Introduction to atomic structure

Rutherford-Geiger-Marsden gold foil experiment in 1909 disproved the Plum Pudding Model and showed that instead of a soup of positive charge, an atom consisted of a small nucleus of stro

Introduction to Atomic Structure

We are made of ATOMS !

Structure of the Atom

Evolution of Atomic Theory

1. First clear concept of Atom starts with the Jain School of Thought in 6th Century BC in India The Jains considered that matter is made of atoms or

“paramanus” The Jain School also developed an elaborate set of theories on how atoms could combine, move, vibrate, etc

2. In Western School, the concept of Atom starts in 5th Century BC through Ionian Philosopher Democritus The concept of atom was similar to Jain School in the sense that atoms were considered to be fundamental particles that can not be cut or broken into parts The word “atom” was coined

by him from the Greek adjective “atomos” meaning uncuttable

3. Atomistic philosophy in Islam was developed around 11th century AD by Imam Ghazali synthesizing the Jain and Greek Schools of thoughts about Atom His atomic theory was more in tune with the Jain School rather than of the Greek School

4. Towards late 18th century scientific developments started renewed philosophical interest in composition of matter Dalton assimilated the

experimental works of many scientists to propose his ultimate modern theory of matter known as Dalton’s Atomic Theory

Dalton’s Atomic Theory

Dalton’s Atomic Theory

1 Elements are made of extremely small particles called atoms.

2 Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.

3 Atoms cannot be subdivided, created, or destroyed.

4 Atoms of different elements combine in simple whole-number ratios to form chemical compounds.

5 In chemical reactions, atoms are combined, separated, or rearranged.

Dalton’s theory forms the foundation of Modern Theoretical Chemistry

Thomson’s Plum Pudding

Thomson’s Plum Pudding Model

1. The model was proposed by Thomson in 1904 before the discovery of nucleus

2. Electrons or “corpuscles” are floating in a soup of positive charge to balance the

negative charges

3. The positive charge was assumed to be like a “pudding”, and the negatively charged

electrons as “plums” and hence the terminology Plum Pudding Model taken from a

British dessert

4. Rutherford-Geiger-Marsden gold foil experiment in 1909 disproved the Plum

Pudding Model and showed that instead of a soup of positive charge, an atom

consisted of a small nucleus of strong positive charge paving the way to Rutherford’s

Atomic Model

“ the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, “… Thomson in Philosophical Magazine, 1904

Rutherford’s Atomic Model

Rutherford-Geiger-Marsden Experiment

Under supervision of Prof Rutherford ( student of Thomson) and scientist Geiger and graduate student Marsden, Thomson’s Plum Pudding Model was discarded by the Gold foil experiment in 1911 establishing Rutherford’s atomic model

Rutherford’s Atomic Model

Rutherford’s model based on Gold Leaf Experiment stated that the atom consists of a small, dense, positively charged core surrounded by negatively charged particles in a planetary model system.

Limitations of Rutherford’s Model

The failure of Rutherford’s Model was in relation to Lamor’s Formula in classical physics which lead to the conclusion that continuous emission of energy by electron will ultimately lead to collapse of the atom Bohr corrected it by postulating that energy of an atom is quantized and can not take any continous values leading to Bohr’s atomic theory.

Black Body Radiation

A black body is an ideal body which allows the whole of the incident

radiation to pass into itself ( without reflecting the energy ) and

absorbs within itself this whole incident radiation (without passing

on the energy) This propety is valid for radiation corresponding to all

wavelengths and to all angels of incidence Therefore, the black body

is an ideal absorber of incident radaition.

A body's behavior with regard to thermal radiation is characterized by its transmission τ, absorption α, and reflection ρ For a black body, τ=0, α=1, and ρ=0

Basic Laws of Radiation:

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects (per unit area) The amount of

energy radiated is proportional to the temperature of the object.

3) The hotter the object, the shorter the wavelength ( λ ) of emitted energy.

Ultraviolet (UV) Catastrophe

The Rayleigh-Jeans Law:

* It agrees with experimental measurements for long

wavelengths.

* It predicts an energy output that diverges towards infinity as

wavelengths grow smaller.

* The failure has become known as the ultraviolet catastrophe.

