C. Johannesson

Ch. 4 - Electrons in Atoms

Section 1 The Development of a New Atomic Model

Objectives

• Explain the mathematical relationship among the speed, wavelength, and frequency of electromagnetic radiation.

• Discuss the dual wave-particle nature of light.

• Discuss the significance of the photoelectric effect and the line-emission spectrum of hydrogen to the development of the atomic model.

• Describe the Bohr model of the hydrogen atom.

C. Johannesson

Electromagnetic Spectrum

LOW

ENERGY

HIGH

ENERGY

Includes all forms of electromagnetic

radiation (energy that exhibits wavelike

behavior as it travels through space)

Waves

Wavelength () - length of one complete wave

Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s

Amplitude (A) - distance from the origin to the trough or crest

C. Johannesson

Waves

Agreater

amplitude

(intensity)

greater frequency

(color)

crest

origin

trough

A

on

EM Spectrum

LOW

ENERGY

HIGH

ENERGY

R O Y G. B I V

red orange yellow green blue indigo violet

LONG

WAVELENGTH

EM Spectrum

Frequency & wavelength are inversely proportional

c = c: speed of light 3.00 108 m/s (in a vacuum): wavelength (m, nm, etc.): frequency (Hz)

EM Spectrum

GIVEN:

= ?

= 434 nm = 4.34 10-7 m

c = 3.00 108 m/s

WORK: = c

= 3.00 108 m/s 4.34 10-7 m

= 6.91 1014 Hz

EX: Find the frequency of a photon with a wavelength of 434 nm.

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Visual Concept

Energy of a Photon

Electrons as Waves

EVIDENCE: DIFFRACTION PATTERNS

ELECTRONSVISIBLE LIGHT

•Electrons, like light waves, can be bent, or diffracted.

•Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening

Development of a New Atomic Model

Day 2Day 2

Bohr Model of the Hydrogen Atom

• Niels Bohr proposed a hydrogen-atom model that linked the atom’s electron to photon emission.

• According to the model, the electron can circle the nucleus only in allowed paths, or orbits.• Electrons are allowed to exist in any one of

a number of energy levels (lowest energy state is closest to the nucleus)

• Only worked for Hydrogen (1 electron)

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Visual Concept

Bohr Model of the Atom

Planck (1900)

Observed - emission of light from hot objects

Concluded - energy is emitted in small, specific amounts (quanta) not continuously as expected by energy in the form of waves

Quantum - minimum amount of energy that can be lost or gained by an atom

Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory

Quantum Theory

Einstein (1905)

Observed - photoelectric effect- emission of electrons from a metal when light shines on the metal

Einstein (1905)

Concluded - light has properties of both waves and particles

“wave-particle duality”

Photon - particle of light that carries a quantum of energy

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Visual Concept

Quantization of Energy

Line-Emission Spectrum

Each element has a unique bright-line emission spectrum. Hydrogen always produced same line-emission spectrum

so releases (emission) energy of only certain values

“Atomic Fingerprint”

Helium

Line-Emission Spectrum Cont…

ground state- lowest energy state

of an atom

excited state- state in which an atom has a higher potential energy than its ground state

ENERGY IN PHOTON OUTLine –emission spectrum is

caused by energy released

when electrons “jump from

higher energy to lower

energy

Quantum Mechanics

Heisenberg Uncertainty Principle

Impossible to know both the velocity and position of an electron (small particle) at the same time

Quantum theory describes mathematically the wave properties of electrons and other very small particles.

Quantum Mechanics

• Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated.

• Instead, they exist in certain regions called orbitals.

• Orbital (“electron cloud”)

Region in space where there is 90% probability of finding an e- three-dimensional space

Orbital

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Visual Concept

Comparing Models of the Atom

Day3

C. Johannesson

Quantum Numbers

UPPER LEVEL

Four Quantum Numbers:

Specify the “address” of each electron in an atom

Specify properties of the atomic orbitals and properties of electrons in it

Quantum Numbers

1. Principal Quantum Number ( n )

Energy level

Size of the orbital

n2 = # of orbitals in the energy level

As n increases, e- energy and distance from nucleus increases

Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l )

Energy sublevel

Shape of the orbital

Number of orbital shapes

possible equal to n

Quantum Numbers

n = # of sublevels per level

n2 = # of orbitals per level

Sublevel sets: 1 s, 3 p, 5 d, 7 f

Electrons Accommodated in Energy Levels and Sublevels

Quantum Numbers

3. Magnetic Quantum Number ( ml )

Orientation of orbital

S-1, p-3,d-5, f-7

Specifies the exact orbitalwithin each sublevel

Quantum Numbers

Orbitals combine to form a spherical

shape.

2s

2pz2py

2px

Quantum Numbers

4. Spin Quantum Number ( ms )

Electron spin +½ or -½

An orbital can hold 2 electrons that spin in opposite directions.

As it spins creates a magnetic field

Quantum Numbers

Pauli Exclusion Principle

No two electrons in an atom can have the same 4 quantum numbers.

Each e- has a unique “address”:

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Visual Concept

Quantum Numbers and Orbitals

Day 3

Electron Configuration

Arrangement of electrons in an atomAtoms of different elements have different

numbers of e-, a distinct electron configuration exists for atoms of each element

e- in atoms tend to assume arrangements that have lowest possible energies (ground-state)

Relative Energies of Orbitals

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Visual Concept

Electron Configuration

General Rules

Pauli Exclusion Principle

Each orbital can hold TWO electrons

with opposite spins.

General Rules

Aufbau Principle

Electrons fill the lowest energy orbitals first.

“Lazy Tenant Rule”

Energies of sub-levels begin to overlap

4s is lower in energy than 3d

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Visual Concept

Aufbau Principle

RIGHTWRONG

General RulesHund’s Rule

Within a sublevel, place one e- per orbital before pairing them.

Separating unpaired electrons into as many orbitals as possible minimizes the repulsion between electrons

O

8e-

Orbital Diagram

Electron Configuration

1s2 2s2 2p4

Notation

1s 2s 2p

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Visual Concept

Orbital Notation

Shorthand Configuration

S 16e-

Valence Electrons

Core Electrons

S 16e- [Ne] 3s2 3p4

1s2 2s2 2p6 3s2 3p4

Notation

Longhand Configuration

Writing Electron Configurations

1

2

3

4

5

6

7

Periodic Patterns

Shorthand Configuration/Nobel Gas Notation

Core e-: Go up one row and over to the Noble Gas.

Valence e-: On the next row, fill in the # of e- in each sublevel.

[Ar] 4s2 3d10 4p2

Periodic Patterns

Example - Germanium

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Visual Concept

Reading Electron-Configuration Notation