energy level to higher energy level. The excited electron being unstable jumps down quickly to lower energy level by emitting energy in the form of light of suitable wavelength and frequency. The difference in the energies of two levels is given as follows

E = E2 – E1 = h where

E1=Energy of the electron in lower energy level

{* At the time, this view was proposed there was no reason for the quantization of momentum in terms of h/2π units except that correct results were obtained by this postulates}.

En = - Z 2 e 4 m 8ε0

2 n2h2

n876

5

4

3

2

1Lyman series (UV)

Balmer series (visible)

Paschen series

Bracket series

fund series

Formation of emission spectra of atomic hydrogen

IR


E2=Energy of the electron in higher energy levelE = Energy difference between the two levels.OTHER IMPORTANT POINTS

a) The stationary states for electron are numbered n = 1,2,3………. These integral numbers are known as Principal quantum numbers.b) The radii of the stationary states are expressed as r n = 0.529 x 10−10 (n 2 ) m As n increases , r n also increases indicating greater separation between the orbit and the nucleus. The radius of first orbit r 1 , is called Bohr radius ( n= 1) is 52.9 pm.The radius for ions such as He+ , Li2+ the radius is given as :

where Z is the atomic number and has values 2 and 3 for He+ , Li2+ respectively.c) The most important property associated with the electron, is the energy of its stationary state. It is given by the expression.En = − RH(1/n2) n=1,2,3…..where RH is called Rydberg constant and its value is 2.18×10–18 J. The energy of the lowest state, also called as the ground state, is E1 = -2.18×10-18 (1/12) = -2.18×10-18 J.The energy of the stationary state for n = 2, will be : E2 = -2.18×10-18J ( 1/22) = = -0.545×10-18 J. 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+, Be3+ and so on. The energies of the stationary states associated with these kinds of ions (also known as hydrogen like species) are given by the expression.En = -2.18 x 10-18(Z2/n2) Jd) Velocity of an electron in nth orbit =2.18ᵪ106 Z/n ms-1

Bohr’s explanation of line spectrum of hydrogen:According to Bohr’s model of an atom the solitary electron of H-atom keeps on rotating in the first energy level in the ground state. In general, when atoms of a substance are exposed to conditions under which energy absorption that is excitation is possible, for example by the use of high temperature or an electrical discharge, the electron will take up energy and various jumps from lower to upper energy levels i.e from inner to outer orbit will occur. The return of the electrons from the various upper levels to the lower levels will result in the liberation of definite amounts of energy and each transition corresponds to a line of definite frequency in the emission spectrum. Since a number of different energy levels are possible in every atom, there will be a number of transitions and hence a series of lines will be observed in spectrum.

In the case of hydrogen the various possibilities by which the electrons fall back from various excited states (higher energy levels) to lower energy levels are depicted in the energy level diagram.


(1) Lyman series( T. Lyman.) When the electrons jump from the energy levels n2 equal to 2,3,4,5,6 etc to the energy level n1 equal to 1, the group of lines obtained is called Lyman series. The frequency of these lines is given by1/ = - = RH [1/n1

2 – 1/ n 22]

Where n2 = 2, 3, 4, 5, 6 etcThese lines were found in the ultraviolet region of the electromagnetic spectrum.(ii)Balmer series:(J. J. Balmer.) When the electrons jump from the energy level n2 equal to 3,4,5,6, etc to the energy level n1

equal to 2, the group of lines obtained is called Balmer series.The frequency of these lines is given by1/ = - = RH [1/(2)2– 1/n2

2) where n2 = 3,4,5,6 etcThese lines were found in the visible region of the electromagnetic spectrum.(3) Paschen series (F.Paschen.)When the electrons jump from the energy level n2 equal to 4,5,6 etc to the energy level n1 equal to 3, the group of lines obtained is called Paschen series. The frequency of these lines is given by- = RH [1/(3)2-1/ n2

2] Where n2 = 4, 5, 6 etcThese lines were found in the infrared region of electromagnetic spectrum(4) Brackett series: (F. S. Brackett.)When the electrons jump from the energy level n2 equal to 5,6 etc to the energy level n1 equal to 4, the group of lines is called Brackett series.The frequency of these lines is given by - = RH [1/ (4)2 - 1 /n2