4

2 )

Planck’s Law of Black Body Radiation

The Planck’s Law of Black Body Radiation states in terms of wavelength:

1

1 5

2 2

) , (

−

=

kT

hc e

hc T

I

λ λ

λ

• The above equation related intensity of emission with Temperature and

wavelength.

• It fits well with experimental observation of black body radiation.

• As opposed to classical model of continuous energy distribution, energy is emitted

in forms of quantized packets, where h is Planck’s constant :

λ

h

Applications of Black Body Radiation

• Roughly we can say that the stars radiate like blackbody radiators This is important

because it means that we can use the theory for blackbody radiators to infer things

about stars like its effective temperature.

• Interesting applications include designing camouflage and radar absorbent

materials.

h = Planck’s Constant = 6.626 x 10 -34 joule seconds (J s)

Energy could be gained or lost in individual units or packets, with energies that are whole

number multiples of the constant, h.

Bohr’s Atomic Model

Bohr’s Postulates

Bohr’s Atomic Model

1 In an atom, the electrons revolve around the nucleus in certain definite

circular paths called orbits, or shells.

2 Each shell or orbit corresponds to a definite energy Therefore, these circular

orbits are also known as energy levels or energy shells.

3 Electrons in an atom can have only certain permissible energies

4 When an electron moves between stationary states, it is accompanied by

the emission or absorption of a photon.This photon's energy is given by

ΔE=hf

Rydberg’s Formula and Bohr’s Theory

Rydberg’s formula is used to explain spectral lines of hydrogen like chemical elements

Utilizing Bohr’s Postulates, it can be deduced that the energy of a photon emitted by a

hydrogen atom is given by the difference of two hydrogen energy levels :

Bohr-Sommerfeld Model

Bohr-Sommerfield Model

• Bohr’s model failed in case of heavier elements where

the spectral lines observed did not corroborate with the

applied magnetic field It was found that spectral lines are

not homogenous but consists of several convenient lines.

• Sommerfield proposed that not only do electrons travel

in certain orbits but the orbits have different shapes and

the orbits could tilt in the presence of a magnetic field

This explained well the splitting of spectral lines observed

for heavier elements

Bohr’s Atomic Model

Advantages and Disadvantages of Bohr-Sommerfield Model

• Sommerfield’s Model predicted the splits in the spectrum The

electrons moving on the two orbits of the same n number but of

different shape have a bit different energies which explained the

splitting of spectral lines or very closely spaced spectral lines

• Sommerfield’s Model also showed that orbits don’t have to lie on

the same plane and could tilt in the presence of a magnetic field

• The fundamental flaw was that orbitals could tilt relative to xy

plane only in certain discrete values However, observation shows

that an atom can be tilted w.r.t x,y,z co-ordinates without restriction.

This flaw is to be corrected by wave mechanics model of Schrodinger

Hydrogen Spectral Series

The Hydrogen Spectral Series can be explained through Rydberg’s formula:

Where n’ = final energy level and n = initial energy level

Balmer Spectral Series

•The Balmer series is particularly useful in astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements

•The familiar red H-alpha spectral line of hydrogen gas in the far right, which is the transition from the

shell n = 3 to the Balmer series shell n = 2, is one of the conspicuous colors of the universe.

Particles act like Waves!

p

h /

=

λ

De- Broglie’s Matter waves was a brilliant idea It proposed:

If light (which is a wave) is quantized (like particles) then particles should also

behave like waves.

Heisenberg’s Uncertainity Principle

• It is impossible to know both the position and momentum exactly, i.e., ∆ x=0 and ∆ p=0

• These uncertainties are inherent in the physical world and have nothing to do with the skill of the observer

• Because h is so small, these uncertainties are not observable in normal everyday situations

π

4 /

∆

Another Consequence of Heisenberg’s Uncertainty Principle

• A quantum particle can never be in a state of rest,

as this would mean we know both its position and momentum precisely

• The more accurately we know the energy of a body,

the less accurately we know how long it possessed

that energy

Quantum Mechanical Model

Orbitals

Orbitals are regions in space where an electron is likely to be found:

– 90% of the time the electron is within the boundaries described by the electron density map

– The exact path of an electron in a given orbital is not known!

