• properties of light

• spectroscopy

• quantum hypothesis

• hydrogen atom

• Heisenberg Uncertainty Principle

• orbitals

ATOMIC STRUCTURE Kotz Ch 7 & Ch 22 (sect 4,5)

ELECTROMAGNETIC RADIATION

• subatomic particles (electron, photon, etc) have both PARTICLE and WAVE properties

• Light is electromagnetic radiation - crossed electric and magnetic waves:

Properties :

Wavelength, λ λ λ λ (nm)

Frequency, ν ν ν ν (s-1, Hz)

Amplitude, A

constant speed. c

3.00 x 108 m.s-1

Electromagnetic Radiation (2)

wavelengthVisible light

wavelength

Ultaviolet radiation

Amplitude

Node

• All waves have: frequency and wavelength

• symbol: νννν ((((Greek letter “nu”) λ λ λ λ ((((Greek “lambda”)

• units: “cycles per sec” = Hertz “distance” (nm)

• All radiation: λλλλ • νννν = c

where c = velocity of light = 3.00 x 108 m/sec

Electromagnetic Radiation (3)

Note: Long wavelength

→→→→ small frequency

Short wavelength

→→→→ high frequency increasing

wavelength

increasing

frequency

Example: Red light has λλλλ = 700 nm.

Calculate the frequency, νννν.

= 3.00 x 10

8 m/s

7.00 x 10 -7 m ==== 4.29 x 10

14 Hz νννν =

c

λλλλ

• Wave nature of light is shown by classical

wave properties such as

• interference

• diffraction

Electromagnetic Radiation (4)

Quantization of Energy

• Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA.

Max Planck (1858-1947)

Solved the “ultraviolet

catastrophe” 4-HOT_BAR.MOV

E = h • νννν

Quantization of Energy (2)

Energy of radiation is proportional to frequency.

where h = Planck’s constant = 6.6262 x 10-34 J•s

Light with large λλλλ (small νννν) has a small E.

Light with a short λλλλ (large νννν) has a large E.

Photoelectric effect demonstrates the

particle nature of light. (Kotz, figure 7.6)

Number of e- ejected does NOT

depend on frequency, rather it

depends on light intensity.

No e- observed until light

of a certain minimum E is used.

Photoelectric Effect

Albert Einstein (1879-1955)

Photoelectric Effect (2)

• Experimental observations can be explained if light consists of

particles called PHOTONS of discrete energy.

• Classical theory said that E of ejected

electron should increase with increase

in light intensity — not observed!

E = h•νννν

= (6.63 x 10-34 J•s)(4.29 x 1014 sec-1)

= 2.85 x 10-19 J per photon

Energy of Radiation

PROBLEM: Calculate the energy of 1.00 mol of photons of red light.

λλλλ = 700 nm νννν = 4.29 x 1014 sec-1

- the range of energies that can break bonds.

E per mol = (2.85 x 10-19 J/ph)(6.02 x 1023 ph/mol)

= 171.6 kJ/mol

Atomic Line Spectra

• Bohr’s greatest contribution to science was in building a simple model of the atom.

• It was based on understanding

the SHARP LINE SPECTRA of excited atoms.

Niels Bohr (1885-1962)

(Nobel Prize, 1922)

Line Spectra of Excited Atoms

• Excited atoms emit light of only certain wavelengths

• The wavelengths of emitted light depend on the element.

H

Hg

Ne

Atomic Spectra and Bohr Model

2. But a charged particle moving in an electric field should emit energy.

+

Electron

orbit

One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.

1. Classically any orbit should be

possible and so is any energy.

End result should be destruction!

Energy of state = - C/n2 where C is a CONSTANT

n = QUANTUM NUMBER, n = 1, 2, 3, 4, ....

• Bohr said classical view is wrong.

• Need a new theory — now called QUANTUM or WAVE MECHANICS.

• e- can only exist in certain discrete orbits

— called stationary states.

• e- is restricted to QUANTIZED energy states.

Atomic Spectra and Bohr Model (2)

• Only orbits where n = integral number are permitted.

Energy of quantized state = - C/n2

• Radius of allowed orbitals

= n2 x (0.0529 nm)

• Results can be used to

explain atomic spectra.

Atomic Spectra and Bohr Model (3)

If e-’s are in quantized energy states, then ∆∆∆∆E of states can have only certain values. This explains sharp line spectra.

n = 1

n = 2 E = -C (1/22)

E = -C (1/12)

Atomic Spectra and Bohr Model (4)

H atom

07m07an1.mov

4-H_SPECTRA.MOV

Calculate ∆∆∆∆E for e- in H “falling” from

n = 2 to n = 1 (higher to lower energy) .

n = 1

n = 2

Energy

so, E of emitted light = (3/4)R = 2.47 x 1015 Hz

and λλλλ = c/νννν = 121.6 nm (in ULTRAVIOLET region)

∆∆∆∆E = Efinal - Einitial = -C[(1/12) - (1/2)2] = -(3/4)C

C has been found from experiment. It is now called R,

the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz

This is exactly in agreement with experiment!

• (-ve sign for ∆∆∆∆E indicates emission (+ve for absorption) • since energy (wavelength, frequency) of light can only be +ve it is best to consider such calculations as ∆∆∆∆E = Eupper - Elower

Atomic Spectra and Bohr Model (5)

Hydrogen atom spectra

Visible lines in H atom

spectrum are called the

BALMER series.

