Chapter 2 structure of atom class 11

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Structure of AtomGRADE 11

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DISCOVERY OF AN ELECTRON An electron was discovered by cathode ray discharge tubes experiment. A cathode ray tube is made of glass containing two thin pieces of metal

called electrodes, sealed in it. The electrical discharge through the gases could be observed only at very low pressures and at very high voltages . The pressure of different gases could be adjusted by evacuation. When sufficiently high voltage is applied across the electrodes , the current starts to flow through a stream of particles moving in the tube from the negative electrode to the positive one . These rays were called the cathode rays or cathode ray particles.

The flow of current from cathode to anode was further checked by making a hole in the anode and coasting the tube behind anode with phosphorescent material called zinc sulphide coating , a bright spot on the coating is developed .

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Results of the experiment The cathode rays start from cathode and move towards the

anode. These rays were not visible but their behaviour could be

observed with a certain kind of material called FLOUROSCENT OR PHOSPHORESCENT MATERIALS.

In the absence of electrical or magnetic field these rays travel in straight lines.

In the presence of electrical or magnetic field , the behaviour of cathode rays are similar to that expected from negatively charged particles suggesting that the cathode rays consist of negatively charged particles called electrons.

The characteristics of cathode rays do not depend upon the material of electrodes nature of the gas present in the tube .

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CHARGE TO MASS RATIO OF ELECTRON

The measure of mass ratio of an electrical charge (e) to the mass of an electron (me) by using the cathode rays discharge tube and applying electrical and magnetic field perpendicular to each other as well as to the path of electrons .

The amount of deviation of the particles from their path in the presence of electrical and magnetic field depend upon:

1) The magnitude of the negative charge on the particle, greater the magnitude of the charge on the particle , greater is the interaction with the electric and magnetic field and thus greater is the deflection.

2) The mass of the particle: lighter the particle , greater the deflection and vice versa.

3) The strength of the electrical and magnetic field-the deflection of electrons from its original path increases with the increase in the voltage across the path electrodes or the strength of the magnetic field.

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When only electric field is applied, the electrons deviate from their path and hit the cathode ray tube at point A.

When only magnetic field is applied electron strikes the cathode ray tube at point C.

When electrons deviate from their path, then both electrical and magnetic field is applied , it is possible to bring them back and electrons go and hit the screen at point B.

  = 1.758820 x 1011 C kg-1

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Discovery of protons and neutrons

Electrical discharge carried out in the modified cathode rays tube led to the discovery of particles carrying positive charge also known as canal rays.

The characteristics of these rays are:⇒ Unlike cathode rays, the positively charges particles depend upon the

nature of gas present in the cathode ray tube.These gases are simple positively charged ions.

⇒ The charge to mass ratio of the particles is found to depend on the gas from which they originate.

⇒ Some of the +vely charged particles carry a multiple of the fundamental unit of electrical charge.

⇒ The behaviour of these particles in the magnetic or electrical field is opposite to that observed for electron or cathode rays.

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The smallest and lightest positive ion was obtained from hydrogen and was called the proton.

Discovery of neutrons: Chadwick felt that by bombarding a thin sheet of beryllium by α-particles. When electrically neutral particles having a mass slightly greater than that of the protons was emitted. He named these neutral particles as neutrons. Thus this discovery Was a very important discovery in the history of chemistry.

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Thomsons model of an atom

According to Thomson, atom was in a spherical in shape which had positive charged particle sand negative charged particles equally distribution and hence it was electrically neutral.

Its observation could be called as a plum pudding model or a watermelon.

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Rutherford’s model of atom

Famous experiment of Rutherford was the α-particle scattering experiment.

A stream of high energy α particles from a radioactive source was directed at a thin foil of a gold metal. The thin foil had a circular fluorescent zinc sulphide screen around it .Whenever α-particles struck the screen, a tiny flash of light was produced at the point.

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The results of this experiment were unexpected. (1) most of the α-particles passed through the gold foil

undeflected. (2)a small fraction of α-particles was deflected by small

angles (3) a very few α-particles (-1 in 20,000) bounced back , that

is were deflected by nearly 180 degree.Observations: Most of the space in the atom is empty as most of the α-

particles passed through the foil undeflected. A few +vely charged α-particles were deflected. The deflection must be due to enormous repulsive force

showing the positive charge in the atom. The positive charge has to be concentrated in a very small

volume that repelled and deflected the positively charged α-particles .

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Conclusions: The positive charge and most of the massof the

atom was densely concentrated in extremely small region. This concentrated region was called nucleus.