Describing Orbitals

Use quantum numbers to describe orbitals A given orbital can be described by

a set of 3 quantum numbers:

1 Principal quantum number (n)

2 Angular momentum quantum number (l)

3 Magnetic quantum number (ml)

Principal Quantum Number (n)

( n) describes the size and energy of the orbital:

– Possible values: whole number integer

– As “n” increases so does the size and energy of the orbital

Angular momentum quantum number (l)

(l) is related to the shape of the orbital:

– Possible values: (l) is an integer between 0 and n-1

– Each (l) value is also assigned a letter designation

Angular momentum quantum number (l)

1 2

3s 3p 3d

1 2 3

4s 4p 4d 4f

36

Magnetic quantum number (ml)

(ml) is related to the orientation of the orbital in 3-D space:

– Possible values: - l to + l

Magnetic quantum number (ml)

Consider the p orbital…it has an l value of 1 and thus the possible ml values are -1,

0, +1

– These 3 ml values correspond to the 3 possible orientations of the p orbital

Quantum Number Summary

– A set of 3 quantum numbers describes a specific orbital

4th Quantum Number!

A 4th quantum number was added to describe the spin on a given electron.

– Called the electron spin quantum number - ms

More on electron spin

• Each orbital can hold a maximum of 2 electrons of opposite spin.

• Pauli exclusion principle states that no two electrons in an atom can have the same set of 4 quantum numbers

• Three quantum numbers describe a specific orbital

– Energy and size, shape, and orientation

• Four quantum numbers describe a specific electron in an atom

43

Stern-Gerlach Experiment

The Stern–Gerlach experiment involves sending a beam of particles through an inhomogeneous magnetic field and observing their deflection The results show that particles possess an intrinsic angular momentum that is most closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values (ie is not continuous)

Important in the field of quantum mechanics, the Stern–Gerlach experiment,after German physicists Otto Stern and Walther Gerlach, is a 1922 experiment

on the deflection of particles, often used to illustrate basic principles of quantum mechanics It can be used to demonstrate that electrons and atoms have

intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured

Aufbau Principle

The Aufbau principle from the German Aufbau meaning "building up, construction":

According to the principle, electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g 1s before 2s)

Pauli’s Exclusion Principle

“No two electrons in a single atom can have the same four quantum numbers”

Hund’s Rule

If two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs Atoms at ground states tend to have as many unpaired electrons as possible.

Schrodinger’s Equation

Schrodinger Equation gives the understanding of Quantum Mechanics Model:

What did this equation do for knowing more about atomic structure?

1. Schroëdinger's equation eliminated the illogical quantum jump of electrons from one orbit to another as seen in Bohr’s Model, replacing it with a transitional process in which the wave pattern gradually fades out, while the new wave pattern fades in, during which time radiation is being emitted

2. Schroëdinger equation can be used to predict and/or calculate the energy of atoms as electrons move around

Wave function Ψ

• A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves Typically, its values are complex numbers and, for a single particle, it is

a function of space and time.

Hamiltonian Operator

• In quantum mechanics, the Hamiltonian is the operator corresponding to the

total energy of the system It is usually denoted by H, also Ȟ or Ĥ Its spectrum is the set of possible outcomes when one measures the total energy of a system Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Particle in a 1-D Box

An electron in a chemical bond is a real time example of a Particle in a 1-D box

How is it so?

Imagine an electron in a C-C single bond Since carbon atoms are

roughly 24000 times more massive than an electron, thinking classically

for a moment, this would be like a ball-bearing between two wrecking

balls, which would certainly seem like two infinitely high walls The box

length for a C-C single bond would be roughly 1.5 Å giving a defined

Applications of Particle in a 1-D Box in Nanotechnology

Energy Levels for 1-D Box:

A Quantum Harmonic Oscillator

Representing a ball on a spring in a classical harmonic oscillator, a quantum

harmonic oscillator is applicable for vibrational motion of a diatomic

molecule where, two atoms are assumed to be attached to a spring

representing the chemical bond

The energy solution is given by:

The energy of a system described by a harmonic oscillator potential cannot have zero energy Thus, physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature Example: Under atmospheric pressure liquid helium will not freeze at absolute zero temperature