Chapter 4

Arrangement of Electrons in Atoms

4-1 The Development of a New Atomic Model Rutherford’s model did not explain where

electrons were – what prevented electrons from being drawn into nucleus?

New model arose from experiments involving absorption and emission of light by matter

4-1 Properties of Light Light can behave as a wave Visible light is a kind of electromagnetic radiation (energy that

exhibits wavelike behavior as it travels through space) EM radiation includes X rays, UV and IR light, microwaves,

radiowaves

4-1 Properties of Light

All EM radiation moves at the same speed in a vacuum: 3.0 x 108 m/s

Wave motion is repetitive Wavelength (λ): distance between

corresponding points on adjacent waves (m, cm, nm)

Frequency (v): number of waves that pass a given point in a specific time, usually one second (1/s, Hz)

4-1 Properties of Light

4-1 Properties of Light

Since speed is constant, frequency and wavelength are related to each other mathematically

c = λv

Wavelength and frequency are INVERSELY proportional because their product is a constant.

4-1 Sample Problem

Determine the frequency of light with wavelength 550 nm. Convert nm to mUse formula c=λν to determine v

4-1 The Photoelectric Effect (Light as a Particle) 1900s – an experiment that

cannot be explained by the wave theory of light

Photoelectric effect – refers to the emission of electrons from a metal surface when light shines on the metal

For a given metal, no electrons are emitted if the light’s frequency is below a certain minimum, regardless of how intense the light or how long it is shone on the metal

4-1 The Photoelectric Effect

Wave theory predicts that ANY frequency of light could supply enough energy to eject an electron from the metal surface

Wave theory can’t explain why light must be of certain minimum frequency

4-1 The Particle Description of Light 1900 – Max Planck –

studying emission of light by hot objects

Proposed matter does not emit energy continuously but in small, specific amounts called quanta

Idea is called Quantum Theory. Planck wins Nobel prize in 1918 for his work.

4-1 The Particle Description of Light Quantum – minimum quantity of energy

that can be lost or gained by an atom Energy of a quantum is related to

frequency

E = hv

4-1 The Particle Description of Light 1905 – Einstein – light

has a dual nature – sometimes it acts like a wave, sometimes it acts like a particle

Light has wave properties Light is also like a stream

of particles, each particle carries a quantum of energy

Einstein called these particles photons

4-1 Explanation for the Photoelectric Effect Electrons are bound to the atom with a certain

amount of energy. Metal surface must be struck by a photon of light

carrying at least this amount of energy to knock the electron loose.

Energy and frequency are directly proportional. (E=hν)

Only frequencies equal to or greater than the threshold frequency will knock an electron off an atom.

4-1 Sample Problem

Calculate the energy associated with a photon of light of frequency 4.1 x 1014 Hz.

4-1 Hydrogen-Atom Line-Emission Spectrum Spectrum – a pattern of

energy observed when matter absorbs and emits energy

Ground state – lowest energy state of an atom or molecule

Excited state –state in which atom or molecule has higher PE than ground state

4-1 Hydrogen-Atom Line-Emission Spectrum

Current passed through vacuum tube with hydrogen gas inside

Pink light passed through prism to separate into specific frequencies of light

4-1 Hydrogen-Atom Line-Emission Spectrum Why does hydrogen give

off only specific frequencies of light?

1913 – Niels Bohr proposed a model for hydrogen atom that linked the atom’s electron with photon emission

Ties line emission spectrum to quantum theory.

4-1 Bohr Model of the Hydrogen Atom Electron can circle nucleus only in allowed

paths, or orbits Orbit closest to nucleus has lowest energy

(ground state) Orbits farther from nucleus have higher energy

(excited states) When electron absorbs energy, it jumps to

higher orbit When electron emits energy, it drops to lower

orbit

4-1 Bohr Model of the Hydrogen Atom Electron can only

exist in certain allowed orbits.

Can only absorb and emit amounts of energy that correspond to energy differences between orbits.

4-1 Bohr Model of the Hydrogen Atom Bohr’s model did not explain the spectra of

atoms with more than one electron Bohr’s theory did not explain the chemical

behavior of atoms

4-2 Electrons as Waves

It was already known that light can behave as a particle or a wave.

1924 – Louis deBroglie asked if electrons could also have dual wave-particle nature

4-2 deBroglie’s Hypothesis

Electrons are particles but they can act like waves

A wave confined to a space can only have certain frequencies – seems to correspond to Bohr’s quantized electron orbits

The electron-wave is confined to a certain space – the region around the nucleus – so electron-waves can only have certain frequencies, which correspond to certain energies (E = hv)

4-2 Wave-Particle Duality of Nature

Particles can have wave properties.

Waves can have particle properties.

4-2 Heisenberg Uncertainty Principle

If the electron is both a particle and a wave, where is it?

