Atomic Structure

Technological Institute of the Philippines363 P. Casal St., Quiapo, Manila

Project in PCHM413L1( Physical Principles 2 )

Prepared by:John P. Bandoquillo

CH41FB1

Required and Checked by:Engr. Frefe C. Rupinta

Technological Institute of the Philippines363 P. Casal St., Quiapo, Manila

Project in PCHM413L1( Physical Principles 2 )

Prepared by:John P. Bandoquillo

CH41FB1

Required and Checked by:Engr. Frefe C. Rupinta

Chapter 3:Chapter 3:

Atomic StructureAtomic Structure

Fundamentals of Physical ChemistryFundamentals of Physical Chemistry

Samuel H. Maron / Jerome B. LandoSamuel H. Maron / Jerome B. Lando

IntroductionIntroduction

The first modern attempt at an The first modern attempt at an explanation of chemical reactivity of explanation of chemical reactivity of chemical elements is chemical elements is Dalton’s atomicDalton’s atomic theorytheory formulated in formulated in 18081808. Dalton . Dalton postulated that every elements consists of postulated that every elements consists of invisible particles called invisible particles called atomsatoms, each of , each of which has the same mass for a given which has the same mass for a given elements, and that these atoms react with elements, and that these atoms react with each other to form compounds.each other to form compounds.

However, he made no effort to establish However, he made no effort to establish any relation between the atoms of various any relation between the atoms of various elements. This was first done in elements. This was first done in 18151815 by by ProutProut, who reasoning from the proximity , who reasoning from the proximity of the atomic weights of elements to whole of the atomic weights of elements to whole numbers on the basis of hydrogen as unity, numbers on the basis of hydrogen as unity, suggested that all elements were composed suggested that all elements were composed of multiples of hydrogen atoms.of multiples of hydrogen atoms.

Another important principle which Another important principle which indicated the existence of a regular indicated the existence of a regular relationship among the elements was the relationship among the elements was the periodic lawperiodic law discovered independently by discovered independently by MendelMendeléeff éeff ((18691869) in Russia and ) in Russia and Lothar Lothar MeyerMeyer ( (18701870) in Germany. This law, that the ) in Germany. This law, that the chemical and physical properties of the chemical and physical properties of the elements are periodic functions of their atomic elements are periodic functions of their atomic weights, pointed to regularities in the structure weights, pointed to regularities in the structure of atoms and to the fact that certain structures of atoms and to the fact that certain structures repeated themselves periodically to yield repeated themselves periodically to yield similarity of chemical and physical properties.similarity of chemical and physical properties.

Finally, the electrical researches of Finally, the electrical researches of NicholsonNicholson and and CarlisleCarlisle, , DavyDavy, , BerzeliusBerzelius and and Faraday Faraday showed that matter and electricity are showed that matter and electricity are intimately associated and that electricity itself intimately associated and that electricity itself is corpuscular in nature. These findings, is corpuscular in nature. These findings, followed by studies of electric discharges followed by studies of electric discharges through rarefied gases and the discovery of through rarefied gases and the discovery of radioactivity, eventually established that atoms radioactivity, eventually established that atoms consist of the same structural units. Primarily, consist of the same structural units. Primarily, these are the electron, the proton and the these are the electron, the proton and the neutron. neutron.

The ElectronThe Electron

Gases are as a rule poor conductors of Gases are as a rule poor conductors of electricity. However, when a tube filled with electricity. However, when a tube filled with gas is evacuated to pressures of 0.01 mm or gas is evacuated to pressures of 0.01 mm or lower and an electric potential is applied lower and an electric potential is applied across a pair of electrodes sealed into the tube, across a pair of electrodes sealed into the tube, a discharge takes place between the electrodes a discharge takes place between the electrodes during which a stream of during which a stream of cathode rayscathode rays is is emitted emitted from the cathodefrom the cathode..

The particles constituting the cathode The particles constituting the cathode rays have been named rays have been named electronselectrons. The fact that . The fact that electrons are independent of the nature of the electrons are independent of the nature of the source from which they come suggests that source from which they come suggests that they are constituents of all matter. From the they are constituents of all matter. From the relations of the forces involved, the ratio of the relations of the forces involved, the ratio of the electron charge electron charge ee to its mass to its mass mm may then be may then be evaluated, and Thomson found thus evaluated, and Thomson found thus e/me/m to be to be 1.79 x 10^7 electromagnetic units per gram1.79 x 10^7 electromagnetic units per gram..

More refined measurements have modified thisMore refined measurements have modified this

value to:value to: e/me/m = 1.75880 x 10^7 emu/g = 1.75880 x 10^7 emu/g

= 1.75880 x 10^8 abs. coulombs/g= 1.75880 x 10^8 abs. coulombs/g

J.J. Thomson’s apparatus for determination of J.J. Thomson’s apparatus for determination of e/me/m for electron. for electron.