The nucleus was surrounded by electrons moving in a very high speed in circular paths called orbits.

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

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Atomic number and mass number

Atomic number(Z)=number of protons present in the nucleus = number of electrons in the neutral atom.

Electrons and protons together ina nucleus are / were called nucleons.

Mass number (A)= number of protons (z)=number of neutrons(n)

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Isobars and isotopes

Isobars are elements having the same mass number but different atomic number.

Whereas isotopes are elements having same atomic number but a different mass number.

Hydrogen has 3 isotopes: protium , deuterium and tritium.Chemical properties of atoms are controlled by the

number of protons in the nucleus therefore they show similar chemical properties and similar chemical behaviour

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Draw backs of Rutherford’s model of atom.

It could not explain the gravitational force in nature.

It could not explain planetary motion under the influence of gravity.

It could not explain Maxwell's electromagnetic radiation property.

It could not explain quantum mechanics as a whole.

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The Electromagnetic Spectrum

Visible light is a small portion of the electromagnetic radiation spectrum detected by our eyes.

Electromagnetic radiation includes radio waves, microwaves and X-rays.

Described as a wave traveling through space.

There are two components to electromagnetic radiation, an electric field and magnetic field.

The Wave Nature of Light

Wavelength, , is the distance between two corresponding points on a wave.

Amplitude is the size or “height” of a wave.

Frequency, , is the number of cycles of the wave passing a given point per second, usually expressed in Hz.

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Planck’s Quantum Theory

Higher T = shorter λ (higher E) maximum. Couldn’t explain with classical physics

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Electromagnetic Radiation In 1900 Max Planck studied black body

radiation and realized that to explain the energy spectrum he had to assume that:

1. energy is quantized2. light has particle character

Planck’s equation is

sJ 10x 6.626 constant s Planck’ h

hc or E h E

34-

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The Wave Nature of Light The fourth variable of light is velocity.

All light has the same speed in a vacuum.

c = 2.99792458 x 108 m/s

The product of the frequency and wavelength is the speed of light.

Frequency is inversely proportional to wavelength.

c

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The Wave Nature of Light Electromagnetic radiation can be categorized in terms of

wavelength or frequency.

Visible light is a small portion of the entire electromagnetic spectrum.

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The Particulate Nature of Light

Photoelectric effect: light striking a metal surface generates photoelectrons.

The light’s energy is transferred to electrons in metal.

With sufficient energy, electrons “break free” of the metal.

Electrons given more energy move faster (have higher kinetic energy) when they leave the metal.

The Particulate Nature of Light

Photoelectric effect is used in photocathodes.

Light strikes the cathode at frequency . Electrons are ejected if exceeds the threshold value 0.

Electrons are collected at the anode.

Current flow is used to monitor light intensity.

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Example Problem 6.1

Neon lights emit an orange-red colored glow. This light has a wavelength of 670 nm. What is the frequency of this light?

We know that c=ʋλTherefore c/λ= and solve.ʋ

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The Particulate Nature of Light

The photoelectric effect is not explained using a wave description but is explained by modeling light as a particle.

Wave-particle duality - depending on the situation, light is best described as a wave or a particle.

Light is best described as a particle when light is imparting energy to another object.

Particles of light are called photons.

Neither waves nor particles provide an accurate description of all the properties of light. Use the model that best describes the properties being examined.

Photoelectric Experiments

a) For > 0, the number of electrons emitted is independent of frequency.Value of 0 depends on metal used.

b) As light intensity increases, the number of photoelectrons increases.

c) As frequency increases, kinetic energy of emitted electrons increases linearly.

d) The kinetic energy of emitted electrons is independent of light intensity.

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The Particulate Nature of Light

The energy of a photon (E) is proportional to the frequency ().

and is inversely proportional to the wavelength ().

h = Planck’s constant = 6.626 x 10-34 J s

E h hc

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The Particulate Nature of Light

Binding Energy - energy holding an electron to a metal.

Threshold frequency, o - minimum frequency of light needed to emit an electron.

For frequencies below the threshold frequency, no electrons are emitted.

For frequencies above the threshold frequency, extra energy is imparted to the electrons as kinetic energy.

Ephoton = Binding E + Kinetic E

This explains the photoelectric effect.

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Example Problem 6.2

The laser in a standard laser printer emits light with a wavelength of 780.0 nm. What is the energy of a photon of this light?

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The Wave Nature of Light Refraction is the bending of light when it passes

from one medium to another of different density. Speed of light changes. Light bends at an angle depending on its wavelength. Light separates into its component colors.