2] Where n2 = 5, 6,7 etcThese lines were found in the 1R region of electromagnetic spectrum. (5) Pfund series(A. H. Pfund.)n2 = 6,7,8n1 = 5The group of lines is called Pfund series.The frequency of these lines is given by 1/ = - = RH [1/(5)2 –1/ n2

2 ] Where n2 = 6,7,8 etcThese lines were found in the IR region of the electromagnetic spectrum.Bohr's theory and Absorption spectrumIf hydrogen is exposed continuously to a strong source of light ( e.g. an arc light ), then according to Bohr's theory, the electron present in the atom of the element may pass from a lower energy to a higher energy level. Suppose the electron pass from a lower energy associated with energy E1 to a level associated with a higher energy E2 . Then an energy equal to (E2 - E1) will be absorbed from the light falling on it. As a result of this the spectral line of frequency corresponding to energy (E2 - E1) will be missing from the spectrum of the light falling on the element. This gives rise to absorption spectrum .Limitations of Bohr’s model: -The main limitations of Bohr’s model of atom are:

1) This model could hardly explain the line spectrum of hydrogen like atoms e.g. He+, Li2+ etc. it failed to explain the spectra of atoms having more than one electron. When the spectral lines of hydrogen atom are observed very closely with the help of highly refined spectroscopes, each line is found to be made up of two closed lines. The existence of such lines could not be explained by Bohr’s model.

2) It failed to explain Zemann effect and stark effect i.e. splitting up of spectral lines under the influence of the strong magnetic field and the electrostatic field respectively.

3) It could not explain that why angular momentum (mvr) of an electron should be integral multiple of h/2

The main objection against Bohr’s model came from two sources:(i) In 1924, Louis de-Broglie suggested that like light electron also displays wave-particle dualism. But the wave nature of electron is not accounted by Bohr’s model.(ii)In 1927, Heisenberg suggested that it is not possible to determine simultaneously the exact position and momentum of a micro particle like electron. It out rightly rejects that electrons revolve in definite orbit


Dual nature of matter: -Einstein had suggested ( 1905 ) that light has dual nature, that is wave nature as well as

particle nature. de Broglie ( 1923 ) proposed that like light, matter also has dual character. It exhibits wave as well as particle nature. He derived a relationship for the calculation of wave length (λ) of the wave associated with a particle of mass ‘m' moving with a velocity ‘v' as given below: λ = h / m v or, λ = h / pwhere ‘ h ' is Planck's constant and p the momentum of the particle.de-Broglie equation: -

Light which consists of electromagnetic radiation’s exhibits both corpuscular (particle) and wave properties based on this analogy, a French physicist, Louis de Broglie (1924) suggested that all material particles such as electrons, protons, neutrons, atoms, molecules etc exhibit wave as well as particle nature. The wave associated with a particle is called a matter wave or pilot wave or de Broglie waves.Derivation of de-Broglie equation: -

By employing Maxwell Planck’s quantum theory of radiation and Einstein’s mass energy equation,de-Broglie derived his equation as follows:

According to planck’s quantum theoryE = hv ----------(1)

Where E is the energy, h is the Planck’s constant and v is the frequency of radiationAccording to Einstein’s mass and energy equation

E = mc2 ----(2)Where E is the energy ,m is the mass and c is the velocity of light,From eq(1) and (2) we get,h = mc2 ------(3)but v = c/substituting the value in eq (3), we geth c/ =mc2

orh/=mcor=h/mc--------------(4)de Broglie pointed out that the above equation is applicable to any material particle. The mass of the photon is replaced by the mass of the material particle and the velocity c of the photon is replaced by the velocity v of the material particle.Thus for any material particle, we may write= h/mvor =h/pWhere p is the momentum (mv) of the particle, the de Broglie’s equation was experimentally verified by Davision and Germer (1927) and independently by G. P. Thomson (1928).Significance of de_Broglie’s equation: -

The de_Broglie’s equation has significance in case of material objects having small mass but it has no significance for objects of relatively larger size because wave length of the wave associated with them is too small to be detected. This can be illustrated by the following examples.Suppose we consider an electron of mass 9.1 x 10-31 kg and moving with a velocity of 107m /s. Its de_Broglie wave length will be= h/mv= 6.62 x 10 -34

9.1 x 10-31 x 107

= 0.727 x 10-10m = 7.27 x 10-11mThis value can be measured experimentally.Let us now consider a ball of mass 10-2kg moving with a velocity of 10-2ms-1. Its de_Broglie wave length will be

= 6.62 x 10 -34

= 6.62 x 10-34m 10-2 x 102

This wavelength is too small to be measured. Thus de_Broglie equation has no significance for such a large object.


