Atomic StructureEdward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

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Heated cathodesemitted cathode "rays"

+

-

Deflected by eithermagnetic or electric fields

Cathode Ray Tube

J.J. Thomson, 1897

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The "beam" carrieda negative charge. +

-

J. J. THOMSON (1897)British Physicist

The ratio of chargeto mass (e/m) was

independent ofthe cathode material.

Why does this indicate thatcathode rays (electrons)

are an integral part of each element?

How did heknow that?

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Photoelectric Effect

+ -

Albert Einstein (1905)German Physicist

Interpreted thePhotoelectric Effect

Confirmed thatlight is corpuscular(possess particle-like properties)

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Gold Foil Experiment(10-4 cm thick)

Kotz & Purcell (1987)

Rutherford, 1911

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Ernest Rutherford (1911)British Chemist

Most of the alpha particles(a, 4He2+) passed straightthrough, buta few weredeflected orreflectedstraightbackwards.

Since alpha particleswere known to have

a positive charge,this indicated thatthe nucleus of an

atom containedmost of the mass,

and that it waspositive in charge

Diagram source unknown

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The Atom Before 1913

Smallest unit of matter which maintains the physical and chemical properties of the element.

Combines with other atoms to form molecules, but it itself is not destroyed.

Consists of a positive nucleus of very small size containing most of the mass of the atom.

Exhibits a volume much larger than the nucleus due to the presence of electrons.

Other physical properties had to be accounted for

All the mass of the atomcannot be accounted for

by only protons and electrons.

hydrogenprism

white lightsource

If white light ispassed througha sample of hydrogen gas,certain selected wavelengthsof light are absorbed by the gas.

If the gas is heateduntil it glowed,

the same wavelengthsof light are emitted

by the gas.

Dark and Bright Line Spectra

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A Possible Solution

A unified theory explaining these facts was proposed by Niels Bohr in 1913.

An atom consists of a positive nucleus surrounded by electrons moving in spherical orbits.• “planetary model” of the atom

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The Bohr Model of the AtomA Break From Classical Mechanics

The electrons continuously circle the nucleuswithout losing energy.

The electron does not lose energyin a degenerating orbit until it

crashes into the nucleus.

This represents a break from classical physicssince any acceleration (including centripetal)

is expected to require some energy.

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The Bohr Model of the AtomRadiation (light) is emitted whenan electron in a higher energy orbitmoves to a lower energy orbit

If energy is absorbedthe electron moves from alower to a higher energy orbit.

energy difference = energy absorbed or emitted

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Energy associatedwith a

spectral line= -R

n nH ( )1 1

12

22

Other Things To Consider

integers

The spectral lines ofhydrogen can be explainedby the Rydberg equation.

(1899)

If white light is passed through a sample of hydrogen gas,certain selected wavelengths of light are absorbed by the gas.

prism

Rydberg constantfor hydrogen

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Bohr Theory (1913)Accounted for two important developments

Rutherford's experimentdemonstrating the conceptof the nucleus.

+ -

Einstein's theory concerningthe energy of a photon.

E = hh = 6.626 x 10–27 erg·s = 6.626 x 10–34 J·s

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Bohr Theory (1913)

Because onlycertain frequencies

are absorbed or emitted

only certainenergy changes

are allowedwithin the atom.

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Bohr Model of the Hydrogen AtomPlanetary Model

Only integralmultiples of h/2

are allowed

integer principalquantum number(1, 2, 3,..., )

2 n h

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Bohr Model of the Hydrogen AtomPlanetary Model

electrons areallowed here

electrons arenot allowed here

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Bohr Model of the Hydrogen AtomPlanetary Model

Different orbitshave different

energies

Lowest energy(most stable)

2nd most stable (n = 2)

3rd most stable (n = 3)

The energy differencebetween levels

corresponds to theobserved lines

in the hydrogen spectrum

Emission and Absorption are Opposite Processes

Emission

AbsorptionAbsorption

Emission and Absorption are Opposite Processes

Bigabsorption

What happens ifan electron moves

to an orbitinfinitely distant

from the nucleus?

IONIZATION

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Hyd

rog

en A

tom

En

erg

y L

evel

s

4

1

2

3

Balmer Series

Red VioletFrequency

Visible Emission Spectrumof Hydrogen

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Horsehead Nebula in Orion48 inch Schmidt Telescope - Hale Observatories

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Visible Solar Spectrum13-foot Heliospectrograph, Mt. Wilson Observatory

1

2

345

3900 4600 Å

4600 5400 Å

5400 6100 Å

6900 Å6100

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A Caveat(Note of Caution)

The Bohr Atom calculations and the Rydberg equation for electronic transitions only work for “hydrogen-like” species.• One electron species: H, He+, Li2+, ...