In order to resolve to resolve this ratio, the charge on the In order to resolve to resolve this ratio, the charge on the electron must be ascertained independently. This electron must be ascertained independently. This determination was first carried out with a high degree of determination was first carried out with a high degree of precision in 1913 by R.A Millikan through his famous precision in 1913 by R.A Millikan through his famous oil-drop experiments.oil-drop experiments.

Millikan’s oil-drop apparatusMillikan’s oil-drop apparatus

If we let If we let νν11 be the rate of fall of the particle under be the rate of fall of the particle under gravity gravity gg, , v2v2 the rate of rise of the particle against gravity the rate of rise of the particle against gravity when an electrostatic field strength when an electrostatic field strength XX is applied, and is applied, and m’m’ and and e’e’ the mass of and charge on the oil droplet, then in the the mass of and charge on the oil droplet, then in the oil drop experiments these quantities are connected by the oil drop experiments these quantities are connected by the relationrelation

v1/v2 = m’g/(Xe’ – m’g)v1/v2 = m’g/(Xe’ – m’g)

Millikan found that Millikan found that e’e’ was not constant. was not constant. However, he did find that there was a However, he did find that there was a common factor for all the values of common factor for all the values of e’e’ which which made the various charges observed whole made the various charges observed whole number multiples of the common factor. The number multiples of the common factor. The value of this least common factor deduced by value of this least common factor deduced by Millikan was Millikan was 4.774 x 10 ^ -10 electrostatic4.774 x 10 ^ -10 electrostatic unitunit, and this must be, therefore, the charge , and this must be, therefore, the charge of the unit of electricity, or the electron.of the unit of electricity, or the electron.

Since this work a redetermination of the Since this work a redetermination of the viscosity of the air and other corrections have viscosity of the air and other corrections have shown that a better value of the electronic shown that a better value of the electronic charge,charge, ee, is, is

ee = 4.80298 x 10^ -10 = 4.80298 x 10^ -10 esu/electronesu/electron

= 1.60210 x 10^ -20 = 1.60210 x 10^ -20 emu/electronemu/electron

= 1.60210 x 10^ -19 = 1.60210 x 10^ -19 abs. abs. coulomb/electron coulomb/electron

From From e/me/m and and ee the mass of the electron the mass of the electron follows asfollows as

mm = = ee/(/(ee//mm))

= 1.60210 x 10^ -19/1.75880 x 10^ 8 = 1.60210 x 10^ -19/1.75880 x 10^ 8

= 9.1091 x 10^ -28 g per electron (Eg. = 9.1091 x 10^ -28 g per electron (Eg. 1)1)

This mass of the electron may be compared This mass of the electron may be compared with the mass of a hydrogen atom, which is, of with the mass of a hydrogen atom, which is, of course, the atomic weight of hydrogen divided course, the atomic weight of hydrogen divided by by Avogadro’s number, namely,Avogadro’s number, namely,

mHmH = 1.00797/6.0225 x 10^ 23 = 1.00797/6.0225 x 10^ 23

= 1.673 x 10^ -24 g= 1.673 x 10^ -24 g

From From mHmH and and mm it is seen that the mass of the it is seen that the mass of the hydrogen atom is hydrogen atom is 18361836 times greater than the times greater than the mass of the electron.mass of the electron.

The mass of the electron given in Eq. 1 is the rest The mass of the electron given in Eq. 1 is the rest mass, the mass when the electron is either at rest or mass, the mass when the electron is either at rest or moving with velocities that are low compared with moving with velocities that are low compared with that of light. However, when the electron is moving at that of light. However, when the electron is moving at very high speeds, then according to the theory of very high speeds, then according to the theory of relativity the mass of the electron is increased in line relativity the mass of the electron is increased in line with the equationwith the equation

mm = = m0m0/[ 1 – (/[ 1 – (vv//cc)^2]^1/2)^2]^1/2Where:Where:

m0 m0 = mass of the electron at rest= mass of the electron at rest mm = mass of the electron is moving = mass of the electron is moving v v = velocity = velocity cc = velocity of light. = velocity of light.

Wave Nature of the ElectronsWave Nature of the Electrons. The duality of . The duality of behavior, exhibited also by light and even behavior, exhibited also by light and even atoms, is an illustration of the atoms, is an illustration of the HeisenbergHeisenberg uncertainty principleuncertainty principle enunciated in enunciated in 19271927, , which states that which states that it is impossible to define it is impossible to define simultaneously the exact momentum andsimultaneously the exact momentum and position of a bodyposition of a body. Precisely, Heisenberg . Precisely, Heisenberg showed that the product of the uncertainty in showed that the product of the uncertainty in the position of a body the position of a body ∆x∆x, and the uncertainty , and the uncertainty in the momentum in the momentum ∆p∆p, and hence the velocity, , and hence the velocity, is even in the perfect experiment related to is even in the perfect experiment related to Planck’s constant Planck’s constant hh..