The wave nature of electron was verified experimentally by Davison and Germer , by carrying out diffraction experiments with a beam of fast moving electrons. This wave nature of electrons is utilised in construction of electron microscope. Derivation of Bohr’s postulate of angular momentum from de Broglie equation. According to Bohr’s model, the electron revolves around the nucleus in circular orbits. According to de Broglie concept, the electron is not only a particle but has a wave character. Thus in order that the wave may be completely in phase (Fig. (a), the circumference of the orbit must be equal to an integral multiple of wavelength ( ) i.e.,

Heisenberg’s uncertainty principle: -One of the important consequences of the dual nature of matter is the uncertainty

principle developed by Werner Heisenberg in 1927. This principle is an important feature of wave mechanics and discusses the relationship between the position and momentum (velocity) of a moving particle. The uncertainty principle states as follows

“ It is impossible to determine simultaneously both the position and movement (velocity) of a moving particle like electron.Explination of uncertainty principle: -

To locate the position of an electron, a supermicroscope and a light of short wave length (i.e. -rays and x-rays) is required. In order to locate the exact position of the electron, the wavelength of the radiation used should match with the size of the electron. In other words, it should be small. The photons of short wave length are associated with large momentum according to de_Broglie equation =h/p. When such photons strike an electron, an unknown amount of momentum is transferred to the electron at the time of collision. This changes the velocity and hence the momentum of the electron.

If the photons of longer wavelength are used which are associated with low momentum, the momentum of the electron is not so appreciably changed but its position will be correspondingly less accurately known.

Thus it is clear that the position and the momentum of an electron can’t be determined simultaneously.

This principle can be stated mathematically asx p h/4x mv h/4


Where x is the uncertainty in the determination of position and p is the uncertainty in the determination of momentum.

The consequences of the uncertainty principle are far reaching and probably take the place of exactness in at.theory. That is why the principle is also known as probability principle.

This principle is important only for the motion of small particles like electrons, protons, atoms, molecules etc. its effect is negligible for the motion of objects like balls, planets etc. Why electron cannot exist in the nucleus? On the basis of Heisenberg’s uncertainty principle, it can be shown why electrons cannot exist within the atomic nucleus. This is because the diameter of the atomic nucleus is of the order of 10-14 m. Hence if the electron were to exist within the nucleus, the maximum uncertainty in its position would have been 10-14 m. Taking the mass of electron as 9.1 × 10-31 kg, the minimum uncertainty in velocity can be calculated by applying uncertainty principle as follows:–

This value is much higher than the velocity of light (viz 3 × 108 ms--1) and hence is not possible.QUATUM MECHANICAL MODEL OF ATOMQuantum mechanics is a theoretical science which deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties. Erwin Schrodinger , in 1926, gave a wave equation to describe the behaviour of electron waves in atoms and molecules. In Schrodinger wave model of atom, the discrete energy levels or orbits proposed by Bohr are replaced by mathematical function Ψ , which are related with probability of finding electrons at various places around the nucleus. Schrodinger put the wave model or quantum mechanical model of atom forward. The behavior of an electron is defined by the mathematical representation:

Where,Ψ = (psi) is a wave function of space coordinates 'x', 'y', 'z' and represents the amplitude of the electron wave.m = mass of the electronE = the total permissible energy level, which the electron can have.V = potential energy of the electron given by ze2/r.h = Planck's constant having the value 6.626 x 10-34 J s.∂= (delta)stands for infinitesimal change.Above equation may be rearranged to produce the eq.

where is a mathematical operator called Hamiltonian. Schrödinger gave a recipe of constructing this operator from the expression for the total energy of the system. The total energy of the system takes into account the kinetic energies of all the sub-atomic particles (electrons, nuclei), attractive potential between the electrons and nuclei and repulsive potential among the electrons and nuclei individually. Solution of this equation gives E and ψ.Important Features of the Quantum Mechanical Model of AtomQuantum mechanical model of atom is the picture of the structure of the atom, which emerges from the application of the Schrodinger equation to atoms. The following are the important features of quantum mechanical model of atom.