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Example Problem 6.3

In a photoelectric experiment, ultraviolet light with a wavelength of 337 nm was directed at the surface of a piece of potassium metal. The kinetic energy of the ejected electrons was measured as 2.30 x 10-19 J. What is the electron binding energy for potassium?

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Atomic Spectra Atomic Spectra: the particular pattern of wavelengths

absorbed and emitted by an element.

Wavelengths are well separated or discrete.

Wavelengths vary from one element to the next.

Atoms can only exist in a few states with very specific energies.

When light is emitted, the atom goes from a higher energy state to a lower energy state.

Atomic Spectra

Electrical current dissociates molecular H2 into excited atoms which emit light with 4 wavelengths.

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Atomic Spectra and the Bohr Atom Every element has a unique spectrum. Thus we can use spectra to identify elements.

This can be done in the lab, stars, fireworks, etc.

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Example Problem 6.4

When a hydrogen atom undergoes a transition from E3 to E1, it emits a photon with = 102.6 nm. Similarly, if the atom undergoes a transition from E3 to E2, it emits a photon with = 656.3 nm. Find the wavelength of light emitted by an atom making a transition from E2 to E1.

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The Bohr Atom Bohr model - electrons orbit the

nucleus in stable orbits. Although not a completely accurate model, it can be used to explain absorption and emission.

Electrons move from low energy to higher energy orbits by absorbing energy.

Electrons move from high energy to lower energy orbits by emitting energy.

Lower energy orbits are closer to the nucleus due to electrostatics.

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The Bohr Atom

Ground state: the lowest state (orbital)where the electrons are initially present is called the ground state.

Excited state: the state where the electrons on gaining energy I subjected to go to a higher energy level is called the excited state.Atoms return to the ground state by emitting

energy as light.

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Atomic Spectra and the Bohr Atom The Rydberg

equation is an empirical equation that relates the wavelengths of the lines in the hydrogen spectrum.

hydrogen of spectrumemission

in the levelsenergy theof

numbers therefer to sn’

n n

m 10 1.097 R

constant Rydberg theis R

n

1

n

1R

1

21

1-7

22

21

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Atomic Spectra and the Bohr Atom

Example 4-8. What is the wavelength of light emitted when the hydrogen atom’s energy changes from n = 4 to n = 2?

2 1

2 21 2

7 -1 2 2

7 -1

7 -1

7 -1

6 -1

n 4 and n 2

1 1 1 R

n n

1 1 1 1.097 10 m

2 4

1 1 1 1.097 10 m

4 16

1 1.097 10 m 0.250 0.0625

1 1.097 10 m 0.1875

1 2.057 10 m

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Atomic Spectra and the Bohr Atom In 1913 Neils Bohr incorporated Planck’s

quantum theory into the hydrogen spectrum explanation.

Here are the postulates of Bohr’s theory.

1. Atom has a number of definite and discrete energy levels (orbits) in which an electron may exist without emitting or absorbing electromagnetic radiation.

As the orbital radius increases so does the energy

1<2<3<4<5......

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Atomic Spectra and the Bohr Atom3. An electron moves in a circular orbit about the

nucleus and it motion is governed by the ordinary laws of mechanics and electrostatics, with the restriction that the angular momentum of the electron is quantized (can only have certain discrete values).

angular momentum = mvr = nh/2h = Planck’s constant n = 1,2,3,4,...(energy levels) v = velocity of electron m = mass of electronr = radius of orbit

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Atomic Spectra and the Bohr Atom Light of a characteristic wavelength (and

frequency) is emitted when electrons move from higher E (orbit, n = 4) to lower E (orbit, n = 1).

This is the origin of emission spectra. Light of a characteristic wavelength (and

frequency) is absorbed when electrons jump from lower E (orbit, n = 2) to higher E (orbit, n= 4)

This is the origin of absorption spectra.

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Atomic Spectra and the Bohr Atom Bohr’s theory correctly explains the H

emission spectrum. The theory fails for all other elements

because it is not an adequate theory.

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The Wave Nature of the ElectronIn 1925 Louis de Broglie published his Ph.D. dissertation.

A crucial element of his dissertation is that electrons have wave-like properties.

The electron wavelengths are described by the de Broglie relationship.

particle of velocity v

particle of mass m

constant s Planck’ hmv

h

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The Wave Nature of the ElectronExample 4.9. Determine the wavelength, in m, of an electron, with mass 9.11 x 10-31 kg, having a velocity of 5.65 x 107 m/s.