Werner Heisenberg, German physicist, 1927

Electrons are detected by hitting them with photons, but hitting them changes their position

It is impossible to determine simultaneously the position and velocity of an electron

4-2 The Schrodinger Wave Equation 1926 – Erwin

Schrodinger uses assumption that electron behaves as a wave to describe mathematically the wave properties of electrons and other very small particles (Quantum theory)

4-2 What does it mean?

Solutions to the Schrodinger equation are called wave functions

Wave functions can give probability of finding an electron at a particular position in the space around the nucleus

An orbital is a 3D region around the nucleus that indicates the probable location of an electron

4-2 Atomic Orbitals and Quantum Numbers Quantum numbers specify the properties

of atomic orbitals and the properties of electrons in orbitals.

Each electron in an atom can be assigned a set of four quantum numbers.

4-2 The Principal Quantum Number

Symbolized by n Indicates the main energy level

occupied by an electron Values of n are positive

integers (ex. n = 1 is the first energy level)

Principal quantum number also gives approximate distance from nucleus/size of energy level or shell

Total number of electrons that can exist in a given energy level, n, is equal to 2n2.

Energy level, n Maximum number of

electrons, 2n2

1 2

2 8

3 18

4 32

5 50

6 72

7 98

4-2 Angular Momentum Quantum Number

Symbolized by l Indicates the shape of the orbital “sublevels” For each energy level, n, the number of

orbital shapes possible is equal to n The first four shapes are given letter

symbols (s, p, d and f)

4-2 Magnetic Quantum Number

Symbolized by m Indicates the orientation of an orbital

around the nucleus

s orbital (1 orientation)

p orbital (3 orientations)

d orbitals (5 orientations)

f orbitals (7 orientations)

sublevel number of orbitals available

number of electrons sublevel can hold

s 1 2

p 3 6

d 5 10

f 7 14

4-2 Spin Quantum Numbers

Electrons in orbitals spin on internal axes. When charged bodies spin, they induce a

magnetic field. An electron can spin in one of two possible

directions. The spin quantum number has two possible

values, + ½ and – ½ A single orbital can hold a total of two electrons,

which MUST have opposite spins.

4-3 Electron Configuration

The arrangement of electrons in an atom Assigns an energy level and sublevel to

each electron in an atom.

4-3 Rules Governing Electron Configurations The Aufbau Principle – an electron

occupies the lowest-energy orbital available. (aufbau is German for “building up”

Electrons fill low energy orbitals before filling higher energy orbitals.

4-3 Electron Configuration

1s has the lowest energy.

Energies of sublevels in different main energy levels begin to overlap in n=3

Use orbital filling diagram to determine order in which sublevels are filled.

start

4-3 Rules Governing Electron Configurations Pauli Exclusion Principle –

no two electrons in the same atom can have the same set of four quantum numbers

In other words, if two electrons are going to occupy the same orbital, they must have opposite spin.

-let horizontal line represent orbital

-an up arrow and a down arrow represent two electrons of opposite spin

4-3 Rules Governing Electron Configurations Hund’s rule – orbitals of equal energy

(degenerate orbitals) are occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin

Bus seat rule

4-3 Ways to Represent Electron Configuration Electron

Configuration Notation

Assigns each electron to an energy level and a sublevel.

Examples:

Na

P

Br

Rb

K

Ar

4-3 Electron Configuration Sample Problems Name the elements indicated by the

following electron configurations:1s22s22p63s23p5

1s22s22p63s23p64s23d5

4-3 Electron Configuration Sample Problems Write the electron configuration for an

element that has the following number of electrons:7141933

4-3 Ways to Represent Electron Configuration Orbital Notation – uses lines and arrows to

represent orbitals and electrons Example: Write the orbital notations for

nitrogen and oxygen.

N

O

4-3 Ways to Represent Electron Configuration Noble Gas Notation – to simplify an

element’s electron configuration, use the preceding noble gas as shorthand to indicate all the electrons possessed by that noble gas

Example – Ne and Na

4-3 Valence Electrons

Valence electrons are electrons in the outermost energy level of an atom, farthest from the nucleus

They are important because they are the electrons that are usually involved in chemical reactions.

How many valence electrons does sodium have?

Bromine?

Silicon?

4-3 Electron Configurations with Special Stability Octet – the outer energy level is

considered filled when the s and p sublevels are completely filled with 8 electrons

A filled outer energy level (8 electrons) is a very stable electron configuration.

The noble gases have filled outer energy levels. This is why they are unreactive.

4-3 Electron Configurations with Special Stability Filled and half-

filled sublevels have special stability (especially d).

This fact sometimes results in electron configurations that deviate from the Aufbau principle.

Chromium

Copper

Molybdenum

Silver

Pig boots!