(∆x) (∆p) ≥ h/(4(∆x) (∆p) ≥ h/(4ππ))

where:where:

h h = 6.6256 x 10^ -27 erg second= 6.6256 x 10^ -27 erg second

Now, in studying the electron in discharge Now, in studying the electron in discharge experiments we concentrate on the exact experiments we concentrate on the exact definition of its velocity and momentum, and definition of its velocity and momentum, and arrive thus at the conclusion that electron is a arrive thus at the conclusion that electron is a particle. On the other hand, when the electron particle. On the other hand, when the electron diffraction experiments are performed, the diffraction experiments are performed, the emphasis is on the position of the electron. emphasis is on the position of the electron.

The ProtonThe Proton

When this atom is converted into ion, it When this atom is converted into ion, it is found that its charge is exactly equal to that is found that its charge is exactly equal to that of the electron but is opposite in sign. Further, of the electron but is opposite in sign. Further, the mass of the positively charged hydrogen the mass of the positively charged hydrogen ion, or ion, or protonproton, is very nearly the same as that , is very nearly the same as that of the hydrogen atom. By perforating the of the hydrogen atom. By perforating the cathode these positive of canal rays can be cathode these positive of canal rays can be made to pass through the holes to the rear, and made to pass through the holes to the rear, and there be studied by the effect of electric and there be studied by the effect of electric and magnetic fields upon them. magnetic fields upon them.

Positive Ray Analysis and Positive Ray Analysis and IsotopesIsotopes

A method of investigating positive rays A method of investigating positive rays is the is the Aston mass spectrographAston mass spectrograph, with which , with which masses of positively charged particles can be masses of positively charged particles can be determined with an accuracy greater than one determined with an accuracy greater than one part in a million. More recent designs of mass part in a million. More recent designs of mass spectrographs dispense with the photographic spectrographs dispense with the photographic plate by substituting for it detecting and plate by substituting for it detecting and recording devices which yield directly plots of recording devices which yield directly plots of current intensity versus atomic mass. current intensity versus atomic mass.

Schematic Diagram of Aston’s SpectrographSchematic Diagram of Aston’s Spectrograph

Atomic Masses Deduced From Mass SpectrometryAtomic Masses Deduced From Mass Spectrometry

Atomic No. Atom Rounded Mass Atomic Weight( C Basis ) Abundance( % )

1 H 1 1.00782 99.985

    2 2.0141 0.015

2 He 3 3.10603 10^ -5

    4 4.0026 100

3 Li 6 6.01511 7.4

    7 7.01599 92.6

4 Be 9 9.01217 100

5 B 10 10.01295 18.83

    11 11.00942 81.17

6 C 12 12 98.892

    13 13.00333 1.108

7 N 14 14.00307 99.64

    15 15.00009 0.36

8 O 16 15.99491 99.76

    17 16.00013 0.04

    18 17.99916 0.2

From a study of the mass spectra it is From a study of the mass spectra it is possible to deduce very precise values of the possible to deduce very precise values of the atomic weights. The mass spectrograph also atomic weights. The mass spectrograph also reveals that many elements, which from reveals that many elements, which from ordinary atomic weight determinations were ordinary atomic weight determinations were considered to consist of atom of the same considered to consist of atom of the same mass, are in reality mixtures of atoms of mass, are in reality mixtures of atoms of different masses although of the same atomic different masses although of the same atomic number. Such atoms of different mass but number. Such atoms of different mass but same atomic number are called same atomic number are called isotopesisotopes..

Hydrogen and DeuteriumHydrogen and DeuteriumAmong the methods which have been Among the methods which have been

employed to separate or enrich isotopes are the employed to separate or enrich isotopes are the mass spectrographmass spectrograph, , diffusiondiffusion, , centrifugingcentrifuging, , thermal diffusionthermal diffusion, , electrolysiselectrolysis, , fractional fractional distillationdistillation and and chemical exchangechemical exchange. It is of . It is of interest to point out the differences found interest to point out the differences found between ordinary hydrogen and its heavier between ordinary hydrogen and its heavier isotope isotope deuteriumdeuterium, symbol , symbol DD. . DeuteriumDeuterium was was discovered spectroscopically in discovered spectroscopically in 19321932 by by UreyUrey and and his co-workershis co-workers at at Columbia UniversityColumbia University. .

In ordinary hydrogen gas deuterium is present In ordinary hydrogen gas deuterium is present as about one part in as about one part in 66006600 parts of light parts of light hydrogen. The heavier isotope is usually hydrogen. The heavier isotope is usually concentrated by electrolysis of aqueous alkali concentrated by electrolysis of aqueous alkali solutions, in which instance the lighter solutions, in which instance the lighter hydrogen atoms escape more rapidly than the hydrogen atoms escape more rapidly than the heavier deuterium, and the solution becomes heavier deuterium, and the solution becomes more concentrated in more concentrated in D2OD2O, , heavy waterheavy water. By . By repeating the electrolysis a number of times, repeating the electrolysis a number of times, pure D2O can be prepared and studied.pure D2O can be prepared and studied.