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Niels Bohr (1913)(Danish Physicist)

Postulated that electrons spin around the nucleus in an orbit.

The energy differencesbetween these orbitscan be used to explainthe various colors of lightemitted and absorbedby gaseous elements.

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Erwin Schrodinger (1926)(Austrian Physicist)

Developed the modern view of the atom, treating electrons as mathematical functions.• sine and cosine wave functions.

Louis de Broglie (1926)(French Physicist)

Proposed that matter has both wave and particle properties.

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Standing Wave(General Equation - One Dimension)

= wavelength = amplitude = displacement of the wave from origin

d d

4

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Schrödinger Equation(One Dimension)

h

d8md

+ V= E

Energy of a Particle

mass positionpotential energy

is a wave function which describes the particle

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Schrödinger Wave Equation(Three Dimensions)

(2

x2

2

y2

2

z2

mEh2 + ( = 0

To solve this equation in three dimensionsfor hydrogen, the energy (E) of the electron

must take on certain (quantized) valuesrelated by integers.

These integers are knownas QUANTUM NUMBERS. Quantum numbers

need not be assumed(as was done by Bohr), but are required

by the mathematics of the system.

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Wave Functionsare composed on sine and cosine terms

2 is the probability of finding anelectron at a specific location

What is the probability of finding an electronat a node?

The wave function ()has no physical significance

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A Mathematical Model of the Atom

These wave equations give a "mathematical model" for the electron.• the electron can be at many different

places The likelihood (probability) of "finding" the

electron at any point depends on• Radial function (distance)• Angular function (direction)

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Orbitals

The region around a nucleus in which an electron has a probability of being located is called an orbital.

Orbitals can vary in• distance from the nucleus (radial function)• direction (angular function)

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Wave Function

(2

x2

2

y2

2

z2 + V2m

E= h2

The shape of the orbital and the energy of the electronis related to the wave function ().

The electron is mathematically describedby the wave function,

the Schrödinger Equation is used to calculatethe energy of that electron.

The wave function is composed of radialand angular functions (in three dimensions).

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Orbitals WithNo Angular Dependence

1s

2ss orbitals have a spherical shape

isotropic orbitals

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Orbitals WithAngular Dependence

p orbitals have a propeller shape

2px

x

y

z

x

y

z

2py

x

y

z

2pz

How can you distinguish px from py or pz?

Anisotropic orbitalsthe angular probability function isnot the same in all directions

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Higher Energy Orbitals

Higher energy levels correspond to higher wave functions including 3s, 3px, 3py, 3pz and d orbitals.

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d Orbitals

xy

z

3dxy

xy

z

3dyz

xy

z

3dxz

xy

z

3dx2

-y2

3dz2

x

y

z

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Quantum Numbers

Each electron in the orbital of the atom can be described by an unique combination of values known as quantum numbers.

There are four different quantum numbers

n , , m, ms

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Principal Quantum Number

n=1n=2n=3n=4n=5n=6n=7

principalquantumnumber

Larger valuesof n refer tohigher energyorbitals(further fromthe nucleus)

range: n = 1, 2, 3, …,

The principal quantum numberis related to the rows of

the periodic table.

Angular Quantum Number

= 0s orbital

(no angulardependence)

= 1p orbital

= 2d orbital

= 3f orbital

range: = 0, … , n-1

Is it possible to have a 2f orbital?

Is it possible to have a 3p orbital?

This is the principal quantum number

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Magnetic Quantum Number

What would be the names of these orbitals?

m = -, … , 0, … , +

Differentiates betweenorbitals with the samen and quantum numbers

In a magnetic field alignedalong the z-axis,

an electron in the 2pz orbitalwill behave differently

than an electron in the 2px or 2py orbitals.

p-1 p0 p+1

How many f-orbitals are there in an f-orbital set?

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Spin Quantum Numberms = -1/2, +1/2

Each orbital can contain up to two electrons

one aligned withan external field

one aligned againstan external field

Which electron has lower energy?

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Quantum Numbersand the Periodic Table

Identify the regions of the periodic table thatcorrespond to the s, p, d and f orbitals

s pd

f

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Four Quantum Numbers

Each electron in an atom can be described uniquely by the four quantum numbers.

Three rules involving quantum numbers • Pauli Exclusion Principle

• Aufbau Principle • Hund's Rule

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Pauli Exclusion Principle

Only one electron in an atom may have the same four quantum numbers.

it’s like a house address

3 1 1 1/2

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Aufbau Principle

In the ground state, electrons fill in the lowest available energy state (orbital) first

it’s like the best houseon the block

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Hund's Rule

If more than one electron occupies a degenerate set of orbitals (orbitals of the same energy), then the electrons will fill in such a way as to maximize the number of orbitals filled.

each electron would prefer to be singlerather than be doubled up

It is more stable for the spin of the electrons to be aligned in the same direction.

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