High E

Short λλλλ

High νννν

Low E

Long λλλλ

Low νννν

Energy

Ultra Violet Lyman

Infrared Paschen

Visible Balmer

En = -1312

n2

6 5

3

2

1

4

n

Bohr’s theory was a great accomplishment and radically changed our view of matter.

But problems existed with Bohr theory —

– theory only successful for the H atom.

– introduced quantum idea artificially.

• So, we go on to QUANTUM or WAVE

MECHANICS

From Bohr model to Quantum mechanics

Quantum or Wave Mechanics

• Light has both wave & particle

properties

• de Broglie (1924) proposed that all moving objects have wave

properties.

• For light: E = hνννν = hc / λλλλ

• For particles: E = mc2 (Einstein) L. de Broglie

(1892-1987)

λλλλ for particles is called the de Broglie wavelength

Therefore, mc = h / λλλλ

and for particles

(mass)x(velocity) = h / λλλλ

WAVE properties of matter

Electron diffraction with

electrons of 5-200 keV

- Fig. 7.14 - Al metal Davisson & Germer 1927

Na Atom Laser beams

λλλλ = 15 micometers (µµµµm) Andrews, Mewes, Ketterle

M.I.T. Nov 1996

The new atom laser emits pulses of coherent atoms,

or atoms that "march in lock-step." Each pulse

contains several million coherent atoms and

is accelerated downward by gravity. The curved

shape of the pulses was caused by gravity and forces

between the atoms. (Field of view 2.5 mm X 5.0 mm.) 4-ATOMLSR.MOV

Schrodinger applied idea of e- behaving as a wave to the problem of electrons in atoms.

Solution to WAVE EQUATION gives set of mathematical expressions called

WAVE FUNCTIONS, ΨΨΨΨ

Each describes an allowed energy state of an e-

Quantization introduced naturally.

E. Schrodinger

1887-1961

Quantum or Wave Mechanics

WAVE FUNCTIONS, ΨΨΨΨ

• ΨΨΨΨ is a function of distance and two angles.

• For 1 electron, ΨΨΨΨ corresponds to an

ORBITAL — the region of space within which an electron is found.

• ΨΨΨΨ does NOT describe the exact

location of the electron.

• ΨΨΨΨ2 is proportional to the probability of

finding an e- at a given point.

Uncertainty Principle

Problem of defining nature of electrons in atoms solved by W. Heisenberg.

Cannot simultaneously define the position and momentum (= m•v) of an electron.

∆∆∆∆x. ∆∆∆∆p = h

At best we can describe the position and velocity of an electron by a

PROBABILITY DISTRIBUTION,

which is given by ΨΨΨΨ2

W. Heisenberg

1901-1976

Wavefunctions (3)

Ψ2 is proportional to the probability

of finding an e- at a given point.

4-S_ORBITAL.MOV (07m13an1.mov)

Orbital Quantum Numbers

An atomic orbital is defined by 3 quantum numbers:

– n l ml

Electrons are arranged in shells and subshells of ORBITALS .

n →→→→ shell

l →→→→ subshell

ml →→→→ designates an orbital within a subshell

Quantum Numbers

ml (magnetic) -l..0..+l Orbital orientation

in space

l (angular) 0, 1, 2, .. n-1 Orbital shape or

type (subshell)

n (major) 1, 2, 3, .. Orbital size and

energy = -R(1/n2)

Total # of orbitals in lth subshell = 2 l + 1

Symbol Values Description

Shells and Subshells

For n = 1, l = 0 and ml = 0

There is only one subshell and that subshell has a single orbital

(ml has a single value ---> 1 orbital)

This subshell is labeled s (“ess”) and we call this orbital 1s

Each shell has 1 orbital labeled s.

It is SPHERICAL in shape.

s Orbitals

All s orbitals are spherical in shape.

p Orbitals

For n = 2, l = 0 and 1

There are 2 types of orbitals — 2 subshells

For l = 0 ml = 0

this is a s subshell

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

this is a p subshell with 3 orbitals

planar node

Typical p orbital

When l = 1, there is

a PLANAR NODE

through the

nucleus.

A p orbital

pz

py

px90 o

The three p

orbitals lie 90o

apart in space

p orbitals (2)

p-orbitals(3)

px py pz

2

3

n=

l =

For l = 2, ml = -2, -1, 0, +1, +2

→→→→ d subshell with 5 orbitals

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

→→→→ p subshell with 3 orbitals

For l = 0, ml = 0

→→→→ s subshell with single orbital

For n = 3, what are the values of l?

l = 0, 1, 2

and so there are 3 subshells in the shell.

d Orbitals

d Orbitals

s orbitals have no planar

node (l = 0) and

so are spherical.

p orbitals have l = 1, and have 1 planar node,

and so are “dumbbell” shaped.

d orbitals (with l = 2)

have 2 planar nodes

typical d orbital

planar node

planar node

IN GENERAL

the number of NODES

= value of angular

quantum number (l)

Boundary surfaces for all orbitals of the n = 1, n = 2 and n = 3 shells

2

1

3d n=

3

There are

n2 orbitals in

the nth SHELL

ATOMIC ELECTRON CONFIGURATIONS AND PERIODICITY

Element Mnemonic Competition

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