Comparison of Properties of Hydrogen IsotopesComparison of Properties of Hydrogen Isotopes

Property H2 D2

Molar Volume of Solid 26.15 cc 23.17 cc

Triple Point 13.92°K 18.58°K

Heat Fusion 28 cal/mole 47 cal/mole

Boiling Point 20.38°K 23.50°K

Heat of Vaporization at Triple Point 217.7 cal/mole 303.1 cal/mole

Comparison of Properties of H2O and D2OComparison of Properties of H2O and D2O

Property H2O D2O

Relative Density, 25° / 25°C 1 1.1079

Melting Point 0.00°C 3.82°C

Boiling Point 100.00°C 101.42°C

Surface Tension, 20°C 72.75 dynes/cm 67.8 dynes/cm

Temperatute of Maximum Density 4.0°C 11.6°C

Dielectric Constant, 25°C 78.54 78.25

Viscosity, 20°C 10.09 millipoises 12.6 millipoises

Heat of Fusion 1436 cal/mole 1510 cal/mole

Heat of Vaporization 10,480 cal/mole 10,740 cal/mole

The NeutronThe NeutronIn In 1920 Rutherford1920 Rutherford suggested that there suggested that there

may also be present in atoms a particles of may also be present in atoms a particles of essentially the same mass as the proton but with essentially the same mass as the proton but with no charge. The existence of such uncharged no charge. The existence of such uncharged particles, called particles, called neutronsneutrons, was actually , was actually established in established in 19321932 by by ChadwickChadwick. These particles . These particles have been found to be independent of their source have been found to be independent of their source in their properties, to be unaffected by electric and in their properties, to be unaffected by electric and magnetic fields, indicating thus absence of charge, magnetic fields, indicating thus absence of charge, and to have a mass of and to have a mass of 1.008661.00866 atomic weight atomic weight units, which is almost identical with that of the units, which is almost identical with that of the proton, proton, 1.007281.00728..

Rutherford’s Theory of the AtomRutherford’s Theory of the Atom

The Alpha (The Alpha (αα) particle:) particle: emission products of certain radioactive emission products of certain radioactive

disintegrations.disintegrations. they have the mass approximately four times they have the mass approximately four times

that of the proton bear two positive charges.that of the proton bear two positive charges. directed against a thin metallic foil should be directed against a thin metallic foil should be

able to pass through it without deflection as able to pass through it without deflection as long as they do not approach too near to a long as they do not approach too near to a positive nucleus. positive nucleus.

• directed as to come near the nucleus, the directed as to come near the nucleus, the strong repulsive force developed between the strong repulsive force developed between the nucleus and the positive nucleus and the positive αα particle causes the particle causes the latter to be deflected sharply.latter to be deflected sharply.

The Charge on the NucleusThe Charge on the Nucleus

The first precise statement that the The first precise statement that the nuclear charge of an atom is identical with its nuclear charge of an atom is identical with its atomic number was made by atomic number was made by van der Broeckvan der Broeck in in 19131913. Nevertheless, the first direct evidence . Nevertheless, the first direct evidence on this point is due to on this point is due to Moseley’sMoseley’s studies studies (1913, 1914)(1913, 1914) of the X radiations emitted by of the X radiations emitted by various elements. The various sets of line thus various elements. The various sets of line thus obtained can be divided into series designated obtained can be divided into series designated in turn as the K, L, M, etc. ,series, while the in turn as the K, L, M, etc. ,series, while the lines within each series are referred to in lines within each series are referred to in sequence as the sequence as the αα, , ββ, , γγ, etc., lines., etc., lines.

Thus, the KThus, the Kαα line is the first line in the K series, line is the first line in the K series, the Lthe Lββ is the second line in the second series, etc. is the second line in the second series, etc. He also found that if we take the frequencies of He also found that if we take the frequencies of any particular line in all the elements, such as the any particular line in all the elements, such as the KKαα or K or Kββ lines, then the frequencies are related to lines, then the frequencies are related to each other by the equation given below. Moseley each other by the equation given below. Moseley concluded that the change in atomic number from concluded that the change in atomic number from element to element represents the regular element to element represents the regular variation in the number of extra nuclear electrons variation in the number of extra nuclear electrons in the neutral atom, the number of extra nuclear in the neutral atom, the number of extra nuclear electrons is identical with the atomic number of electrons is identical with the atomic number of an element.an element.

v ^ ½ = a (Z –k)v ^ ½ = a (Z –k)

where:where:

vv = frequency of any particular K = frequency of any particular Kαα or or KKββ

ZZ = atomic number = atomic number

a a and and kk = constant for any particular type of = constant for any particular type of line. line.

Distribution of Electrons, Protons Distribution of Electrons, Protons and Neutrons in an Atomand Neutrons in an Atom

Rutherford believed that the external Rutherford believed that the external electrons may occupy any and all positions electrons may occupy any and all positions outside the nucleus and possess thereby outside the nucleus and possess thereby energies with can vary continuously. However, energies with can vary continuously. However, this concept of continuous variation in energy this concept of continuous variation in energy is contradicted by atomic spectra, which are is contradicted by atomic spectra, which are not continuous but discontinuous. not continuous but discontinuous.