1) The energy of electrons in atoms is quantised ( i.e., can have certain specific values).2) The existence of quantised electronic energy levels is a direct result of the wave like

properties of electrons.

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3) Both exact position and exact velocity of an electron in an atom cannot be determined simultaneously (Heisenberg uncertainty principle). The path of the electron in an atom can, therefore, be never determined or known.

4) An atomic orbital is the wave function Ψ for an electron in an atom. Whenever an electron is described by a wave function, we say that the electron occupies that orbital. Since many such wave functions are possible for an electron, there are many atomic orbitals in an atom. These orbitals form the basis of the electronic structure of atoms. In each orbital electron has a definite energy. An orbital cannot contain more than two electrons. In multi-electron atom, the electrons are filled in various orbitals in the order of increasing energy For each electron of multi-electron atom, the electrons are filled in various orbitals in the order of increasing energy. For each electron of multi-electron atom, there shall, therefore, be an orbital wave function characteristic of the orbital it occupies. All the information about the electron in an atom is stored in its orbital wave function Y and quantum mechanics makes it possible to extract this information out of Ψ .

5) The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., | Ψ |2 at that point . | Ψ |2 is known asprobability density and is always positive. From the value of | Ψ |2 at different points within an atom , it is possible to predict the region around the nucleus where electron will most probably be found .

ORBIT AND ORBITALOrbit and orbital are synonymous. An orbit , as proposed by Bohr , is a circular path around the nucleus in which an electron moves. A precise description of this path of electron is impossible according to Heisenberg's uncertainty principle. Bohr's orbits, therefore, have no real meaning and their existence can never be demonstrated experimentally. An orbital is a quantum mechanical concept and refers to the one electron wave function Ψ in an atom. It is characterized by three quantum numbers (n , l and ml) and its values depends upon the three coordinates of the electron. Ψ has , by itself, no physical meaning. Its square of the wave function | Ψ|2 which has a physical meaning. | Ψ |2 at any point in the atom gives the value of probability density at that point. Probability density | Ψ |2 is the probability per unit volume and a small volume (called a volume element) yields the probability of finding the electron in that volume (the reason for specifying a small volume element is that | Ψ |2 varies from one region to another in space but its value can be assumed to be constant within a small volume element). The total probability of finding electron in a given volume can be calculated by the sum of all the products of | Ψ |2and the corresponding volume elements. It is thus possible to the probable distribution of electron in an orbital. An orbital may be defined as a region in space around the nucleus where the probability of finding the electron is maximum.

The main difference between orbit and orbital are summed up below.

Orbit Orbital1 It is a circular path around the

nucleus in which an electron revolves.

It is a region of space around the nucleus, where the electron is most likely to be found.

2 It represents planar motion of It represents three-dimensional motion of


an electron. an electron around the nucleus.3 The maximum number of

electrons in an orbit is 2 n 2 , where 'n' stands for the number of orbit.

An orbital cannot accommodate more than two electrons.

4 Orbits are circular in shape. Orbitals have different shapes, e.g. s-orbitals are spherically symmetrical, whereas, p-orbitals are dumb-bell shaped.

5 Orbits are non-directional in character and hence they cannot explain shapes of molecules.

Orbitals(except s-orbitals) have directional character and hence they can account for shapes of molecules.

6 Concept of well-defined orbit is against Heisenberg's uncertainty principle.

Concept of orbitals is in accordance with Heisenberg's uncertainty principle.