Remember Planck’s constant is 6.626 x 10-34 Js which is also equal to 6.626 x 10-34 kg m2/s.

m 1029.1

m/s 1065.5kg 109.11

ss/m kg 10626.6

mv

h

11

731-

2234

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The Quantum Mechanical Picture of the Atom

Werner Heisenberg in 1927 developed the concept of the Uncertainty Principle.

It is impossible to determine simultaneously both the position and momentum of an electron (or any other small particle). Detecting an electron requires the use of

electromagnetic radiation which displaces the electron!

Electron microscopes use this phenomenon

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The Quantum Mechanical Model of the Atom

Quantum mechanical model replaced the Bohr model of the atom.

Bohr model depicted electrons as particles in circular orbits of fixed radius.

Quantum mechanical model depicts electrons as waves spread through a region of space (delocalized) called an orbital.

The energy of the orbitals is quantized like the Bohr model.

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The Quantum Mechanical Model of the Atom

Diffraction of electrons shown in 1927.

Electrons exhibit wave-like behavior.

Wave behavior described using a wave function, the Schrödinger equation.

H is an operator, E is energy and is the wave function. H E

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Potential Energy and Orbitals

Total energy for electrons includes potential and kinetic energies.

Potential energy more important in describing atomic structure; associated with coulombic attraction between positive nucleus and negative electrons.

Multiple solutions exist for the wave function for any given potential interaction.

n is the index that labels the different solutions.

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On solving the Schrödinger equation we get three set of number which are called the quantum numbers which give us the location space and the 3-D spatial orientation of the orbital.

The probability density gives us the probability of an electron in the region that is where the electrons in most probable to be.

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Potential Energy and Orbitals

n can be written in terms of two components.

Radial component, depends on the distance from the nucleus.

Angular component, depends on the direction or orientation of electron with respect to the nucleus.

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Potential Energy and Orbitals

The wave function may have positive and negative signs in different regions. Square of the wave function, 2, is always positive and gives

probability of finding an electron at any particular point.

Each solution of the wave function defines an orbital. Each solution labeled by a letter and number combination:

1s, 2s, 2p, 3s, 3p, 3d, etc. An orbital in quantum mechanical terms is actually a region

of space rather than a particular point.

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Quantum Numbers

Quantum numbers - solutions to the functions used to solve the wave equation.

Quantum numbers used to name atomic orbitals.

Vibrating string fixed at both ends can be used to illustrate a function of the wave equation.

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Quantum Numbers

When solving the Schrödinger equation, three quantum numbers are used.

Principal quantum number, n (n = 1, 2, 3, 4, 5, …)

Secondary quantum number, l

Magnetic quantum number, ml

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Quantum Numbers

The principal quantum number, n, defines the shell in which a particular orbital is found.

n must be a positive integer

n = 1 is the first shell, n = 2 is the second shell, etc.

Each shell has different energies.

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Quantum Numbers The secondary quantum number, l, indexes energy

differences between orbitals in the same shell in an atom. l has integral values from 0 to n-1.

l specifies subshell Each shell contains as many l values as its value of n.

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Quantum Numbers

The energies of orbitals are specified completely using only the n and l quantum numbers.

In magnetic fields, some emission lines split into three, five, or seven components.

A third quantum number describes splitting.

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Quantum Numbers The third quantum number is the magnetic

quantum number, ml.

ml has integer values.

ml may be either positive or negative.

ml’s absolute value must be less than or equal to l.

For l = 1, ml = -1, 0, +1

Quantum Numbers

Note the relationship between number of orbitals within s, p, d, and f and ml.

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Electron spin-s

The 3 quantum numbers labeling an atomic orbital can be equally used to well define its energy, shape and its orientation.

A new quantum number was introduced called the electron spin quantum numbers-ms .

It had its own axis,, these had angular momentum and two orientation or spins that is ½ and -½ and were normally represented by two arrows ↑ and ↓showing that these have opposite spins.

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Summing up n defines the shell ,determines the size of the orbital

and also to a large extent the energy of the orbital. There are n subshells in the nth shell. l identifies the

sub shell and determines the shape of the orbital there are (2l+1)orbitals of each type in a subshells that is one s orbital (l=0) three p orbitals(l=1) and 5 d orbitals(l= 2) per subshells. To some extent l also determines the energy of the orbital in a multi electron atom.

designates the orientation of the electron of the orbital . For a given value of l or has (2l+1) values , the same as the number of orbitals per subshells. it means that the number of orbitals is equal to the number of ways in which they are oriented

refers to orientation of the spin of the electron

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Shapes of atomic orbitals According to max born the square of the wave

function at a point gives the probability density of the electron at that point.