To overcome this difficulties inherent in the To overcome this difficulties inherent in the Rutherford atom, Rutherford atom, Niels BohrNiels Bohr advanced in advanced in 19131913 his famous theory of atomic structure. his famous theory of atomic structure. Before this theory can be presented, however, Before this theory can be presented, however, two other subjects must be introduced first: two other subjects must be introduced first: the the quantum theory of radiation, and the emission quantum theory of radiation, and the emission of line spectra by excited atoms. of line spectra by excited atoms.

The Quantum Theory of RadiationThe Quantum Theory of Radiation

When radiation strikes any surface of a When radiation strikes any surface of a body, part of the radiant energy is generally body, part of the radiant energy is generally reflected, part is absorbed, and part is reflected, part is absorbed, and part is transmitted. The reason for the incomplete transmitted. The reason for the incomplete absorption is that ordinary bodies are as a rule absorption is that ordinary bodies are as a rule imperfect absorbers of radiation. In contrast to imperfect absorbers of radiation. In contrast to this, we have the this, we have the black bodyblack body, which by , which by definition is the perfect absorber of energy and definition is the perfect absorber of energy and retains any radiant energy that strikes it. retains any radiant energy that strikes it.

A black body is not only a perfect absorber of A black body is not only a perfect absorber of radiant energy, but also a perfect radiator. In radiant energy, but also a perfect radiator. In fact, all bodies heated to a given temperature, fact, all bodies heated to a given temperature, it is the black body which will radiate the it is the black body which will radiate the maximum amount of energy possible for the maximum amount of energy possible for the given temperature. The total amount of energy given temperature. The total amount of energy E radiated by a black body per unit area and E radiated by a black body per unit area and time is given by time is given by Stefan-Boltzmann fourth Stefan-Boltzmann fourth power law.power law.

Stefan-Boltzmann fourth power Stefan-Boltzmann fourth power law:law:

E = E = σσTTwhere:where:

T T = absolute temperature= absolute temperature

σσ = universal constant equal to = universal constant equal to 5.6697 x 10^-55.6697 x 10^-5

for energy in ergs, time in second, for energy in ergs, time in second, and are and are

in square centimetersin square centimeters

Max PlanckMax Planck in in 19901990 says that black says that black bodies radiate energy not continuously, bodies radiate energy not continuously, but discontinuously in energy packets but discontinuously in energy packets called quanta.called quanta.

E = hvE = hv

where:where:

EE = quantum of energy radiated = quantum of energy radiated

vv = frequency = frequency

h h = Planck’s constant equal to 6.6256 x = Planck’s constant equal to 6.6256 x 10^-2710^-27

ergs-second.ergs-second.

This equation is the fundamental relation of This equation is the fundamental relation of the quantum theory of radiation. Planck the quantum theory of radiation. Planck considered the black body to consist of considered the black body to consist of oscillators of molecular dimensions, each with oscillators of molecular dimensions, each with a fundamental vibration frequency v, and that a fundamental vibration frequency v, and that each oscillator could emit energy either in the each oscillator could emit energy either in the unit quantum E1 = hv, or in the whole number unit quantum E1 = hv, or in the whole number multiples n thereof, En = nhv. On this basis he multiples n thereof, En = nhv. On this basis he was able to deduce for the energy Ewas able to deduce for the energy Eλλ radiated radiated by a black body at any wave length by a black body at any wave length λλ given by given by the relation: the relation:

Relation:Relation:

EEλλ = [ 8 = [ 8ππhc/hc/λλ ] [ 1/(e^hc/kT ] [ 1/(e^hc/kTλλ) – 1 ) – 1 ]]

where:where:

cc = velocity of light = velocity of light

TT = absolute temperature = absolute temperature

kk = gas constant per molecule or R/N = gas constant per molecule or R/N

Planck’s success with the quantization of black Planck’s success with the quantization of black body radiation led Albert Einstein in 1905 to a body radiation led Albert Einstein in 1905 to a generalization of quantum theory. Einstein generalization of quantum theory. Einstein postulated that all radiate energy must be postulated that all radiate energy must be absorbed or emitted by a body in quanta absorbed or emitted by a body in quanta whose magnitude depends in the frequency whose magnitude depends in the frequency according to Planck’s equation or multiples according to Planck’s equation or multiples thereof. thereof.

The Line Spectra of AtomsThe Line Spectra of AtomsGases and vapors yield a series of lines Gases and vapors yield a series of lines

called line spectra, or bands called band called line spectra, or bands called band spectra, which consist of many lines spectra, which consist of many lines close together. The band spectra are close together. The band spectra are radiations emitted by molecules, radiations emitted by molecules, whereas line spectra are due to atoms. whereas line spectra are due to atoms. Each series of lines is related by a Each series of lines is related by a formula, which for the Balmer series, formula, which for the Balmer series, appearing in the visible spectral range, appearing in the visible spectral range, takes the formtakes the form

1/1/λλ = v = RH [( 1/2²) – (1/n²)] = v = RH [( 1/2²) – (1/n²)]

Here Here λλ is the wave length of line, whose is the wave length of line, whose reciprocal, v, is called the wave number, the reciprocal, v, is called the wave number, the number of wave per centimeter, RH is a number of wave per centimeter, RH is a constant called the Rydberg constant and equal constant called the Rydberg constant and equal to 109,677.58/cm, and n is a running number to 109,677.58/cm, and n is a running number taking on for the various lines of this series taking on for the various lines of this series values of 3, 4, 5, etc. values of 3, 4, 5, etc.