Quantum numbers:The set of four index numbers required to define the state of an electron in an atom are called quantum numbers. The Bohr’s model introduced a single quantum number ‘n’ to describe an orbit. The quantum mechanical model uses three quantum numbers (n,l,m) to describe an orbital. The three quantum numbers are the results of Schrodinger wave equation.Principal quantum number:It is designated by ‘n’ and gives the number of principal shell to which an electron belongs. It designates the average distance of the electron from the nucleus; hence this quantum number represents the size of the electron orbit. The energy of the electron also depends upon this quantum number.

The energy of different energy levels is given by the equation.En = -1312 kJ mol-1

n2

Where En represents the energy of the electron in nth level and ‘n’ can have integral values theoretically ranging from 1 to but practically only from 1 to 7. The energy levels are designated as K, L, M, N, O, P, Q or 1,2,3,4,5,6,7

The maximum number of electrons in n shell is given by 2n2.Azimuthal quantum number:This quantum number is also known as the second, subsidiary, the lesser or the orbital quantum number. It is designated by ‘l’.

Each shell is made up of number of sub-shells. The azimuthal quantum number describes the subshell to which the electron belongs and also describes the shape of the orbital. For a particular value of ‘n’ , l can have values ranging from 0 to n-1. Since each value of ‘l’ represents a different subshell. Therefore l = 0 (s-subshell) l =1 (p-subsehll), l = 2 (d-subshell) and l = 3 (f-subshell).

The letters s,p,d and f have been derived from the names of the spectral lines sharp, principal, diffused and fundamental respectively.

In a particular energy level the energies of its sub shell are in the order s, < p, < d< f. This is attributed to the shielding effect of electrons.Magnetic quantum number:It is designated by ‘m’. This quantum number has been introduced to account for the Zemann effect (i.e, splitting of spectral lines under the influence of an applied magnetic field)

A shell is made up of number of subshells and each shell is made of various orbitals. The number of these orbitals is given by n2

Where n represents the principal quantum number.For a given value of l, there are 2l + 1 permitted values of m ranging from l through 0 to

+l. Thus for l = 0, m = 0’ l = 1, m = -1, 0, +1; l = 2, m = -2, -1, 0, +1, +2; l = 3, m = -3, -2, -1, 0, +1, +2, +3

This means that s-sub shell will have 1, p-sub shell will have 3, d-sub shell will have 5 and 7 sub shell will have 7 values of m i.e. orbitals.Spin quantum number:-It is designated by ‘s’. This quantum number arises from the spectral evidence that an electron in its motion around the nucleus in an orbit also rotates or spins about its own axis. This


quantum number gives the direction in which the electron is spinning clockwise () or counter clockwise ().The values associated with clockwise and anticlockwise spins of the electron are +1/2 and –1/2 respectively.

Aufbau Principle:The word Aufbau is a German word which means ‘building up’. The building up means filling up of orbitals with electrons. The principle states that in the ground state of the atom, orbitals belonging to different sub shells are filled with electrons in the order of increasing energies. In simple words, the orbitals of lower energy are filled first followed by the orbitals of higher energy. To decide about energy of an orbital, the following two rules are used(n + l) rule: The rule states that the orbital having lower value of (n + l) has lower energy than the orbital having higher value of (n + l) where n and l are principal and azimuthal quantum numbers respectively. e.g.,3d 4sn = 3 n = 4l = 2 l = 0(n + l) = 5 (n + l) = 4The value of (n + l) is equal to 4 for 4s-orbital and 5 for 3d orbital. Therefore, 4s orbital has lower energy than 3d orbital and will be filled first by electrons. (n ) rule : This rule states that if two orbitals have same value of (n + l) then the orbital with lower value of n has lower energy e.g.2p 3sn = 2 n = 3l = 1 l = 0 (n + l) = 3 (n + l) = 3The value of ‘n’ is equal to 2 for 2p orbital and 3 for 3s orbital. Therefore, 2p orbital has lower energy than 3s orbital and will be filled first by electrons.The increasing order of energy of various orbitals is:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7s -----.This sequence is represented graphically in the below given figure.

This order of electron build up holds good in various elements but fails in certain cases especially in transition and inner-transition elements.