For 1s orbital the probability density is maximum at the nucleus and its decreases sharply as we move away from it

For a 2s orbital the probability density first decreases sharply to zero and then again starts increases.

After reaching a small maxima it decreases again and approaches zero as the value of r increases further.

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The region where this probability of finding an electron reduces to zero is called nodal surfaces or simply nodes.

In general, for an ns orbital , an ns orbital has (n-1)nodes, that is number of nodes increases with the increase of quantum number n.therefore for 2s it will be 1 and for 3s it will be 2.

Boundary surface diagrams of constant probability density for different orbitals give a fairly good representation of the shapes of the orbitals . In this representation, a boundary surface or a contour surface is drawn in space for an orbital on which the value of probability density is constant.

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In the boundary surface diagrams the nucleus is taken to be at the origin or rather it is . Here, , diagrams are not spherical like the s-orbital. Here the p-orbital consists of two section s called lobes. That are on either sides of the plane where the two lobes touch each other. The size, shape and energy of the three orbitals are identical .

Since the lobes are considered along the x, y and the z axis they are designated as the above:-

It should be understood that there is no relation between first magnetic quantum number and x, y, z directions

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Boundary surface diagrams for 2p orbitals

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d- orbitals The 5 d-orbitals are designated as:-

The shapes of the first four d-orbitals are similar to each other , where as the fifth one is different form others, but all 5 have 3d- orbitals and are equivalent in energy.

The d- orbitals for which n is greater than 3 also have shapes similar to 3d orbital , but differ in energy.

When two nodal planes pass through the same origin and bisecting the xy-pane and z-plane these nodes are called angular nodes.

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Angular nodes are denoted by ’l’.There are one angular node for the p-orbitals and 2

angular nodes for d-orbitalsThe total number of nodes are given by (n-1)i.e the

sum of l angular nodes are (n-l-1) radial nodes.Energies of orbitals:-Energy increasing order in the orbitals is given as

follows:-1s<2s=2p<3s=3p=3d<4s=4p=4d=4f<As 2p and 2s orbitals are different, an electron has

the same energy as it is present in the 2p or the 2s orbital.

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The orbitals which have the same energy are called degenerate. The 1s orbital in a hydrogen atom corresponds to the most stable condition and is called the ground state. And an electron residing in this orbital is strongly held by the nucleus

The electrons residing in the 2s , 2p or higher orbitals in the hydrogen atom are said to be in the excited state.

The attractive interactions of an electron increases with the increase of the positive charge (Ze) on the nucleus.

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Due to the presence of electrons in the inner shells, the electron in the outer shells will not experience full positive charge of the nucleus.

The effect will be lowered due to the partial screening of positive charge on the nucleus by the inner shell electrons. This is known as shielding of outer electrons from the nucleus by the inner shell electrons and the net positive charge experienced by the outer electrons is known as effective nuclear charge.( )

In other word the energy of interaction b/w the nucleus and electron decreases with the increase of atomic number Z.

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Aufbau principle Aufbau principle deals with filling up of electrons.

The principle states:- In the ground state of the atoms , the orbitals are filled in order of the increasing energies.

In other words, electrons first occupy the lowest energy orbitals available tot hem and then enter into higher energy orbital only after lower energy orbital is filled.

Order of increasing order of energies in the orbital is as follows:- 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,4f,5d,6p,7s……..

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Order of filling up of electrons

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Pauli exclusion principle According to this principle :- no two electrons

in this atom have the same set of four quantum numbers.

OrIt can also be stated otherwise as only two

electrons may exist in the same orbital and these orbital must have opposite spins

The maximum number of electrons which can be accommodated in the shell with the quantum

number n is according to the 2n2 rule.

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Hund’s rule of maximum multiplicity

This rule deals filling of electrons in the orbitals belonging to the same subshells of equal energy called degenerate orbitals.

It states that pairing of electrons in the orbitals belonging to the same sub shell (p,d, or f) does not take place until each orbital of that sub shell gets one electron that is singly occupied.

Some of the orbitals acquire extra stability due to their symmetry.

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Electronic configuration The distribution of electrons into orbitals of an

atom is called its electronic configuration. Electronic configuration can be represented in

two ways:-(a)Normal notation and (b) orbital diagramAs given in the textbook.The electron in the completely filled electronic shell

with the highest principal quantum number are called valence electrons.