V = RH [(1/n1²) – (1/n2²)]V = RH [(1/n1²) – (1/n2²)]where:where:n1n1 and and n2n2 = spectral series observed in atomic = spectral series observed in atomic

hydrogenhydrogen

Spectral Series Observed in Atomic HydrogenSpectral Series Observed in Atomic Hydrogen

Series n1 n2 Spectral Region

Lyman 1 2, 3, 4… Ultraviolet

Balmer 2 3, 4, 5… Visible

Paschen 3 4, 5, 6… Infrared

Brackett 4 5, 6, 7… Infrared

Pfund 5 6, 7… Infrared

Bohr’s Theory of Atomic StructureBohr’s Theory of Atomic StructureBohr considered the atom to consist of a Bohr considered the atom to consist of a

nucleus with electrons revolving about it. Bohr nucleus with electrons revolving about it. Bohr postulated that the only possible orbits for postulated that the only possible orbits for electron revolution are those for which the electron revolution are those for which the angular momentum is a whole number angular momentum is a whole number multiple n of quantity (multiple n of quantity (h/2h/2ππ), ), hh being Planck’s being Planck’s constant. The second postulate introduces the constant. The second postulate introduces the concept that there are definite energy levels or concept that there are definite energy levels or stationary states within the atom in which an stationary states within the atom in which an electron possesses a definite and invariable electron possesses a definite and invariable energy content.energy content.

Finally, Bohr assumed as his third postulate Finally, Bohr assumed as his third postulate that each line observed in the spectrum of an that each line observed in the spectrum of an element results from the passage of an electron element results from the passage of an electron from an orbit in which the energy is E2 to one from an orbit in which the energy is E2 to one of lower energy E1 and that this difference in of lower energy E1 and that this difference in energy is emitted as a quantum of radiation of energy is emitted as a quantum of radiation of frequency v in line with the equationfrequency v in line with the equation

∆∆E = E2 –E1 = hvE = E2 –E1 = hv

Coulomb’s Law as Coulomb’s Law as Ze²/r²:Ze²/r²:

Ze²/r² = mv²/rZe²/r² = mv²/r

Angular Momentum of the electron is mvr:Angular Momentum of the electron is mvr:

Mvr = nh / 2Mvr = nh / 2ππ

Substitute angular momentum to Coulomb’sSubstitute angular momentum to Coulomb’s

Law:Law:

R = n²h² / 4R = n²h² / 4ππ²mZe²²mZe²

The total energy E of the electrons The total energy E of the electrons in its orbit is the sum of its kinetic in its orbit is the sum of its kinetic and potential energies. The kinetic and potential energies. The kinetic energy is given by ½ energy is given by ½ mv²mv², and the , and the potential energy by potential energy by -Ze²/r-Ze²/r. .

E = ½ mv² - Ze²/rE = ½ mv² - Ze²/r

E = Ze²/2r - Ze²/r = -Ze²/2rE = Ze²/2r - Ze²/r = -Ze²/2r

By substitution methodBy substitution method

E = -2E = -2ππ²mZ²e / n²h²²mZ²e / n²h²nn = principal quantum number = principal quantum number

Origin of Spectral Series in Atomic Hydrogen (Schematic)Origin of Spectral Series in Atomic Hydrogen (Schematic)

Ionization PotentialsIonization PotentialsIn the previous figure the lowest energy In the previous figure the lowest energy level of the electron is the one for which level of the electron is the one for which n = 1n = 1. This level is called the . This level is called the ground ground statestate of the electron. Again, the highest of the electron. Again, the highest energy level is the one for which energy level is the one for which n = ∞n = ∞, , and this state corresponds to the and this state corresponds to the removal of the electron from the removal of the electron from the influence of the nucleus ionization of the influence of the nucleus ionization of the atom. The energy, atom. The energy, II, required to produce , required to produce ionization from the normal or ground ionization from the normal or ground state of the electron is called the state of the electron is called the ionization potentialionization potential, and it is usually , and it is usually expressed in expressed in electron voltselectron volts, , eVeV..

