HISTORY OF ATOM MODEL

BOHR’S ATOM MODEL & POSTULATES

HYDROGEN SPECTRA

PAULI’S EXCLUSION PRINCIPLE

SOMMERFELD MODEL

QUNATUM NUMBERS

VECTOR ATOM MODEL

Atomic Models: Atomic Models: GreekGreek

Democritus Democritus (460-370 (460-370 B.C.)B.C.) Matter can Matter can

not be divided forevernot be divided forever

Smallest piece = Smallest piece = “atom”“atom”

(Gk “atomos” = “not to be (Gk “atomos” = “not to be cut”)cut”)

He had no way of He had no way of knowing what atoms knowing what atoms looked like!looked like!

Gold Go ld

The word “The word “atomatom” comes from a ” comes from a Greek word that means Greek word that means

“unable to be cut”“unable to be cut”

Imagine you had a piece of gold that you then cut in half…

…and then you cut one of these smaller pieces in half…

The word “The word “atomatom” comes from ” comes from a Greek word that means a Greek word that means

“unable to be cut”“unable to be cut”

…and kept going… …and kept

going…

Eventually you would have 1 piece of gold left. If you cut it in half, you wouldn’t

have gold any more – you’d have something

else. This tiny, tiny single piece of gold is called an atom of gold. An atom is the smallest particle of an element that acts like the

element.

An atom of gold

Atomic Models : Atomic Models : DaltonDalton

1. Elements composed of atoms; 1. Elements composed of atoms; atoms are indestructibleatoms are indestructible

2. Atoms of the same element 2. Atoms of the same element are exactly alikeare exactly alike

3. Atoms of different elements 3. Atoms of different elements are differentare different

4. Compounds formed by joining 4. Compounds formed by joining 2 atoms2 atoms

Atomic Models: J.J. Atomic Models: J.J. ThompsonThompson

The atoms are The atoms are neutral… How?neutral… How?

+ charges must + charges must be present to be present to balance - balance - chargescharges

+ & - lumped in + & - lumped in a cluster he said a cluster he said looked like looked like “plum pudding”“plum pudding”

Thompson’s ModelThompson’s Model

Atomic Models: Atomic Models: RutherfordRutherford

Passed + Charged Particles Passed + Charged Particles through gold foilthrough gold foil Most passed right through

Atom is mostly empty space Some bounced off at odd angles

Nucleus must be + Calculate size of nucleus

Rutherford’s Gold Foil Rutherford’s Gold Foil ExperimentExperiment

Rutherford’s WorkRutherford’s Work

Rutherford’s ModelRutherford’s Model

Okay…Okay…

So the atom is made So the atom is made up of positive and up of positive and negative particles.negative particles. Where are the Where are the

electrons found in the electrons found in the atom?atom?

Atomic Models: BohrAtomic Models: Bohr

Electrons Electrons are found in are found in specific specific energy energy levelslevels Like planets

around the sun

Sommerfeld ModelSommerfeld Model

Vector Atom Model

Niels Henrik David Bohr. (1884-1962)

In 1913, Bohr suggested his atom model for which he was awarded Nobel Prize for

Physics in 1922

Positively charged nucleus are at the centre and negatively charged electrons revolve round the nucleus in various circular orbit.

1

The electrons revolving round the nucleus only in certain permitted orbits are called energy levels. i.e. orbits of certain radii are allowed.

2

Energy

level

Each energy level has a certain fixed amount of energy. The larger the orbit (i.e. larger radius), the greater is the energy of electrons.

3

Electrons gives out energy in the form of electromagnetic radiation when it jumps from higher to lower level.

4

Nucleus

Electron

An atom consists of positively charged nucleus at the centre

1

Nucleus

ElectronThe negatively

charged electrons move round the nucleus in various orbits known as stationary energy levels.

2

The electrons can’t emit radiations when moving in their own stationary level

Nucleus

Electron

The Coulombian and Newtonian

forces are applicable in the domain of

the atom

3

The angular momentum for electron mvr = nh/2π

4

Coulomb

force

When an electron jumps from a higher energy level to a lower energy level, it gives out EM radiations of a particular frequency

5

Wn2 – Wn1 = hv

Wn3

hv

Wn2

Wn1

Nucleus

Nucleus of charge E = Ze

Electron of charge = e

Radius of an orbit = r

The electrostatic force of attraction

Fe = Ee / 4πε0 r2 ….. (1)

The centripetal force

Fc = mv2/ r …………(2)

Let us consider an atom having

The condition for dynamically stable orbit is Fe = Fc

Electron

E

e

rn1

n2

n3

mv2/ r = Ze2 / 4πε0 r2

mv2 = Ze2 / 4πε0r ………(3)

We know, the angular momentum,

mvr = nh / 2π

or, v = nh / 2πmr ……(4)

Eqn (3) becomes

m( nh/2πmr)2 = Ze2 / 4πε0r

r = ε0n2h2 / πmZe2 ….(5)

This is the eqn for radius →

Nucleus

Electron

E

e

rn1

n2

n3

From eqn (5) r ∞ n2

So the radii are in the ratio of 1 : 4 : 9 : 16 etc . From equation (5) the radius of the first orbit of hydrogen r = 5.29 x 10-11m, where n =1 and Z = 1