NS

(I) (II) (III)


Mnemonic diagram for the building up order (diagonal rule)Pauli’s exclusion principle:The number of electrons to be filled in various orbitals is restricted by the exclusion principle, given by the Austrian scientist Wolfgang Pauli in 1925. The principle states that “no two electrons in an atom can have the same set of four quantum numbers”. This implies that if two electrons in an atom have the same values for three quantum numbers, then they must have different values of fourth quantum number. The most important consequence of this principle is that an orbital can accommodate not more than two electrons and that too with opposite spins. This principle is helpful to determine the number of electrons present in an orbital, subshell and shell e.g., an orbital can accommodate at the most two electrons with opposite spins, s,p,d and f subshells can accommodate 2,6,10 and 14 electrons respectively i.e., 2(2ℓ + 1) electrons and first, second, third, fourth and fifth shells can accommodate at the most 2,8,18,32 and 50 electrons respectively i.e., 2n2 electrons. Inf:-According to thermodynamics, a system having lower energy is maximum stable.Therefore, the state with the lower energy(opposite spins) is preferred and electrons entering the same orbital must have opposite spins.Hund’s rule of maximum multiplicity:-This rule deals with the filling of electrons into the orbitals of same subshell (i.e. orbitals of equal energy, called degenerate orbitals). It states as under:-

The pairing of electrons in the orbitals belonging to the same sub shell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each (i.e. is singly occupied). Moreover, the singly occupied orbitals must have the electrons with parallel spins.

For example, there are three orbitals in the p. subshell i.e. Px, Py and Pz orbitals. If three electrons are to be filled then there are three possible ways to do it.

Px Py Pz Px Py Pz Px Py Pz

Thus, according Hund’s rule the last distribution (III) is correct. The reason for such a tendency is that the electrons are negatively changed and repel

each other. In order to minimize, the forces of repulsion, they spread out and occupy the identical orbitals singly with spins in the same direction (clock wise or anti-clockwise). Hence the energy is minimum and stability is maximum. Further same spin leads to lower energy state and maximum stability state.

Pairing occurs because less energy is needed to do so than the energy required to place the electron in the next higher empty orbital. {* Hund’s rule is called maximum multiplicity rule because, out of the various electronic configurations only that configuration is correct for which the total spin value is maximum e.g. total spin of the unpaired electrons in configurations (I), (II) and (III) are: -(I) ½ + ½ + ½ = 11/2 (II) + ½ - ½ + ½ = ½ (III) ½ }Electronic configuration of elements:

The distribution of electrons into shells, sub shells and orbitals of an atom in the ground state is called its electronic configuration. The following steps are used to write the electronic configuration of elements.The main energy level or shell (1,2,3-----) is written first.The subshell (s, p, d or f) is written next.The number of electrons in a particular sub shell is shown as the superscript to the sub shell. The electronic configuration of first 30 elements is given below:


Stability of half filled and completely filled orbitals:According to Aufbau principle, the outer configuration of Cr(Z = 24) is 3d4 4s2 and that of Cu (Z = 29) is 3d9 4s2 but the experimentally supported configuration is 3d5 4s1 for Cr and 3d10, 4s1 for

1s2 2s2 2p6

3d5


Cu. The reason for these deviations are attributed to the extra stability associated with half filled or completely filled orbitals.Cause of extra stabilityFollowing are the reasons for extrastability of half filled and completely filled orbitalsSymmetry of orbitals:The configurations in which all the degenerate orbitals of the same sub shell are half-filled or completely filled have symmetrical distribution of electrons. Such configurations are more stable than those in which the distribution is not symmetrical. As symmetry leads to stability, such electronic configurations are preferred.Following configurations are stable.Ne = 10

Cr = 24

Cu = 29

Exchange Energy:In an atom, electrons present in various orbitals of the same sub shell tend to exchange their positions mutually and during this process small amount of energy is lost, it is called exchange energy. Larger the exchange energy greater is the stability. Maximum exchange of energy is possible in half filled and completely filled sub shells so that maximum amount of exchange energy is released in these configurations. This allows for greater stability in such symmetrical configuration than the other symmetrical configuration. Thus electronic configuration 3d5, 4s1 and 3d10 4s1 are preferred over respective 3d4, 4s2 and 3d9, 4s2configuration.

3d10

(symmetrical distributions)

4s1

4s1

atomic structure 2011

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