Ionization Potentials of AtomsIonization Potentials of Atoms

Element Atomic Number I (eV) 1 I (eV) 2 I (eV) 3 I (eV) 4 I (eV) 5

H 1 13.6 0 0 0 0

He 2 24.58 54.4 0 0 0

Li 3 5.39 75.62 122.42 0 0

Be 4 9.32 18.21 153.85 217.66 0

B 5 8.3 25.15 37.92 259.3 338.5

C 6 11.26 24.38 47.86 64.48 390.1

N 7 14.54 29.61 47.43 77.45 97.4

O 8 13.61 35.15 54.93 77.39 113

F 9 17.42 34.98 62.65 87.23 113.7

Ne 10 21.56 41.07 64 97.16 0

Na 11 5.14 47.29 71.65 98.88 0

Mg 12 7.64 15.03 80.12 109.29 0

Quantum NumberQuantum NumberThe appearance of multiple fine lines in The appearance of multiple fine lines in

place of a single line is referred to as mutiplet place of a single line is referred to as mutiplet or fine structure of spectral lines. The or fine structure of spectral lines. The spinspin quantum number squantum number s arises from a suggestion arises from a suggestion made by made by Uhlenbeck Uhlenbeck and and GoudsmitGoudsmit in in 19251925 that an electron in its motion in an orbit may that an electron in its motion in an orbit may rotate or spin about its own axis. rotate or spin about its own axis.

The four quantum numbers and the The four quantum numbers and the values they may take on may be summarized values they may take on may be summarized as follows: as follows:

1.1. Principal Quantum Number, Principal Quantum Number, nn. This . This number can only have the integral values, number can only have the integral values, nn = 1, 2, 3, etc.= 1, 2, 3, etc.

2.2. Azimuthal Quantum Number, Azimuthal Quantum Number, ll. For each . For each value of value of nn there may be there may be nn values of values of ll, namely , namely ll = 0, 1, 2…,( = 0, 1, 2…,(nn = 1). = 1).

3.3. Magnetic Quantum Number, Magnetic Quantum Number, mm. For each . For each value of value of ll there may be (2 there may be (2ll + 1) values of + 1) values of mm. . These range from These range from mm = -l through = -l through mm = 0 to = 0 to mm = +l in integral values.= +l in integral values.

4. 4. Spin Quantum Number, Spin Quantum Number, ss. There . There are only two possible values of are only two possible values of ss, , ss = = ½ and ½ and s s = -½, for each value of = -½, for each value of ll..

Pauli’s Exclusion PrinciplePauli’s Exclusion Principle – no two – no two electrons in an atom may have all electrons in an atom may have all four quantum numbers the same. four quantum numbers the same.

Electrons Shells and SubshellsElectrons Shells and SubshellsJust as the energy levels of electrons in Just as the energy levels of electrons in

atoms may be considered to be divided into atoms may be considered to be divided into levels and sublevels, so may the electrons be levels and sublevels, so may the electrons be considered to exist in groups and subgroups, considered to exist in groups and subgroups, referred to respectively as shells and subshells. referred to respectively as shells and subshells. This concept finds its justification in the This concept finds its justification in the explanation of the origin of X-ray spectra. The explanation of the origin of X-ray spectra. The ordinary line spectra of elements are due to ordinary line spectra of elements are due to electrons present in the outermost shell, the electrons present in the outermost shell, the optical electronsoptical electrons..

The Periodic Table and Atomic The Periodic Table and Atomic StructureStructure

The periodicity of the elements definitely The periodicity of the elements definitely rules out mass as the determining factor in rules out mass as the determining factor in chemical reactivity, and hence the nuclei of chemical reactivity, and hence the nuclei of atoms cannot possibly be responsible for atoms cannot possibly be responsible for chemical behavior. The first satisfaction chemical behavior. The first satisfaction suggestion about the number of electrons in suggestion about the number of electrons in various shells and their possible arrangement various shells and their possible arrangement was advanced in 1921 independently by was advanced in 1921 independently by BuryBury and and BohrBohr. .

These men proposed that the maximum These men proposed that the maximum number of electrons in each shell should be number of electrons in each shell should be given by 2n², where n is the principal quantum given by 2n², where n is the principal quantum number. This would give for the maximum number. This would give for the maximum number of electrons in successive shells 2, 8, number of electrons in successive shells 2, 8, 18, 32, and 50. Further, Bury and Bohr 18, 32, and 50. Further, Bury and Bohr suggested that there can be present no more suggested that there can be present no more than eight electrons in the outermost shell of than eight electrons in the outermost shell of an atom before the next shell is started. In an atom before the next shell is started. In other words, in shells where more than eight other words, in shells where more than eight electrons can be present, only eight of these electrons can be present, only eight of these enter then a new shell is started, and the enter then a new shell is started, and the incompleted shell is left to be filled in later.incompleted shell is left to be filled in later.

Arrangement of Electrons in AtomsArrangement of Electrons in Atoms

The elements are ordered according to The elements are ordered according to chemical similarity in vertical groups, and chemical similarity in vertical groups, and horizontally in repetitive periods. The first horizontally in repetitive periods. The first period consists of only 2 elements, hydrogen period consists of only 2 elements, hydrogen and helium. The second and third, again, and helium. The second and third, again, contain 8 elements each, with each period contain 8 elements each, with each period terminating with a rare gas, neon and argon. terminating with a rare gas, neon and argon. On the other hand, before the next rare gas, On the other hand, before the next rare gas, krypton, is reached in the fourth period 18 krypton, is reached in the fourth period 18 elements are traversed. elements are traversed.