Substituting r in eqn (4)

v = Ze2 / 2ε0nh

Nucleus

Electron

E

e

r

This equation shows that v is inversely proportional to n

n3

n2

n1

Nucleus

Electron

E

e

r

The energy is partly potential and partly kinetic

The potential energy of electron =

r0

2

4

Ze - P.E

And kinetic energy of electron

r

Ze

r

Zemv

0

2

0

22

842

1

2

1 K.E

n1

n2

n3

Nucleus

Electron

E

e

r

Total energy E = P.E + K.E

r

Ze

r

Ze

r

ZeE

0

2

0

2

0

2

884

…….(7)

Now from eqn (5) & (7) 222

0

24

8 hn

ZmeE

When an electron jumps from energy level n2 to energy level n1

22

21

220

24 11

8 nnh

ZmeE

n1

n2

n3

Nucleus

Electron

E

e

r

Wn2 – Wn1 = E = hv

Again we know

22

21

320

24 11

8 nnh

Zme

22

21

320

4 11

8 nnh

mec

Since C= υλ & Z=1 for H2

22

21

320

4 11

8

1

nnch

me

22

21

11

nnR

Where υ = 1/λ = Wave number R= Rydberg constant

n3

n2

n1

It can not explain the origin of the fine structure of the spectral lines.

There is an ad hoc nature in the assumptions of Bohr where the quantum ideas of the stationary orbits is mixed up with the classical idea of Coulomb force.

Though it can explain the spectral lines of H2 but it can not explain the spectral lines of multi-electron systems like Helium.

1

2

3

Lyman Series

Balmer Series

Bracket Series

Pfund Series

n1

n3

n4

n5

n6

n2

Paschen Series

(1) Lyman Series : Outer orbits → n1 .

Here, n1=1, n2=2, 3, 4, 5……..RR

4

3

2

1

1

122

(2) Balmer Series : Outer orbits → n2 . It is in the visible region of the spectrum. Here, n1=2, n2= 3, 4, 5…

(3) Paschen Series : Outer orbits → n3 .

Here, n1=3, n2= 4, 5……..

(4) Bracket Series : Outer orbits → n4 .

Here, n1=4, n2= 5, 6……..

(5) Pfund Series : Outer orbits → n5 . Here, n1=5, n2= 6, 7……..

→ According to Sommerfeld - the orbits of electrons doesn't have to be spherical but can also be elliptic. The electrons can move only on some, allowed ellipses.

→ He coined a second number l which was called the secondary quantum number or the azimuthal quantum number. The number defined the shape, the oblateness of an orbit.

Arnold Sommerfeld

(1868-1951)

→ For n=1 the orbit can be only spherical (l=0), for n=2 there are two orbits of different shapes (l= 0 - the elliptic one, l= 1 - the spherical one). For any n there are n kinds of shapes of the orbits.

The electrons moving on the two orbits of the same n number but of different shape have a bit different energies. That explaines the discovered structure of the spectral lines

Therefore, vector atom model was introduced partly by analogy, partly by empirical methods in the interpretation of more complex spectral phenomena and their relation to atomic structure.

Wha

t

is th

is

!

This model is an extension of the Rutherford-Bohr–Sommerfelds model. Bohr and Sommerfeld model were quite inadequate to explain fine structure of spectral lines of atom and to tackle more complex atoms.

The two essential features that characterize this model and differentiate it from the other models are :

a. The conception of quantization of direction or spatial quantization

b. Spinning of electron.As the different components that determine the state of the atom such as the orbital and spin motions are all quantised vectors, the atom model built on such considerations is called VECTOR ATOM MODEL to which vector laws apply.

Wha

t

is th

is

!

CHARACTERISTICS

It is the quantisation of direction of orientation of the orbits in space. This spatial quantisation makes the orbits vector quntities.

The fact to determine the quantised orientations relative to field direction is that the projections of the orbits on the field direction must themselves be quantised.

Spatial Quantisation :

B

According to this characteristic, the electron revolves not only in an orbit round the nucleus but also about an axis of its own.

Spinning electron :

CHARACTERISTICS

A total quantum number n :

Also used in Bohr-Sommerfeld theory. It can take any integral values 1, 2, 3, etc

1

2A orbital quantum number l : Also used in Sommerfeld theory as azimuthal quantum no. It can take any integral values between 0 and (n-1). If n =4, l = 0 (S electron) =1 (p electron) =2 (d electron) =3 (f electron) and so on

n1

n2

A spin quantum number s : The magnitude is always 1/2

3

4

A total angular quantum number j : Here, j = l+s = l 1/2

5

A magnetic orbital quantum number ml : It is the numerical value of the projection of l on the field direction. If θ is the angle between l and field direction, the projection

ml = l cos θ

The permitted values of ml are from + l to - l and according to arithmetical progression the total number is (2l+1) .

6

A magnetic spin quantum number ms : It is the numerical value of the projection of s on the field direction. Like l , the permitted values of ms are from + s to - s , excluding zero and according to arithmetical progression the total number is (2s+1) .

Since s is always equal to 1/ 2 and never zero, therefore, ms can have only two values + 1/2 and – 1/2

7

A magnetic total angular quantum number mj : It is the numerical value of the projection of j on the field direction. The permitted values of mj are from + j to – j , excluding zero and permitted orientations are (2j+1) .

→ Every completely defined quantum state in an atom can be occupied by only one electron.

→ It is impossible for two electrons in an atom to be identical as regards all their quantum numbers, i.e., one of the two will be excluded from entering into the constitution of the atom.