Of these the 8 elements potassium, gallium, Of these the 8 elements potassium, gallium, calcium, germanium, arsenic, selenium, calcium, germanium, arsenic, selenium, bromine and krypton. The latter are generally bromine and krypton. The latter are generally referred to as the transition elements. In the referred to as the transition elements. In the fifth period the situation is exactly the same as fifth period the situation is exactly the same as in the fourth, the period is consisting again of in the fourth, the period is consisting again of 18 elements. However, when we come to the 18 elements. However, when we come to the sixth period, we find that 32 elements are sixth period, we find that 32 elements are involved here. A study this shows that they involved here. A study this shows that they may be divided into three groups: may be divided into three groups:

a.a. 8 more or less “normal” elements: cesium, 8 more or less “normal” elements: cesium, barium, thallium, lead, bismuth, polonium, barium, thallium, lead, bismuth, polonium, astatine, and radonastatine, and radon

b.b. 10 transition elements ranging from 10 transition elements ranging from lanthanum to mercurylanthanum to mercury

c.c. The rate earth falling between Z = 58 and Z The rate earth falling between Z = 58 and Z = 71.= 71.

Spectral TermsSpectral Terms

When more than one electrons When more than one electrons is present, a different scheme has to is present, a different scheme has to be employed to designate the energy be employed to designate the energy levels. The system commonly used is levels. The system commonly used is that based on Russell-Saunders that based on Russell-Saunders coupling, and takes the formcoupling, and takes the form

n ^ (2S’ + 1)LJn ^ (2S’ + 1)LJ

The symbol The symbol nn refers to the major refers to the major energy level of the atom.energy level of the atom.

Quantum MechanicsQuantum Mechanics

In In 1925-1926 Werner Heisenberg1925-1926 Werner Heisenberg and and Erwin SchrödingerErwin Schrödinger independently independently proposed a new quantum or wave proposed a new quantum or wave mechanics which takes cognizance of mechanics which takes cognizance of the wave and particle duality of matter the wave and particle duality of matter and which deals with atomic and and which deals with atomic and molecular atomic scale problems in a molecular atomic scale problems in a totally different manner. totally different manner. Schrödinger wave EquationSchrödinger wave Equation::

V²V²ΨΨ + (8 + (8ππ²m/h²)(E – U)²m/h²)(E – U)ΨΨ = 0 = 0

Nature and Significance of Nature and Significance of ΨΨ. The . The Schrödinger Equation implies in essence that a Schrödinger Equation implies in essence that a moving body of mass moving body of mass mm, velocity , velocity vv, potential , potential energy energy UU, and total energy E has a wave , and total energy E has a wave associated with it of an amplitude given by the associated with it of an amplitude given by the wave function wave function ΨΨ..

The particular values of The particular values of ΨΨwhich yields which yields satisfactory solution of this equation are called satisfactory solution of this equation are called eigenfunctions eigenfunctions or characteristic wave or characteristic wave functions, while values of the energy which functions, while values of the energy which correspond to the eigenfunctions are called the correspond to the eigenfunctions are called the eigenvalueseigenvalues of the system. of the system.

Quantum Mechanics of the Hydrogen Quantum Mechanics of the Hydrogen AtomAtom. Consider an atom consisting of a . Consider an atom consisting of a nucleus of mass m’ and charge Ze around nucleus of mass m’ and charge Ze around which revolves one electron of mass m. In which revolves one electron of mass m. In mechanics such a combination can be looked mechanics such a combination can be looked upon as a particle of reduced mass upon as a particle of reduced mass μμ given by given by

1/1/μμ = 1/m + 1/m’ = 1/m + 1/m’

The Hydrogenlike Wave FunctionsThe Hydrogenlike Wave Functions. The . The wave function for an electron in an atom is wave function for an electron in an atom is called an called an atomic orbitalatomic orbital. Consider first the . Consider first the radial distribution to radial distribution to ΨΨ for the hydrogen atom. for the hydrogen atom. In each instance In each instance R²R² represents the probability represents the probability of finding the electron at a point between of finding the electron at a point between r r and and r + drr + dr in space. However, it is more in space. However, it is more illuminating to consider the probability of illuminating to consider the probability of finding the electron in a spherical shell of finding the electron in a spherical shell of thickness thickness drdr at distance at distance rr from a center of the from a center of the mass, which practically identical with the mass, which practically identical with the position of the nucleus.position of the nucleus.

This probability D(r), called the radial This probability D(r), called the radial distributiondistribution

function, is given by the expression function, is given by the expression

D(r) = 4D(r) = 4ππr²R²r²R²

Plots of the angular Parts of the Hydrogen Atom Wave FunctionsPlots of the angular Parts of the Hydrogen Atom Wave Functions

The End of Slide Show…The End of Slide Show…THANK YOU!!!THANK YOU!!!